It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
On 3/20/2025 8:31 PM, Richard Damon wrote:
On 3/20/25 11:02 AM, olcott wrote:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
In other words, you are admitting you logic system isn't properly
defined.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
But your idea of a "logic system" isn't what logic is, while you claim
your idea apply to it.
Remember, you don't get to change the rules for an existing system.
If I am showing the details of exactly logic can be transformed
into correct reasoning without losing anything besides inconsistency
and undecidability THEN I DO GET TO SUPERSEDE AND OVERRIDE THE
RULES OF EXISTING SYSTEMS WITH MY CORRECTIONS.
You can say that in Olcott Logic, that a Truth Predicate can exist,
but you first have to convince people that they should care because
you logic system can do something useful.
Try and show anything that the set of all knowledge that
can be expressed in language doesn't know that other
formal systems do know.
Since, by your admittion, it can't handle the properties of the
Natural Numbers, as a statement about one of those properties is a
"type mismatch error", you show how limited your system is.
Natural numbers themselves don't actually have
any properties other than an ordered set of finite
strings of digits. Operations can be defined on the
basis of this single property. These derived
operations are not actually properties themselves.
The problem is until you can actually define what you can do in your
system in a precise manner, it is just worthless.
Yes of course even people with a million IQ would have
no idea what can possibly be done with elements of the
set of all knowledge that can be expressed using language.
When you use the term "inference" with these million IQ
people they think you are saying "in fer rents", like you
owe rent and are OK with paying it.
So, in WORTHLESS Olcott logic, we have an unproven claim (since you
haven't established enough of a system to prove something in it) about
your truth predicate, but until someone has a use for your system,
that is pretty worthless.
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all
classical logic, since Truth is different than Knowledge. In a
good logic system, Knowledge will be a subset of Truth, but you
have defined that in your system, Truth is a subset of Knowledge,
so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
;
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these
basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you
are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements.
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some statement,
the context isn't precisely known or the statement is known to be an
approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability
cannot possibly exist.
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:49 AM, olcott wrote:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
And thus your concept of truth breaks.
Truth, by its definition is an immutable thing, but you just defined
it to be mutable.
How often do we need to re-verify our truths?
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems,
certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
But you aren't begining with basic facts, but with what has been
assumed to be the basic facts.
That is not what I stipulated.
When we begin with what actual are the set of basic
facts and are only allowed to apply truth preserving
operations to these basic facts then it is self-evident
that True(X) must always be correct.
We don't actually KNOW the basics principles for many things, but haveThen these are not included in the set of knowledge.
been working to understand them.
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the set ofIt is stipulated that analytic knowledge is limited to the set >>>>>>>>>>> of knowledge that can be expressed using language or derived >>>>>>>>>>> by applying truth preserving operations to elements of this >>>>>>>>>>> set.
Which just means that you have stipulated yourself out of all >>>>>>>>>> classical logic, since Truth is different than Knowledge. In a >>>>>>>>>> good logic system, Knowledge will be a subset of Truth, but you >>>>>>>>>> have defined that in your system, Truth is a subset of
Knowledge, so you have it backwards.
general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts
anything that can be inferred from the set of general knowledge. >>>>>>>>
(a) Not useful unless (b) it returns TRUE for (c) no X thatBecause my system begins with basic facts and actual facts can't >>>>>>> contradict each other and no contradiction can be formed by
contradicts anything (d) that can be inferred from the set of >>>>>>> > general knowledge.
;
applying only truth preserving operations to these basic facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect
statements.
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some
statement, the context isn't precisely known or the statement is
known to be an approximation of unknown accuracy, so doesn't
actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something.When the proof is only syntactic then it isn't directly connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semanticsYes, proof is a validatation of truth, but truth does not need to be
encoded syntactically AKA Montague Grammar of Semantics then a proof
means validation of truth.
able to be validated.
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all >>>>>>>>>> classical logic, since Truth is different than Knowledge. In a >>>>>>>>>> good logic system, Knowledge will be a subset of Truth, but >>>>>>>>>> you have defined that in your system, Truth is a subset of >>>>>>>>>> Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts
anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
;
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these
basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements. >>>>>>
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some
statement, the context isn't precisely known or the statement is
known to be an approximation of unknown accuracy, so doesn't
actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something.
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be
able to be validated.
True(X) ONLY validates that X is true and does nothing else.
On 3/22/2025 5:11 AM, joes wrote:^
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
Because my system begins with basic facts and actual facts can't >>>>>>>>> contradict each other and no contradiction can be formed by
applying only truth preserving operations to these basic facts >>>>>>>>> there are no contradictions in the system.
The liar sentence is contradictory.
^It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability >>>>>>> cannot possibly exist.
Not self-evident was Gödel's disproof of that.
Try explaining differently, then. What does your supposed truth predicateYou must pay complete attention to ALL of my words or you get theNot if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semanticsYes, proof is a validatation of truth, but truth does not need to be
encoded syntactically AKA Montague Grammar of Semantics then a proof >>>>> means validation of truth.
able to be validated.
meaning that I specify incorrectly.
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all classical >>>> logic, since Truth is different than Knowledge. In a good logic system, >>>> Knowledge will be a subset of Truth, but you have defined that in your >>>> system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unless
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:It is self evidence that for every element of the set of human
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your >>>>>>>> system, Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything >>>>>> that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
;
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these
basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you
are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements.
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some statement,
the context isn't precisely known or the statement is known to be an
approximation of unknown accuracy, so doesn't actually specify a "fact". >>>
knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something.
When the proof is only syntactic then it isn't directly
connected to any meaning.
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:It is self evidence that for every element of the set of human
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>>>
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything >>>>>>>> that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
;
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these
basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you >>>>>> are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements. >>>>>>
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some statement, >>>>>> the context isn't precisely known or the statement is known to be an >>>>>> approximation of unknown accuracy, so doesn't actually specify a "fact". >>>>>
knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something.
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be
able to be validated.
True(X) ONLY validates that X is true and does nothing else.
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
The liar sentence is contradictory.I can't parse that.True(X) always returns TRUE for every element in the set of >>>>>>>>>> general knowledge that can be expressed using language.It is stipulated that analytic knowledge is limited to the set >>>>>>>>>>>> of knowledge that can be expressed using language or derived >>>>>>>>>>>> by applying truth preserving operations to elements of this >>>>>>>>>>>> set.
Which just means that you have stipulated yourself out of all >>>>>>>>>>> classical logic, since Truth is different than Knowledge. In a >>>>>>>>>>> good logic system, Knowledge will be a subset of Truth, but you >>>>>>>>>>> have defined that in your system, Truth is a subset of
Knowledge, so you have it backwards.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts
anything that can be inferred from the set of general knowledge. >>>>>>>>>
(a) Not useful unless (b) it returns TRUE for (c) no X that >>>>>>>> > contradicts anything (d) that can be inferred from the set of >>>>>>>> > general knowledge.Because my system begins with basic facts and actual facts can't >>>>>>>> contradict each other and no contradiction can be formed by
;
applying only truth preserving operations to these basic facts >>>>>>>> there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually understand what >>>>>>> you are trying to define.
"Human Knowledge" is full of contradictions and incorrect
statements.
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some
statement, the context isn't precisely known or the statement is >>>>>>> known to be an approximation of unknown accuracy, so doesn't
actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability >>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something.When the proof is only syntactic then it isn't directly connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semanticsYes, proof is a validatation of truth, but truth does not need to be
encoded syntactically AKA Montague Grammar of Semantics then a proof
means validation of truth.
able to be validated.
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:49 AM, olcott wrote:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
And thus your concept of truth breaks.
Truth, by its definition is an immutable thing, but you just defined it
to be mutable.
How often do we need to re-verify our truths?
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain) >>>> that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
But you aren't begining with basic facts, but with what has been
assumed to be the basic facts.
That is not what I stipulated.
When we begin with what actual are the set of basic
facts and are only allowed to apply truth preserving
operations to these basic facts then it is self-evident
that True(X) must always be correct.
We don't actually KNOW the basics principles for many things, but haveThen these are not included in the set of knowledge.
been working to understand them.
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the set of >>>>>>>>>>> general knowledge that can be expressed using language.It is stipulated that analytic knowledge is limited to the set >>>>>>>>>>>>> of knowledge that can be expressed using language or derived >>>>>>>>>>>>> by applying truth preserving operations to elements of this >>>>>>>>>>>>> set.
Which just means that you have stipulated yourself out of all >>>>>>>>>>>> classical logic, since Truth is different than Knowledge. In a >>>>>>>>>>>> good logic system, Knowledge will be a subset of Truth, but you >>>>>>>>>>>> have defined that in your system, Truth is a subset of >>>>>>>>>>>> Knowledge, so you have it backwards.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>> anything that can be inferred from the set of general knowledge. >>>>>>>>>>
> (a) Not useful unless (b) it returns TRUE for (c) no X that >>>>>>>>> > contradicts anything (d) that can be inferred from the set of >>>>>>>>> > general knowledge.
>
Because my system begins with basic facts and actual facts can't >>>>>>>>> contradict each other and no contradiction can be formed by
applying only truth preserving operations to these basic facts >>>>>>>>> there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually understand what >>>>>>>> you are trying to define.
"Human Knowledge" is full of contradictions and incorrect
statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>> statements into context, but the problem is that for some
statement, the context isn't precisely known or the statement is >>>>>>>> known to be an approximation of unknown accuracy, so doesn't
actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability >>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something.When the proof is only syntactic then it isn't directly connected to >>>>> any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semanticsYes, proof is a validatation of truth, but truth does not need to be
encoded syntactically AKA Montague Grammar of Semantics then a proof >>>>> means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
On 3/22/2025 11:04 AM, joes wrote:
Am Sat, 22 Mar 2025 10:13:12 -0500 schrieb olcott:
On 3/22/2025 5:11 AM, joes wrote:^
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
Because my system begins with basic facts and actual facts can't >>>>>>>>>>> contradict each other and no contradiction can be formed by >>>>>>>>>>> applying only truth preserving operations to these basic facts >>>>>>>>>>> there are no contradictions in the system.
The liar sentence is contradictory.
^It is self evidence that for every element of the set of human >>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>> cannot possibly exist.
Not self-evident was Gödel's disproof of that.
You must pay complete attention to ALL of my words or you get theNot if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semantics >>>>>>> encoded syntactically AKA Montague Grammar of Semantics then a proof >>>>>>> means validation of truth.Yes, proof is a validatation of truth, but truth does not need to be >>>>>> able to be validated.
meaning that I specify incorrectly.
Try explaining differently, then. What does your supposed truth predicate
say about unknown truths?
The body of human general knowledge that can be expressed
using language contains zero unknown truths.
When we expect a True(X) predicate to be the actual omniscient
mind-of-God our expectations are out of whack.
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
On 3/22/2025 11:32 AM, Mikko wrote:
On 2025-03-21 12:43:39 +0000, olcott said:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all
classical logic, since Truth is different than Knowledge. In a
good logic system, Knowledge will be a subset of Truth, but you
have defined that in your system, Truth is a subset of Knowledge,
so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unless
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
Can you parse "It might be useful if it would return something else that
TRUE for some X, especially if that X contradicts something that can be
inferred from the set of general knowledge." ?
True(X) implements a membership algorithm for elements of the
body of human general knowledge that can be expressed using language.
On 3/22/2025 12:43 PM, Richard Damon wrote:No need to apologise.
On 3/22/25 1:40 PM, olcott wrote:
On 3/22/2025 11:32 AM, Mikko wrote:
On 2025-03-21 12:43:39 +0000, olcott said:
On 3/21/2025 3:41 AM, Mikko wrote:
Then it is Known(x) not True(x).Can you parse "It might be useful if it would return something elseTrue(X) implements a membership algorithm for elements of the body of
that TRUE for some X, especially if that X contradicts something that
can be inferred from the set of general knowledge." ?
human general knowledge that can be expressed using language.
Sorry, you just admitted to your fraud.
It is pretty stupid to claim that Knowledge "⊂" Truth is an example of fraud.But not for unknown truths.
True(X) works perfectly within the body of knowledge that can be
expressed using language.
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of >>>>>>>>>>>> all classical logic, since Truth is different than
Knowledge. In a good logic system, Knowledge will be a >>>>>>>>>>>> subset of Truth, but you have defined that in your system, >>>>>>>>>>>> Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>>>>>
True(X) always returns TRUE for every element in the set >>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>> anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>> >
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these >>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand
what you are trying to define.
"Human Knowledge" is full of contradictions and incorrect
statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>> statements into context, but the problem is that for some
statement, the context isn't precisely known or the statement is >>>>>>>> known to be an approximation of unknown accuracy, so doesn't
actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability >>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something.
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be
able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a proof.
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 3:03 PM, olcott wrote:
On 3/22/2025 12:40 PM, Richard Damon wrote:
On 3/22/25 1:36 PM, olcott wrote:
On 3/22/2025 11:04 AM, joes wrote:
Am Sat, 22 Mar 2025 10:13:12 -0500 schrieb olcott:
On 3/22/2025 5:11 AM, joes wrote:^
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
Because my system begins with basic facts and actual >>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>> applying only truth preserving operations to these basic >>>>>>>>>>>>>>> facts
there are no contradictions in the system.
The liar sentence is contradictory.
^It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that
undecidability
cannot possibly exist.
Not self-evident was Gödel's disproof of that.
You must pay complete attention to ALL of my words or you get the >>>>>>> meaning that I specify incorrectly.Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of itsYes, proof is a validatation of truth, but truth does not need >>>>>>>>>> to be
semantics
encoded syntactically AKA Montague Grammar of Semantics then >>>>>>>>>>> a proof
means validation of truth.
able to be validated.
Try explaining differently, then. What does your supposed truth
predicate
say about unknown truths?
The body of human general knowledge that can be expressed
using language contains zero unknown truths.
But from them, we can express unknown truths.
When we can express all known truths then we can
give LLM systems the basis to get on social media
and make all those asserting dangerous lies look
ridiculously foolish even to themselves.
LLMs are not "Truth Perseving" operations. PERIOD.
You are certainly correct as they currently stand.
Getting from Generative AI to Trustworthy AI:
What LLMs might learn from Cyc
Doug Lenat, Gary Marcus
https://arxiv.org/abs/2308.04445
To the best of my recollection derived the above same
idea about the same time that Doug Lenat did.
We also have real time fact checking for politicians.
Not only will these systems be able to reject false
statements they will be able to instantly prove how
they know they are false.
Nope, As pointed out the sum of all "Human Knowledge" is not a truth
based logic system, but is full of inconsistencies.
Actual knowledge itself has no inconsistencies by definition.
Your first problem would be getting the people you are trying to "fact
check" to admit that you initial knowledge base was correct, as most
of it was actually based on opinions. Yes, what is the generally
accepted beleifs, but the people you are trying to persuade, don't
accept those beliefs, so won't believe your results.
We begin with the hypothetical body of all general knowledge
that is expressed using language and try to find any element
that could not be validated with a True(X).
Your problem is you just don't understand the nature of the problem,
because your thinking is just too stupid and immature.
If that was true you could find a counter-example.
Because you know that is not true ad hominem is all that you have.
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 3:03 PM, olcott wrote:
On 3/22/2025 12:40 PM, Richard Damon wrote:
On 3/22/25 1:36 PM, olcott wrote:
On 3/22/2025 11:04 AM, joes wrote:
Am Sat, 22 Mar 2025 10:13:12 -0500 schrieb olcott:
On 3/22/2025 5:11 AM, joes wrote:^
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
Because my system begins with basic facts and actual >>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>> applying only truth preserving operations to these basic >>>>>>>>>>>>>>> facts
there are no contradictions in the system.
The liar sentence is contradictory.
^It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that
undecidability
cannot possibly exist.
Not self-evident was Gödel's disproof of that.
You must pay complete attention to ALL of my words or you get the >>>>>>> meaning that I specify incorrectly.Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of itsYes, proof is a validatation of truth, but truth does not need >>>>>>>>>> to be
semantics
encoded syntactically AKA Montague Grammar of Semantics then >>>>>>>>>>> a proof
means validation of truth.
able to be validated.
Try explaining differently, then. What does your supposed truth
predicate
say about unknown truths?
The body of human general knowledge that can be expressed
using language contains zero unknown truths.
But from them, we can express unknown truths.
When we can express all known truths then we can
give LLM systems the basis to get on social media
and make all those asserting dangerous lies look
ridiculously foolish even to themselves.
LLMs are not "Truth Perseving" operations. PERIOD.
You are certainly correct as they currently stand.
Getting from Generative AI to Trustworthy AI:
What LLMs might learn from Cyc
Doug Lenat, Gary Marcus
https://arxiv.org/abs/2308.04445
To the best of my recollection derived the above same
idea about the same time that Doug Lenat did.
We also have real time fact checking for politicians.
Not only will these systems be able to reject false
statements they will be able to instantly prove how
they know they are false.
Nope, As pointed out the sum of all "Human Knowledge" is not a truth
based logic system, but is full of inconsistencies.
Actual knowledge itself has no inconsistencies by definition.
Your first problem would be getting the people you are trying to "fact
check" to admit that you initial knowledge base was correct, as most
of it was actually based on opinions. Yes, what is the generally
accepted beleifs, but the people you are trying to persuade, don't
accept those beliefs, so won't believe your results.
We begin with the hypothetical body of all general knowledge
that is expressed using language and try to find any element
that could not be validated with a True(X).
Your problem is you just don't understand the nature of the problem,
because your thinking is just too stupid and immature.
If that was true you could find a counter-example.
Because you know that is not true ad hominem is all that you have.
On 3/22/2025 2:10 PM, joes wrote:No, but unknowns are still true.
Am Sat, 22 Mar 2025 14:07:17 -0500 schrieb olcott:
Is it really that hard to understand that knowledge does not include unknowns?It is pretty stupid to claim that Knowledge "⊂" Truth is an example of >>> fraud.But not for unknown truths.
True(X) works perfectly within the body of knowledge that can be
expressed using language.
On 3/23/2025 10:24 AM, joes wrote:
Am Sat, 22 Mar 2025 14:15:48 -0500 schrieb olcott:
On 3/22/2025 2:10 PM, joes wrote:No, but unknowns are still true.
Am Sat, 22 Mar 2025 14:07:17 -0500 schrieb olcott:
Is it really that hard to understand that knowledge does not includeIt is pretty stupid to claim that Knowledge "⊂" Truth is an example of >>>>> fraud.But not for unknown truths.
True(X) works perfectly within the body of knowledge that can be
expressed using language.
unknowns?
When we define the set of all general knowledge
that can be expressed using language then we
have the basis for creating artificial general
intelligence.
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:27 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 12:11 PM, olcott wrote:
On 3/22/2025 8:37 AM, Richard Damon wrote:
On 3/21/25 11:14 PM, olcott wrote:
On 3/21/2025 9:31 PM, Richard Damon wrote:Yes, and that is that there does not exist a number that satifies
On 3/21/25 8:47 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:49 AM, olcott wrote:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>> sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
And thus your concept of truth breaks.
Truth, by its definition is an immutable thing, but you just >>>>>>>>>> defined it to be mutable.
How often do we need to re-verify our truths?
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful >>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>>
But you aren't begining with basic facts, but with what has >>>>>>>>>> been assumed to be the basic facts.
That is not what I stipulated.
When we begin with what actual are the set of basic
facts and are only allowed to apply truth preserving
operations to these basic facts then it is self-evident
that True(X) must always be correct.
But you can't stipulate that you cant' get to things that you
can get to.
If your system can define the Natural Numbers, then we get Godel >>>>>>>> and Tarski, and you can't stop it.
The entire semantics of G is defined in the body of human general >>>>>>> knowledge that can be expressed in language henceforth called (BOK). >>>>>>
a particular involved Primative Recursive Relationship.
That you provide reasonable replies that show good
insight some of the time seems to prove that you
are capable of having good insight.
So, you admit that I shows you something that breaks your claim?
Not at all. What I said and you agreed with
it that G is provable in in the same
way the G is provable in meta-math.
No it isn't as the GKEUL can't have the axioms that enumerate the
axioms, and thus doesn't have the information needed to do the proof
in the meta-math.(GKEUL)
How-so-ever any human ever did this before (GKEUL)
knows how to do that.
On 3/23/2025 4:46 PM, Richard Damon wrote:
On 3/23/25 2:01 PM, olcott wrote:
On 3/23/2025 10:24 AM, joes wrote:
Am Sat, 22 Mar 2025 14:15:48 -0500 schrieb olcott:
On 3/22/2025 2:10 PM, joes wrote:No, but unknowns are still true.
Am Sat, 22 Mar 2025 14:07:17 -0500 schrieb olcott:
Is it really that hard to understand that knowledge does not include >>>>> unknowns?It is pretty stupid to claim that Knowledge "⊂" Truth is anBut not for unknown truths.
example of
fraud.
True(X) works perfectly within the body of knowledge that can be >>>>>>> expressed using language.
When we define the set of all general knowledge
that can be expressed using language then we
have the basis for creating artificial general
intelligence.
Nope, you just don't understand how AI works.
There is a computational barrier that limits how many "facts" the
"neuron cluster" can remember based on its "size", and the
computational requirement grow exponentially with size, so the
limitation isn't how much "data" we can provide the system, but how
well we can pre-organize things so it doesn't need to actually "learn"
stuff.
I am referring to a tree of knowledge similar to the work of Doug Lenat.
This is not any sort of neural network.
Your problem is you just don't understand the nature of what you talk
about, but seem to have read just the CliffsNotes version and think
you understand the details which were never actually discussed in the
abreviation given.
This causes you to not know what you don't know, and then your nature
seems to assume that you can make up what every you want and just
assume it to be true, which just makes you system broken.
If this was not pure bullshit you would have not started
with the assumption that AI <is> neural networks.
Sorry, you are proven that you are totally ignorant of the basics of
the things you talk about, and that your "arguments" are just based on
the FRAUD of using incorrect definitions for core terms, because you
think you are allowed to change the.
On 3/23/2025 6:07 AM, Richard Damon wrote:
On 3/23/25 12:24 AM, olcott wrote:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the >>>>>>>>>>>>>>>>> set ofIt is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>> to the set
of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived
by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>> of this
set.
Which just means that you have stipulated yourself out >>>>>>>>>>>>>>>>>> of all
classical logic, since Truth is different than >>>>>>>>>>>>>>>>>> Knowledge. In a
good logic system, Knowledge will be a subset of >>>>>>>>>>>>>>>>>> Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>>>>>> anything that can be inferred from the set of general >>>>>>>>>>>>>>>> knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) no >>>>>>>>>>>>>>> X that
> contradicts anything (d) that can be inferred from >>>>>>>>>>>>>>> the set of
> general knowledge.
>
Because my system begins with basic facts and actual >>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>> applying only truth preserving operations to these basic >>>>>>>>>>>>>>> facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually
understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>> putting the
statements into context, but the problem is that for some >>>>>>>>>>>>>> statement, the context isn't precisely known or the >>>>>>>>>>>>>> statement is
known to be an approximation of unknown accuracy, so doesn't >>>>>>>>>>>>>> actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that
undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>When the proof is only syntactic then it isn't directly
connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of itsYes, proof is a validatation of truth, but truth does not need >>>>>>>>>> to be
semantics
encoded syntactically AKA Montague Grammar of Semantics then >>>>>>>>>>> a proof
means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the meaning >>>>>> of the core terms and stay in the system, so you are just
admitting that all your work is based on strawmen, and thus frauds. >>>>>>
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so you
just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
The original set theory is now named naive set theory.
No you don't, and your example does say you can.
ZFC didn't "redefine" set theory,
Then why the Hell is the original set theory now called
naive set theory? Might as well have called it clueless
brain-dead set theory.
The gist of the notion of the set of general knowledge
that can be expressed in language was mostly inconceivable
until Montague Grammar of natural language semantics.
This provides the means for a computer to have actual
understanding of all of these ideas.
A True(X) predicate for a set of knowledge is merely
a membership algorithm for this set. A Tree of knowledge
can be searched in finite time.
they defined a new set theory, ZFC Set Theory that got adopted by the
community,
Since you are not "the community", you don't get to change the meaning
the generic term points to,.
Since you think you do, you are just showing that you don't
fundamentally understand how words get their meaning.
Sorry, you are just proving your stupidity.
On 3/22/2025 9:53 PM, Richard Damon wrote:What about them?
On 3/22/25 3:12 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 12:22 PM, olcott wrote:
Ideas that have a truth value that cannot be derived from applyingIf a formal system only contains a finite set of basic facts andNo it hasn't, as the finite set of basic facts, if they are a good
facts are only derived by applying truth preserving operations to
elements of this set then True(X) has already been implicitly
defined for every element of this set.
enough set of facts, allows the creation of an INFINITE set of ideas
to look at, and True(x) hasn't been defined for all of them.
truth preserving operations to the set of basic facts.
I want to dispute the notion that there are only finitely many unsolved problems.But the problem is that there DO exist statements, that HAVE a truthSince you and I know that this does not derive knowledge I can't
value, because they CAN be derived by applying truth perserving
operations (abet an infinite number of them) to the set of basic facts
understand why you keep bringing it up. (GKEUL) will have a finite list
of all unsolved problems as a part of its basic facts.
Any reason for that?exist. Such statements can not be proven, and the assumption of a TruthThe set of all general knowledge that can be expressed in language can
Predicate that answers for them causes a contradiction.
You are just too stupid to understand that aspect of truth allowing
infinite chains to establish things, one simple (in concept) is the
idea that some statement may require checking every Natural Number
individually to confirm a universal attribute (either ALL or NONE) for
every one of them.
That TRUTH can not be proved by trying to enumerate every case, as that
enumeration can't be written out and shown, as those operation can only
be done finitely, which is why proofs must be finite.
have all basic facts that cannot be derived from other facts finitely
listed.
The infinite set of expressions of language of general knowledge can be derived by applying truth preserving operations to these basic facts.Not sure of that either.
On 3/22/2025 9:53 PM, Richard Damon wrote:And not for true non-elements.
On 3/22/25 1:49 PM, olcott wrote:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It <is> as I have always said that it <is> a True(X) predicate for every element of the set of general knowledge that can be expressed inThen it isnt a truth predicate, but a Knowledge predicate, and thus youTrue(X) is a predicate implementing a membership algorithm for theTrue(X) ONLY validates that X is true and does nothing else.We can believe the "nothing else" part. The rest would require a
proof.
body of general knowledge that can be expressed using language.
are admitting to just being a liar about all you claimed.
language.
That you just can't keep track of this is your mistake not my deception.Your deception is that you call all unknowns false.
It excludes things like what you had for lunch today what a rose smells like... It includes every word of every textbook every written encodedIt also excludes unknown truths.
in such a way that it fully understands all of these words.
On 3/23/2025 7:37 PM, joes wrote:
Am Sun, 23 Mar 2025 16:10:46 -0500 schrieb olcott:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 1:49 PM, olcott wrote:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It <is> as I have always said that it <is> a True(X) predicate for every >>> element of the set of general knowledge that can be expressed inThen it isnt a truth predicate, but a Knowledge predicate, and thus you >>>> are admitting to just being a liar about all you claimed.True(X) is a predicate implementing a membership algorithm for theTrue(X) ONLY validates that X is true and does nothing else.We can believe the "nothing else" part. The rest would require a
proof.
body of general knowledge that can be expressed using language.
language.
And not for true non-elements.
It will know when X is true and ~Y is true
and LP is not true and ~LP is not true.
That you just can't keep track of this is your mistake not my deception.Your deception is that you call all unknowns false.
True(X) with a domain of the set of general knowledge that
can be expressed in language works the same way as Prolog.
Can X be derived by applying Prolog Rules to Prolog Facts?
It excludes things like what you had for lunch today what a rose smells
like... It includes every word of every textbook every written encoded
in such a way that it fully understands all of these words.
It also excludes unknown truths.As any set of knowledge must do.
On 3/22/2025 8:37 AM, Richard Damon wrote:
On 3/21/25 11:03 PM, olcott wrote:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>>>>>
True(X) always returns TRUE for every element in the set >>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything >>>>>>>>>> that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>> >
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these >>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you >>>>>>>> are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements. >>>>>>>>
Adittedly, most of them can be resolved by properly putting the >>>>>>>> statements into context, but the problem is that for some statement, >>>>>>>> the context isn't precisely known or the statement is known to be an >>>>>>>> approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability >>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something.
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be
able to be validated.
True(X) ONLY validates that X is true and does nothing else.
But can't do that, as Tarski shows, as it creates contradictions when
the system is able to generate unprovable truths.
Unless we do what ZFC did to redefine the foundations
of set theory and redefine the notion of a formal system.
On 3/22/2025 11:32 AM, Mikko wrote:
On 2025-03-21 12:43:39 +0000, olcott said:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all classical >>>>>> logic, since Truth is different than Knowledge. In a good logic system, >>>>>> Knowledge will be a subset of Truth, but you have defined that in your >>>>>> system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unless
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
Can you parse "It might be useful if it would return something else that
TRUE for some X, especially if that X contradicts something that can be
inferred from the set of general knowledge." ?
True(X) implements a membership algorithm for elements of the
body of human general knowledge that can be expressed using language.
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>>>>>
True(X) always returns TRUE for every element in the set >>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything >>>>>>>>>> that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>> >
can't contradict each other and no contradiction can be
formed by applying only truth preserving operations to these >>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you >>>>>>>> are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements. >>>>>>>>
Adittedly, most of them can be resolved by properly putting the >>>>>>>> statements into context, but the problem is that for some statement, >>>>>>>> the context isn't precisely known or the statement is known to be an >>>>>>>> approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human
knowledge that can be expressed using language that undecidability >>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something.
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be
able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a proof.
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the set of >>>>>>>>>>>>>>> general knowledge that can be expressed using language. >>>>>>>>>>>>>>> It never gets confused by paradoxes.It is stipulated that analytic knowledge is limited to the set
of knowledge that can be expressed using language or derived >>>>>>>>>>>>>>>>> by applying truth preserving operations to elements of this >>>>>>>>>>>>>>>>> set.
Which just means that you have stipulated yourself out of all >>>>>>>>>>>>>>>> classical logic, since Truth is different than Knowledge. In a >>>>>>>>>>>>>>>> good logic system, Knowledge will be a subset of Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>>>> anything that can be inferred from the set of general knowledge. >>>>>>>>>>>>>>
> (a) Not useful unless (b) it returns TRUE for (c) no X that >>>>>>>>>>>>> > contradicts anything (d) that can be inferred from the set of
> general knowledge.
>
Because my system begins with basic facts and actual facts can't >>>>>>>>>>>>> contradict each other and no contradiction can be formed by >>>>>>>>>>>>> applying only truth preserving operations to these basic facts >>>>>>>>>>>>> there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually understand what >>>>>>>>>>>> you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>>>>>> statements into context, but the problem is that for some >>>>>>>>>>>> statement, the context isn't precisely known or the statement is >>>>>>>>>>>> known to be an approximation of unknown accuracy, so doesn't >>>>>>>>>>>> actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>When the proof is only syntactic then it isn't directly connected to >>>>>>>>> any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semantics >>>>>>>>> encoded syntactically AKA Montague Grammar of Semantics then a proof >>>>>>>>> means validation of truth.Yes, proof is a validatation of truth, but truth does not need to be >>>>>>>> able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the meaning of
the core terms and stay in the system, so you are just admitting that
all your work is based on strawmen, and thus frauds.
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so you
just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain) >>>> that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
On 3/22/2025 11:32 AM, Mikko wrote:
On 2025-03-21 12:43:39 +0000, olcott said:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all
classical logic, since Truth is different than Knowledge. In a
good logic system, Knowledge will be a subset of Truth, but you
have defined that in your system, Truth is a subset of Knowledge,
so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unless
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
Can you parse "It might be useful if it would return something else that
TRUE for some X, especially if that X contradicts something that can be
inferred from the set of general knowledge." ?
Before we can get into these details it must first be
acknowledged that True(X) would necessarily work correctly
for the set of actual knowledge that can be expressed in
language.
True(X) for this set proves Tarski was wrong that no True(X)
can ever be consistently defined. Silly self-contradictory
expressions are simply rejected as not members of the
body of knowledge.
On 3/25/2025 5:03 AM, Mikko wrote:
On 2025-03-22 17:49:01 +0000, olcott said:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of >>>>>>>>>>>>>> all classical logic, since Truth is different than >>>>>>>>>>>>>> Knowledge. In a good logic system, Knowledge will be a >>>>>>>>>>>>>> subset of Truth, but you have defined that in your system, >>>>>>>>>>>>>> Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>>>>>>>
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>> anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>> can't contradict each other and no contradiction can be
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>> >
formed by applying only truth preserving operations to these >>>>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand >>>>>>>>>> what you are trying to define.
"Human Knowledge" is full of contradictions and incorrect
statements.
Adittedly, most of them can be resolved by properly putting >>>>>>>>>> the statements into context, but the problem is that for some >>>>>>>>>> statement, the context isn't precisely known or the statement >>>>>>>>>> is known to be an approximation of unknown accuracy, so
doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to
be able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a proof. >>>>
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
What does your True(X) say when X means that there is no method to
determine whether a sentence of the first order group theory can
be proven.
That is either in the body of knowledge or not.
When something like deep learning eventually
causes it to have a deeper understanding than
humans it may prove that human understanding
of this is incorrect.
On 3/25/2025 4:50 AM, Mikko wrote:
On 2025-03-23 04:24:51 +0000, olcott said:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the >>>>>>>>>>>>>>>>> set ofIt is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>> to the set
of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived
by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>> of this
set.
Which just means that you have stipulated yourself out >>>>>>>>>>>>>>>>>> of all
classical logic, since Truth is different than >>>>>>>>>>>>>>>>>> Knowledge. In a
good logic system, Knowledge will be a subset of >>>>>>>>>>>>>>>>>> Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>>>>>> anything that can be inferred from the set of general >>>>>>>>>>>>>>>> knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) no >>>>>>>>>>>>>>> X that
> contradicts anything (d) that can be inferred from >>>>>>>>>>>>>>> the set of
> general knowledge.
>
Because my system begins with basic facts and actual >>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>> applying only truth preserving operations to these basic >>>>>>>>>>>>>>> facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually
understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>> putting the
statements into context, but the problem is that for some >>>>>>>>>>>>>> statement, the context isn't precisely known or the >>>>>>>>>>>>>> statement is
known to be an approximation of unknown accuracy, so doesn't >>>>>>>>>>>>>> actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that
undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>When the proof is only syntactic then it isn't directly
connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of itsYes, proof is a validatation of truth, but truth does not need >>>>>>>>>> to be
semantics
encoded syntactically AKA Montague Grammar of Semantics then >>>>>>>>>>> a proof
means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the meaning >>>>>> of the core terms and stay in the system, so you are just
admitting that all your work is based on strawmen, and thus frauds. >>>>>>
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so you
just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
No, you can't. The nearest you can is to create a new term that
is homonymous to an old one. But you can't use two homonymous
terms in the same opus.
Original set theory became "naive set theory".
ZFC set theory corrected its shortcomings.
GKEUL provides the means for a True(X) predicate
to be defined for this entire domain of knowledge.
It cannot be fooled by silly self-contradictory
expressions.
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly >>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture >>>>>> or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems,
certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
On 3/25/2025 4:54 AM, Mikko wrote:
On 2025-03-22 16:22:46 +0000, olcott said:
On 3/22/2025 8:37 AM, Richard Damon wrote:
On 3/21/25 11:03 PM, olcott wrote:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of >>>>>>>>>>>>>> all classical logic, since Truth is different than >>>>>>>>>>>>>> Knowledge. In a good logic system, Knowledge will be a >>>>>>>>>>>>>> subset of Truth, but you have defined that in your system, >>>>>>>>>>>>>> Truth is a subset of Knowledge, so you have it backwards. >>>>>>>>>>>>>>
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>> anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>> can't contradict each other and no contradiction can be
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>> >
formed by applying only truth preserving operations to these >>>>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand >>>>>>>>>> what you are trying to define.
"Human Knowledge" is full of contradictions and incorrect
statements.
Adittedly, most of them can be resolved by properly putting >>>>>>>>>> the statements into context, but the problem is that for some >>>>>>>>>> statement, the context isn't precisely known or the statement >>>>>>>>>> is known to be an approximation of unknown accuracy, so
doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to
be able to be validated.
True(X) ONLY validates that X is true and does nothing else.
But can't do that, as Tarski shows, as it creates contradictions
when the system is able to generate unprovable truths.
Unless we do what ZFC did to redefine the foundations
of set theory and redefine the notion of a formal system.
The notion of a formal system is sufficiently generic that there is no
need to redefine it. If you want something else then call it something
else.
ZFC got rid of the issues of pathological self-reference
from set theory. The same thing can be done for formal
systems.
On 3/25/2025 8:00 PM, Richard Damon wrote:
On 3/25/25 10:32 AM, olcott wrote:
On 3/25/2025 5:03 AM, Mikko wrote:
On 2025-03-22 17:49:01 +0000, olcott said:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>> derived by applying truth preserving operations to >>>>>>>>>>>>>>>>> elements
of this set.
Which just means that you have stipulated yourself out >>>>>>>>>>>>>>>> of all classical logic, since Truth is different than >>>>>>>>>>>>>>>> Knowledge. In a good logic system, Knowledge will be a >>>>>>>>>>>>>>>> subset of Truth, but you have defined that in your >>>>>>>>>>>>>>>> system, Truth is a subset of Knowledge, so you have it >>>>>>>>>>>>>>>> backwards.
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that
contradicts anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>>>> can't contradict each other and no contradiction can be >>>>>>>>>>>>> formed by applying only truth preserving operations to these >>>>>>>>>>>>> basic facts there are no contradictions in the system. >>>>>>>>>>>>>
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>>>> >
No, you system doesn't because you don't actually understand >>>>>>>>>>>> what you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly putting >>>>>>>>>>>> the statements into context, but the problem is that for >>>>>>>>>>>> some statement, the context isn't precisely known or the >>>>>>>>>>>> statement is known to be an approximation of unknown
accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>> knowledge that can be expressed using language that
undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need >>>>>>>> to be able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a
proof.
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
What does your True(X) say when X means that there is no method to
determine whether a sentence of the first order group theory can
be proven.
That is either in the body of knowledge or not.
When something like deep learning eventually
causes it to have a deeper understanding than
humans it may prove that human understanding
of this is incorrect.
You just don't understand how "AI" works.
Current AI has ZERO understanding of what it is processing.
Work to try to make processing have understanding is running in the
problem of complexity.
You are wrong again https://www.technologyreview.com/2024/03/04/1089403/large-language- models-amazing-but-nobody-knows-why/
On 3/25/2025 4:54 AM, Mikko wrote:
On 2025-03-22 16:22:46 +0000, olcott said:
On 3/22/2025 8:37 AM, Richard Damon wrote:
On 3/21/25 11:03 PM, olcott wrote:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>> can't contradict each other and no contradiction can be
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>> >
formed by applying only truth preserving operations to these >>>>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you
are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>>>> statements into context, but the problem is that for some statement, >>>>>>>>>> the context isn't precisely known or the statement is known to be an >>>>>>>>>> approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be >>>>>> able to be validated.
True(X) ONLY validates that X is true and does nothing else.
But can't do that, as Tarski shows, as it creates contradictions when
the system is able to generate unprovable truths.
Unless we do what ZFC did to redefine the foundations
of set theory and redefine the notion of a formal system.
The notion of a formal system is sufficiently generic that there is no
need to redefine it. If you want something else then call it something
else.
ZFC got rid of the issues of pathological self-reference
from set theory. The same thing can be done for formal
systems.
On 3/25/2025 5:03 AM, Mikko wrote:
On 2025-03-22 17:49:01 +0000, olcott said:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>> can't contradict each other and no contradiction can be
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>> >
formed by applying only truth preserving operations to these >>>>>>>>>>> basic facts there are no contradictions in the system.
No, you system doesn't because you don't actually understand what you
are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>>>> statements into context, but the problem is that for some statement, >>>>>>>>>> the context isn't precisely known or the statement is known to be an >>>>>>>>>> approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be >>>>>> able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a proof. >>>>
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
What does your True(X) say when X means that there is no method to
determine whether a sentence of the first order group theory can
be proven.
That is either in the body of knowledge or not.
On 3/25/2025 4:50 AM, Mikko wrote:
On 2025-03-23 04:24:51 +0000, olcott said:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the set of >>>>>>>>>>>>>>>>> general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>> It never gets confused by paradoxes.It is stipulated that analytic knowledge is limited to the set
of knowledge that can be expressed using language or derived
by applying truth preserving operations to elements of this >>>>>>>>>>>>>>>>>>> set.
Which just means that you have stipulated yourself out of all
classical logic, since Truth is different than Knowledge. In a
good logic system, Knowledge will be a subset of Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>>>>>> anything that can be inferred from the set of general knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) no X that
> contradicts anything (d) that can be inferred from the set of
> general knowledge.
>
Because my system begins with basic facts and actual facts can't
contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>> applying only truth preserving operations to these basic facts >>>>>>>>>>>>>>> there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>>>>>>>> statements into context, but the problem is that for some >>>>>>>>>>>>>> statement, the context isn't precisely known or the statement is >>>>>>>>>>>>>> known to be an approximation of unknown accuracy, so doesn't >>>>>>>>>>>>>> actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>When the proof is only syntactic then it isn't directly connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
Not if X is unknown (but still true).True(X) ONLY validates that X is true and does nothing else.When the body of human general knowledge has all of its semantics >>>>>>>>>>> encoded syntactically AKA Montague Grammar of Semantics then a proofYes, proof is a validatation of truth, but truth does not need to be >>>>>>>>>> able to be validated.
means validation of truth.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the meaning of >>>>>> the core terms and stay in the system, so you are just admitting that >>>>>> all your work is based on strawmen, and thus frauds.
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so you
just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
No, you can't. The nearest you can is to create a new term that
is homonymous to an old one. But you can't use two homonymous
terms in the same opus.
Original set theory became "naive set theory".
ZFC set theory corrected its shortcomings.
On 3/25/2025 8:47 PM, Richard Damon wrote:
On 3/25/25 9:28 PM, olcott wrote:
On 3/25/2025 8:00 PM, Richard Damon wrote:
On 3/25/25 10:32 AM, olcott wrote:
On 3/25/2025 5:03 AM, Mikko wrote:
On 2025-03-22 17:49:01 +0000, olcott said:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>>>>>> can't contradict each other and no contradiction can be >>>>>>>>>>>>>>> formed by applying only truth preserving operations to these >>>>>>>>>>>>>>> basic facts there are no contradictions in the system. >>>>>>>>>>>>>>>
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>>>>>> >
No, you system doesn't because you don't actually understand what you
are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>>>>>>>> statements into context, but the problem is that for some statement,
the context isn't precisely known or the statement is known to be an
approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be >>>>>>>>>> able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a proof.
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
What does your True(X) say when X means that there is no method to >>>>>> determine whether a sentence of the first order group theory can
be proven.
That is either in the body of knowledge or not.
When something like deep learning eventually
causes it to have a deeper understanding than
humans it may prove that human understanding
of this is incorrect.
You just don't understand how "AI" works.
Current AI has ZERO understanding of what it is processing.
Work to try to make processing have understanding is running in the
problem of complexity.
You are wrong again
https://www.technologyreview.com/2024/03/04/1089403/large-language-
models-amazing-but-nobody-knows-why/
Doesn't say it understands what it is doing.
Note, "Arithmetic" is a purely symbolic operation, actually definable
with a fairly small set of rules.
You are just again looking at summaries of ideas and think you know how
they actually work.
It says that its abilities baffle its own designers.
On 3/22/2025 11:32 AM, Mikko wrote:
On 2025-03-21 12:43:39 +0000, olcott said:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
Which just means that you have stipulated yourself out of all classical >>>>>> logic, since Truth is different than Knowledge. In a good logic system, >>>>>> Knowledge will be a subset of Truth, but you have defined that in your >>>>>> system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set
of general knowledge that can be expressed using language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge.
I can't parse that.
(a) Not useful unless
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge.
Can you parse "It might be useful if it would return something else that
TRUE for some X, especially if that X contradicts something that can be
inferred from the set of general knowledge." ?
Before we can get into these details it must first be
acknowledged that True(X) would necessarily work correctly
for the set of actual knowledge that can be expressed in
language.
True(X) for this set proves Tarski was wrong that no True(X)
can ever be consistently defined.
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly >>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture >>>>>> or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain) >>>>>> that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>> is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture >>>>>>>> or its negation. Then the predicate True is no longer complete. >>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
On 3/25/2025 8:47 PM, Richard Damon wrote:
On 3/25/25 9:28 PM, olcott wrote:
On 3/25/2025 8:00 PM, Richard Damon wrote:
On 3/25/25 10:32 AM, olcott wrote:
On 3/25/2025 5:03 AM, Mikko wrote:
On 2025-03-22 17:49:01 +0000, olcott said:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:It is self evidence that for every element of the set of human >>>>>>>>>>>>> knowledge that can be expressed using language that
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>> to the
set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements
of this set.
Which just means that you have stipulated yourself out >>>>>>>>>>>>>>>>>> of all classical logic, since Truth is different than >>>>>>>>>>>>>>>>>> Knowledge. In a good logic system, Knowledge will be a >>>>>>>>>>>>>>>>>> subset of Truth, but you have defined that in your >>>>>>>>>>>>>>>>>> system, Truth is a subset of Knowledge, so you have it >>>>>>>>>>>>>>>>>> backwards.
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that >>>>>>>>>>>>>>>> contradicts anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>>>>>> can't contradict each other and no contradiction can be >>>>>>>>>>>>>>> formed by applying only truth preserving operations to these >>>>>>>>>>>>>>> basic facts there are no contradictions in the system. >>>>>>>>>>>>>>>
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general >>>>>>>>>>>>>>> knowledge.
;
No, you system doesn't because you don't actually
understand what you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>> putting the statements into context, but the problem is >>>>>>>>>>>>>> that for some statement, the context isn't precisely known >>>>>>>>>>>>>> or the statement is known to be an approximation of >>>>>>>>>>>>>> unknown accuracy, so doesn't actually specify a "fact". >>>>>>>>>>>>>
undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need >>>>>>>>>> to be able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a >>>>>>>> proof.
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
What does your True(X) say when X means that there is no method to >>>>>> determine whether a sentence of the first order group theory can
be proven.
That is either in the body of knowledge or not.
When something like deep learning eventually
causes it to have a deeper understanding than
humans it may prove that human understanding
of this is incorrect.
You just don't understand how "AI" works.
Current AI has ZERO understanding of what it is processing.
Work to try to make processing have understanding is running in the
problem of complexity.
You are wrong again
https://www.technologyreview.com/2024/03/04/1089403/large-language-
models-amazing-but-nobody-knows-why/
Doesn't say it understands what it is doing.
Note, "Arithmetic" is a purely symbolic operation, actually definable
with a fairly small set of rules.
You are just again looking at summaries of ideas and think you know
how they actually work.
It says that its abilities baffle its own designers.
Sorry, but you are just proving your natural stupidity.
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>> is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the
conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, >>>>>>>> certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
How do we know what we think to be True is actually True?
Stimulated relations between finite strings are necessarily
true. "cats" <are> "animals"
In FORMAL systems we can rigorously define what is true in that
system, as we start with a defined set of given facts (which is why
you can't change the definitions and stay in the system, as those
definitions are what made the system).
Almost the same idea as basic facts.
When you talk about "Human Knowledge" for the "Real World" you run
into the problem that we don't have a listing of the fundamental facts
that define the system, but are trying to discover our best
explainations by observation.
Basic facts that cannot be derived from anything else.
Thus we hit the problem that Philosophers debate about how can we know
what we know?
Epistemology is my favorite subject.
This is, as I just explained, only a problem in the "real world", as
in a Formal System, Truth has a precise definition, as does Knowledge.
There is no real world problem with the actual set of knowledge
that can be expressed using language.
Your problem is your "True" predicate detects the later, not actually
Truth, and thus calling it True is just a lie.
It is stipulated that the system is the actual set of knowledge
that can be expressed in language. For this set the True(X)
predicate is infallible.
On 3/25/2025 7:56 PM, Richard Damon wrote:
On 3/25/25 10:28 AM, olcott wrote:
On 3/25/2025 4:50 AM, Mikko wrote:
On 2025-03-23 04:24:51 +0000, olcott said:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the >>>>>>>>>>>>>>>>>>> set ofIt is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>>>> to the set
of knowledge that can be expressed using language >>>>>>>>>>>>>>>>>>>>> or derived
by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>>>> of this
set.
Which just means that you have stipulated yourself >>>>>>>>>>>>>>>>>>>> out of all
classical logic, since Truth is different than >>>>>>>>>>>>>>>>>>>> Knowledge. In a
good logic system, Knowledge will be a subset of >>>>>>>>>>>>>>>>>>>> Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that >>>>>>>>>>>>>>>>>> contradicts
anything that can be inferred from the set of general >>>>>>>>>>>>>>>>>> knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) >>>>>>>>>>>>>>>>> no X that
> contradicts anything (d) that can be inferred from >>>>>>>>>>>>>>>>> the set of
> general knowledge.
>
Because my system begins with basic facts and actual >>>>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be >>>>>>>>>>>>>>>>> formed by
applying only truth preserving operations to these >>>>>>>>>>>>>>>>> basic facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually >>>>>>>>>>>>>>>> understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>>>> putting the
statements into context, but the problem is that for some >>>>>>>>>>>>>>>> statement, the context isn't precisely known or the >>>>>>>>>>>>>>>> statement is
known to be an approximation of unknown accuracy, so >>>>>>>>>>>>>>>> doesn't
actually specify a "fact".
It is self evidence that for every element of the set of >>>>>>>>>>>>>>> human
knowledge that can be expressed using language that >>>>>>>>>>>>>>> undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove >>>>>>>>>>>>>> something.When the proof is only syntactic then it isn't directly >>>>>>>>>>>>> connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
True(X) ONLY validates that X is true and does nothing else. >>>>>>>>>> Not if X is unknown (but still true).When the body of human general knowledge has all of its >>>>>>>>>>>>> semanticsYes, proof is a validatation of truth, but truth does not >>>>>>>>>>>> need to be
encoded syntactically AKA Montague Grammar of Semantics >>>>>>>>>>>>> then a proof
means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the
meaning of the core terms and stay in the system, so you are
just admitting that all your work is based on strawmen, and thus >>>>>>>> frauds.
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so
you just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
No, you can't. The nearest you can is to create a new term that
is homonymous to an old one. But you can't use two homonymous
terms in the same opus.
Original set theory became "naive set theory".
ZFC set theory corrected its shortcomings.
GKEUL provides the means for a True(X) predicate
to be defined for this entire domain of knowledge.
It cannot be fooled by silly self-contradictory
expressions.
But then your "True(x)" isn't a "Truth Predicate" but a "Knowledge
Predicate" so your system is just defined to be based on a lie, as
Truth and Knowledge are different things.
It <is> a truth predicate for the domain of knowledge that
can be expressed using language.
It inherently has no undecidability because it is anchored
in notions such as Wittgenstein's rebuke of Gödel / Prolog's Rules
applied to Facts. https://www.liarparadox.org/Wittgenstein.pdf
This has always been my same idea when I anchor this idea
in the domain of knowledge that can be expressed in language
then this idea becomes self-evidently correct.
Something it seems you do not understand due to your ignorance and
stupidity.
If I actually was ignorant you could point out
specific gaps in my reasoning. Since there are
no gaps on my side you can't do this.
You know that I am not stupid and I know that you
are not stupid.
On 3/26/2025 2:58 AM, Mikko wrote:
On 2025-03-25 14:28:49 +0000, olcott said:
On 3/25/2025 4:50 AM, Mikko wrote:
On 2025-03-23 04:24:51 +0000, olcott said:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the >>>>>>>>>>>>>>>>>>> set ofIt is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>>>> to the set
of knowledge that can be expressed using language >>>>>>>>>>>>>>>>>>>>> or derived
by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>>>> of this
set.
Which just means that you have stipulated yourself >>>>>>>>>>>>>>>>>>>> out of all
classical logic, since Truth is different than >>>>>>>>>>>>>>>>>>>> Knowledge. In a
good logic system, Knowledge will be a subset of >>>>>>>>>>>>>>>>>>>> Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that >>>>>>>>>>>>>>>>>> contradicts
anything that can be inferred from the set of general >>>>>>>>>>>>>>>>>> knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) >>>>>>>>>>>>>>>>> no X that
> contradicts anything (d) that can be inferred from >>>>>>>>>>>>>>>>> the set of
> general knowledge.
>
Because my system begins with basic facts and actual >>>>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be >>>>>>>>>>>>>>>>> formed by
applying only truth preserving operations to these >>>>>>>>>>>>>>>>> basic facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually >>>>>>>>>>>>>>>> understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>>>> putting the
statements into context, but the problem is that for some >>>>>>>>>>>>>>>> statement, the context isn't precisely known or the >>>>>>>>>>>>>>>> statement is
known to be an approximation of unknown accuracy, so >>>>>>>>>>>>>>>> doesn't
actually specify a "fact".
It is self evidence that for every element of the set of >>>>>>>>>>>>>>> human
knowledge that can be expressed using language that >>>>>>>>>>>>>>> undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove >>>>>>>>>>>>>> something.When the proof is only syntactic then it isn't directly >>>>>>>>>>>>> connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
True(X) ONLY validates that X is true and does nothing else. >>>>>>>>>> Not if X is unknown (but still true).When the body of human general knowledge has all of its >>>>>>>>>>>>> semanticsYes, proof is a validatation of truth, but truth does not >>>>>>>>>>>> need to be
encoded syntactically AKA Montague Grammar of Semantics >>>>>>>>>>>>> then a proof
means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the
meaning of the core terms and stay in the system, so you are
just admitting that all your work is based on strawmen, and thus >>>>>>>> frauds.
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so
you just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
No, you can't. The nearest you can is to create a new term that
is homonymous to an old one. But you can't use two homonymous
terms in the same opus.
Original set theory became "naive set theory".
ZFC set theory corrected its shortcomings.
The original one is Cantor's. But that his presentation was too informal
to determine whether Russell's set is expressible. But he did show that
one can construct from nothing enough sets for natural number arithmetic.
Russell's set cannot be constructed.
My whole point is that a broken system was fixed by redefining it.
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>> is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the
conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, >>>>>>>> certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very small
part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
On 3/26/2025 6:01 PM, Richard Damon wrote:
On 3/26/25 1:50 PM, olcott wrote:
On 3/26/2025 6:12 AM, Richard Damon wrote:
On 3/25/25 10:15 PM, olcott wrote:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>> sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful >>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
SO that means that "Cats are Dogs" is part of Knowldedge?
Try re-reading what I said as many times as needed
until you notice ALL of the words.
I have, and you can't explain the difference.
How do we know what we think to be True is actually True?
Stimulated relations between finite strings are necessarily
true. "cats" <are> "animals"
Only if "cats" and "animals" have the appropriate definitions.
Do think that anyone ever wrote these down?
Then they exist in the body of general knowledge expressed in language.
So anything written down is true?
Thus climare change must not be real, since THAT "fact" has been
written down and accepted by a large number of peoplel
The trator down the street that is a "cat" isn't an animal, but
sometimes the person that operates it can be a bit of one.
General knowledge.
But "cat" is a term for a type of tractor.
In FORMAL systems we can rigorously define what is true in that
system, as we start with a defined set of given facts (which is
why you can't change the definitions and stay in the system, as
those definitions are what made the system).
Almost the same idea as basic facts.
Yes, but more than basic facts. Note,
What formal system has an axiom that defines
ice cream as a diary product?
Many,
When you talk about "Human Knowledge" for the "Real World" you run >>>>>> into the problem that we don't have a listing of the fundamental
facts that define the system, but are trying to discover our best
explainations by observation.
Basic facts that cannot be derived from anything else.
So what makes them true?
What makes a dairy cow not a kind of rattlesnake.
Stipulated relations between finite strings that
provides their semantic meaning.
No, stipulated relationships between concepts.
OK, I will give you that and qualify my original statement.
Stipulated relations between concepts that are labeled by
finite strings, thus ultimately stipulated relations between
finite strings, the ultimate formalism.
Note, EVERYTHING we know about the real world starts with
observations, and observations are always only approximate.
So the integer 5 is in the fake world?
The NUMBER 5, is a construct of logic, so not of the "real world"
Thus we hit the problem that Philosophers debate about how can we
know what we know?
Epistemology is my favorite subject.
Then why are you so ignorant of it?
This is, as I just explained, only a problem in the "real world",
as in a Formal System, Truth has a precise definition, as does
Knowledge.
There is no real world problem with the actual set of knowledge
that can be expressed using language.
So, you admit that you system won't be able to rebute the climate
deniers, as that problem can't be expressed?
The set of general knowledge expressed in language
already proves the truth of climate change.
No it doesn't. Show the PROOF.
An easier case to understand is that there never has been
any actual evidence of election fraud that could have
possibly changed the outcome of the 2020 presidential election.
Which doesn't PROVE that there wasn't any.
It proves that all claims of this election fraud are baseless
thus deceptive.
Your problem is your "True" predicate detects the later, not
actually Truth, and thus calling it True is just a lie.
It is stipulated that the system is the actual set of knowledge
that can be expressed in language. For this set the True(X)
predicate is infallible.
And is itself just a lie, as it is really a knowledge predicate, and
not even a good one as it is knowledge at a given point in time
predicate.
It <is> a Truth predicate for a specific domain.
It cannot possibly get confused by self-contradictory
expressions. It has is no undecidability.
But the domain isn't one anyone wants.
That True(X) is defined for one domain proves
that True(X) <is> definable thus refuting Tarski
that "proved" this is impossible.
Your problem is you like to stipulate yourself out of the problem
domain that people are interested in.
People are not interested in preventing tyrants
from taking all their freedom using well crafted lies?
Sure they are, but not it it means we can never learn anything new.
All you system seems to be able to do is say, "We already knew that
one".
On 3/26/2025 8:22 PM, Richard Damon wrote:
On 3/26/25 2:01 PM, olcott wrote:
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the
conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful
sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>> that can be expressed using language then every element in this >>>>>>>>> set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language >>>>>>>> is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very small >>>> part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
So, How do we know what is in that?
It is the defined set such that every expression of
language has the semantic property of true.
How do you intend to construct this system?
This is 100% totally irrelevant until after the very
simple idea that a True(X) predicate would necessarily
exist for this set is totally accepted.
On 3/26/2025 6:01 PM, Richard Damon wrote:
On 3/26/25 6:04 PM, olcott wrote:
On 3/26/2025 2:58 AM, Mikko wrote:
On 2025-03-25 14:28:49 +0000, olcott said:
On 3/25/2025 4:50 AM, Mikko wrote:
On 2025-03-23 04:24:51 +0000, olcott said:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in >>>>>>>>>>>>>>>>>>>>> the set ofIt is stipulated that analytic knowledge is >>>>>>>>>>>>>>>>>>>>>>> limited to the set
of knowledge that can be expressed using language >>>>>>>>>>>>>>>>>>>>>>> or derived
by applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>> elements of this
set.
Which just means that you have stipulated yourself >>>>>>>>>>>>>>>>>>>>>> out of all
classical logic, since Truth is different than >>>>>>>>>>>>>>>>>>>>>> Knowledge. In a
good logic system, Knowledge will be a subset of >>>>>>>>>>>>>>>>>>>>>> Truth, but you
have defined that in your system, Truth is a >>>>>>>>>>>>>>>>>>>>>> subset of
Knowledge, so you have it backwards. >>>>>>>>>>>>>>>>>>>>>>
general knowledge that can be expressed using >>>>>>>>>>>>>>>>>>>>> language.
It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that >>>>>>>>>>>>>>>>>>>> contradicts
anything that can be inferred from the set of >>>>>>>>>>>>>>>>>>>> general knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) >>>>>>>>>>>>>>>>>>> no X that
> contradicts anything (d) that can be inferred >>>>>>>>>>>>>>>>>>> from the set of
> general knowledge.
>
Because my system begins with basic facts and actual >>>>>>>>>>>>>>>>>>> facts can't
contradict each other and no contradiction can be >>>>>>>>>>>>>>>>>>> formed by
applying only truth preserving operations to these >>>>>>>>>>>>>>>>>>> basic facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually >>>>>>>>>>>>>>>>>> understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly >>>>>>>>>>>>>>>>>> putting the
statements into context, but the problem is that for some >>>>>>>>>>>>>>>>>> statement, the context isn't precisely known or the >>>>>>>>>>>>>>>>>> statement is
known to be an approximation of unknown accuracy, so >>>>>>>>>>>>>>>>>> doesn't
actually specify a "fact".
It is self evidence that for every element of the set >>>>>>>>>>>>>>>>> of human
knowledge that can be expressed using language that >>>>>>>>>>>>>>>>> undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove >>>>>>>>>>>>>>>> something.When the proof is only syntactic then it isn't directly >>>>>>>>>>>>>>> connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
True(X) ONLY validates that X is true and does nothing else. >>>>>>>>>>>> Not if X is unknown (but still true).When the body of human general knowledge has all of its >>>>>>>>>>>>>>> semanticsYes, proof is a validatation of truth, but truth does not >>>>>>>>>>>>>> need to be
encoded syntactically AKA Montague Grammar of Semantics >>>>>>>>>>>>>>> then a proof
means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the >>>>>>>>>> meaning of the core terms and stay in the system, so you are >>>>>>>>>> just admitting that all your work is based on strawmen, and >>>>>>>>>> thus frauds.
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so >>>>>>>> you just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
No, you can't. The nearest you can is to create a new term that
is homonymous to an old one. But you can't use two homonymous
terms in the same opus.
Original set theory became "naive set theory".
ZFC set theory corrected its shortcomings.
The original one is Cantor's. But that his presentation was too
informal
to determine whether Russell's set is expressible. But he did show that >>>> one can construct from nothing enough sets for natural number
arithmetic.
Russell's set cannot be constructed.
My whole point is that a broken system was fixed by redefining it.
But you haven't shown the old system was broke.
It is the same stupid shit of pathological self-reference
that derived Russell's Paradox.
On 3/26/2025 10:29 PM, Richard Damon wrote:
On 3/26/25 10:46 PM, olcott wrote:
On 3/26/2025 9:32 PM, Richard Damon wrote:
On 3/26/25 9:27 PM, olcott wrote:
On 3/26/2025 6:01 PM, Richard Damon wrote:
On 3/26/25 1:50 PM, olcott wrote:
On 3/26/2025 6:12 AM, Richard Damon wrote:
On 3/25/25 10:15 PM, olcott wrote:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
SO that means that "Cats are Dogs" is part of Knowldedge?
Try re-reading what I said as many times as needed
until you notice ALL of the words.
I have, and you can't explain the difference.
So anything written down is true?
How do we know what we think to be True is actually True?
Stimulated relations between finite strings are necessarily
true. "cats" <are> "animals"
Only if "cats" and "animals" have the appropriate definitions. >>>>>>>>
Do think that anyone ever wrote these down?
Then they exist in the body of general knowledge expressed in language. >>>>>>
Thus climare change must not be real, since THAT "fact" has been
written down and accepted by a large number of peoplel
The trator down the street that is a "cat" isn't an animal, but >>>>>>>> sometimes the person that operates it can be a bit of one.
General knowledge.
But "cat" is a term for a type of tractor.
In FORMAL systems we can rigorously define what is true in that system,
as we start with a defined set of given facts (which is why you can't
change the definitions and stay in the system, as those definitions are
what made the system).
Almost the same idea as basic facts.
Yes, but more than basic facts. Note,
What formal system has an axiom that defines
ice cream as a diary product?
Many,
When you talk about "Human Knowledge" for the "Real World" you run into
the problem that we don't have a listing of the fundamental facts that
define the system, but are trying to discover our best explainations by
observation.
Basic facts that cannot be derived from anything else.
So what makes them true?
What makes a dairy cow not a kind of rattlesnake.
Stipulated relations between finite strings that
provides their semantic meaning.
No, stipulated relationships between concepts.
OK, I will give you that and qualify my original statement.
Stipulated relations between concepts that are labeled by
finite strings, thus ultimately stipulated relations between
finite strings, the ultimate formalism.
So, tho only thing you know to bo true are what you stipulated to be true. >>>>
Sorry, that isn't a logic system.
Actually it <is> a logic system because it only includes
relations between finite strings.
I said the body of
(a) General knowledge (thus finite)
(b) Knowledge (thus true)
(c) Expressed in language (corrects analytic/synthetic distinction)
So, what *ARE* your relationships. Logics systems are, by their
definition, a system for DEDUCING things from rules of INFERENCE.
As long as they are truth preserving any operation is permitted.
On 3/26/2025 3:07 AM, Mikko wrote:
On 2025-03-25 14:32:31 +0000, olcott said:
On 3/25/2025 5:03 AM, Mikko wrote:
On 2025-03-22 17:49:01 +0000, olcott said:
On 3/22/2025 11:38 AM, Mikko wrote:
On 2025-03-22 03:03:39 +0000, olcott said:
On 3/21/2025 9:31 PM, Richard Damon wrote:
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said:
On 3/20/2025 6:00 AM, Richard Damon wrote:
On 3/19/25 10:42 PM, olcott wrote:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>>>> of this set.
Which just means that you have stipulated yourself out of all classical
logic, since Truth is different than Knowledge. In a good logic system,
Knowledge will be a subset of Truth, but you have defined that in your
system, Truth is a subset of Knowledge, so you have it backwards.
True(X) always returns TRUE for every element in the set >>>>>>>>>>>>>>> of general knowledge that can be expressed using language. >>>>>>>>>>>>>>> It never gets confused by paradoxes.
Not useful unless it returns TRUE for no X that contradicts anything
that can be inferred from the set of general knowledge. >>>>>>>>>>>>>>
I can't parse that.
(a) Not useful unlessBecause my system begins with basic facts and actual facts >>>>>>>>>>>>> can't contradict each other and no contradiction can be >>>>>>>>>>>>> formed by applying only truth preserving operations to these >>>>>>>>>>>>> basic facts there are no contradictions in the system. >>>>>>>>>>>>>
(b) it returns TRUE for
(c) no X that contradicts anything
(d) that can be inferred from the set of general knowledge. >>>>>>>>>>>>> >
No, you system doesn't because you don't actually understand what you
are trying to define.
"Human Knowledge" is full of contradictions and incorrect statements.
Adittedly, most of them can be resolved by properly putting the >>>>>>>>>>>> statements into context, but the problem is that for some statement,
the context isn't precisely known or the statement is known to be an
approximation of unknown accuracy, so doesn't actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>> knowledge that can be expressed using language that undecidability >>>>>>>>>>> cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>
When the proof is only syntactic then it isn't directly
connected to any meaning.
But Formal Logic proofs ARE just "syntactic"
When the body of human general knowledge has all of its
semantics encoded syntactically AKA Montague Grammar of
Semantics then a proof means validation of truth.
Yes, proof is a validatation of truth, but truth does not need to be >>>>>>>> able to be validated.
True(X) ONLY validates that X is true and does nothing else.
We can believe the "nothing else" part. The rest would require a proof. >>>>>>
True(X) is a predicate implementing a membership algorithm
for the body of general knowledge that can be expressed
using language.
Infinite proofs cannot be provided. Find a counter-example
where an element of the set of general knowledge that can
be expressed using language(GKEUL) would fool a True(X)
predicate into providing the wrong answer.
"This sentence is not true" cannot be derived by applying
truth preserving operations to basic facts thus is rejected
as not a member of (GKEUL).
What does your True(X) say when X means that there is no method to
determine whether a sentence of the first order group theory can
be proven.
That is either in the body of knowledge or not.
It is.
Unless human understanding of this is not infallible.
On 3/26/2025 10:29 PM, Richard Damon wrote:
On 3/26/25 10:46 PM, olcott wrote:
On 3/26/2025 9:32 PM, Richard Damon wrote:
On 3/26/25 9:27 PM, olcott wrote:
On 3/26/2025 6:01 PM, Richard Damon wrote:
On 3/26/25 1:50 PM, olcott wrote:
On 3/26/2025 6:12 AM, Richard Damon wrote:
On 3/25/25 10:15 PM, olcott wrote:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using >>>>>>>>>>>>>> language
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>> to the
set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all >>>>>>>>>>>>>>>>>>> inference
is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>>>>>> sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of >>>>>>>>>>>>>>>> the conjecture
or its negation. Then the predicate True is no longer >>>>>>>>>>>>>>>> complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful >>>>>>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth >>>>>>>>>>>>>>> preserving
to the giant semantic tautology of the set of human >>>>>>>>>>>>>>> knowledge
that can be expressed using language then every element >>>>>>>>>>>>>>> in this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
SO that means that "Cats are Dogs" is part of Knowldedge?
Try re-reading what I said as many times as needed
until you notice ALL of the words.
I have, and you can't explain the difference.
How do we know what we think to be True is actually True?
Stimulated relations between finite strings are necessarily
true. "cats" <are> "animals"
Only if "cats" and "animals" have the appropriate definitions. >>>>>>>>
Do think that anyone ever wrote these down?
Then they exist in the body of general knowledge expressed in
language.
So anything written down is true?
Thus climare change must not be real, since THAT "fact" has been
written down and accepted by a large number of peoplel
The trator down the street that is a "cat" isn't an animal, but >>>>>>>> sometimes the person that operates it can be a bit of one.
General knowledge.
But "cat" is a term for a type of tractor.
In FORMAL systems we can rigorously define what is true in >>>>>>>>>> that system, as we start with a defined set of given facts >>>>>>>>>> (which is why you can't change the definitions and stay in the >>>>>>>>>> system, as those definitions are what made the system).
Almost the same idea as basic facts.
Yes, but more than basic facts. Note,
What formal system has an axiom that defines
ice cream as a diary product?
Many,
When you talk about "Human Knowledge" for the "Real World" you >>>>>>>>>> run into the problem that we don't have a listing of the
fundamental facts that define the system, but are trying to >>>>>>>>>> discover our best explainations by observation.
Basic facts that cannot be derived from anything else.
So what makes them true?
What makes a dairy cow not a kind of rattlesnake.
Stipulated relations between finite strings that
provides their semantic meaning.
No, stipulated relationships between concepts.
OK, I will give you that and qualify my original statement.
Stipulated relations between concepts that are labeled by
finite strings, thus ultimately stipulated relations between
finite strings, the ultimate formalism.
So, tho only thing you know to bo true are what you stipulated to be
true.
Sorry, that isn't a logic system.
Actually it <is> a logic system because it only includes
relations between finite strings.
I said the body of
(a) General knowledge (thus finite)
(b) Knowledge (thus true)
(c) Expressed in language (corrects analytic/synthetic distinction)
So, what *ARE* your relationships. Logics systems are, by their
definition, a system for DEDUCING things from rules of INFERENCE.
As long as they are truth preserving any operation is permitted.
The most important one is semantically entailed.
I haven't heard you talk about any way to make an inference,
Truth preserving operations.
and once you do you create a TRUTH that isn't "True"
You have left the subject being discussed.
by your predicate, as it isn't in the original knowledge set.
Also, how do you determine (b), isn't you claim that you have removed
all that is thought to be knowledge but isn't actually.
On 3/26/2025 10:29 PM, Richard Damon wrote:
On 3/26/25 10:58 PM, olcott wrote:
On 3/26/2025 8:22 PM, Richard Damon wrote:
On 3/26/25 2:01 PM, olcott wrote:
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>> sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful >>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very
small
part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
So, How do we know what is in that?
It is the defined set such that every expression of
language has the semantic property of true.
So How?
How many times do I have to repeat myself.
Basic Facts stipulated to be true.
Truth preserving operations applied to these basic facts.
Boom, Done!!! Now the 100% complete essence of my
system is fully specified.
How do you intend to construct this system?
This is 100% totally irrelevant until after the very
simple idea that a True(X) predicate would necessarily
exist for this set is totally accepted.
Nope, you are just falling into the trap of Naive Set Theory of not
being able to define what you are talking about.
By stipulating a set of basic facts
and every expression that can be derived
by applying truth preserving operations
to these basic facts we now fully have
the set of knowledge that can be expressed
in language.
In such a system no counter example such
that True(X) is incorrect can be provided.
Membership in the original set of axioms for the system is NOT a Truth
Predicate for any logic system which has the power to make inferences.
Inferences that are not truth preserving are disallowed.
Full semantics is always integrated into the language.
You are just proving your stupidity and ignorance.
Things that someone says when they don't understand
the meaning of all of the big words that are used.
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>> is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture >>>>>>>> or its negation. Then the predicate True is no longer complete. >>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very small
part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture >>>>>>>>>> or its negation. Then the predicate True is no longer complete. >>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>> that can be expressed using language then every element in this >>>>>>>>> set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language >>>>>>>> is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere.
Only general knowledge
Ae also know that many expressions of language that are written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
On 3/26/2025 2:58 AM, Mikko wrote:
On 2025-03-25 14:28:49 +0000, olcott said:
On 3/25/2025 4:50 AM, Mikko wrote:
On 2025-03-23 04:24:51 +0000, olcott said:
On 3/22/2025 9:53 PM, Richard Damon wrote:
On 3/22/25 2:33 PM, olcott wrote:
On 3/22/2025 12:34 PM, Richard Damon wrote:
On 3/22/25 11:13 AM, olcott wrote:
On 3/22/2025 5:11 AM, joes wrote:
Am Fri, 21 Mar 2025 22:03:39 -0500 schrieb olcott:
On 3/21/2025 9:31 PM, Richard Damon wrote:The liar sentence is contradictory.
On 3/21/25 9:24 PM, olcott wrote:
On 3/21/2025 7:50 PM, Richard Damon wrote:
On 3/21/25 8:40 PM, olcott wrote:
On 3/21/2025 6:49 PM, Richard Damon wrote:
On 3/21/25 8:43 AM, olcott wrote:
On 3/21/2025 3:41 AM, Mikko wrote:
On 2025-03-20 14:57:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>> On 3/20/2025 6:00 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/19/25 10:42 PM, olcott wrote:
I can't parse that.True(X) always returns TRUE for every element in the set of >>>>>>>>>>>>>>>>>>> general knowledge that can be expressed using language. >>>>>>>>>>>>>>>>>>> It never gets confused by paradoxes.It is stipulated that analytic knowledge is limited to the set
of knowledge that can be expressed using language or derived
by applying truth preserving operations to elements of this
set.
Which just means that you have stipulated yourself out of all
classical logic, since Truth is different than Knowledge. In a
good logic system, Knowledge will be a subset of Truth, but you
have defined that in your system, Truth is a subset of >>>>>>>>>>>>>>>>>>>> Knowledge, so you have it backwards.
Not useful unless it returns TRUE for no X that contradicts >>>>>>>>>>>>>>>>>> anything that can be inferred from the set of general knowledge.
> (a) Not useful unless (b) it returns TRUE for (c) no X that
> contradicts anything (d) that can be inferred from the set of
> general knowledge.
>
Because my system begins with basic facts and actual facts can't
contradict each other and no contradiction can be formed by >>>>>>>>>>>>>>>>> applying only truth preserving operations to these basic facts
there are no contradictions in the system.
Not self-evident was Gödel's disproof of that.No, you system doesn't because you don't actually understand what
you are trying to define.
"Human Knowledge" is full of contradictions and incorrect >>>>>>>>>>>>>>>> statements.
Adittedly, most of them can be resolved by properly putting the
statements into context, but the problem is that for some >>>>>>>>>>>>>>>> statement, the context isn't precisely known or the statement is
known to be an approximation of unknown accuracy, so doesn't >>>>>>>>>>>>>>>> actually specify a "fact".
It is self evidence that for every element of the set of human >>>>>>>>>>>>>>> knowledge that can be expressed using language that undecidability
cannot possibly exist.
SO, you admit you don't know what it means to prove something. >>>>>>>>>>>>>>When the proof is only syntactic then it isn't directly connected to
any meaning.
But Formal Logic proofs ARE just "syntactic"
True(X) ONLY validates that X is true and does nothing else. >>>>>>>>>> Not if X is unknown (but still true).When the body of human general knowledge has all of its semantics >>>>>>>>>>>>> encoded syntactically AKA Montague Grammar of Semantics then a proofYes, proof is a validatation of truth, but truth does not need to be
means validation of truth.
able to be validated.
You must pay complete attention to ALL of my words
or you get the meaning that I specify incorrectly.
The problem is that statement, you don't get to change the meaning of >>>>>>>> the core terms and stay in the system, so you are just admitting that >>>>>>>> all your work is based on strawmen, and thus frauds.
<sarcasm>
In the exact same way that ZFC totally screwed up
and never resolved Russell's Paradox because they
were forbidden to limit how sets are defined.
When the definition of a set allowed pathological
self-reference they should have construed this
as infallible and immutable.
</sarcasm>
IN other words, you admit that you can't refute what I said, so you >>>>>> just go off beat.
By the freaking concrete example that I provided
YES YOU DO GET TO CHANGE THE MEANING OF THE TERMS.
No, you can't. The nearest you can is to create a new term that
is homonymous to an old one. But you can't use two homonymous
terms in the same opus.
Original set theory became "naive set theory".
ZFC set theory corrected its shortcomings.
The original one is Cantor's. But that his presentation was too informal
to determine whether Russell's set is expressible. But he did show that
one can construct from nothing enough sets for natural number arithmetic.
Russell's set cannot be constructed.
My whole point is that a broken system was fixed by redefining it.
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the
conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful
sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>> that can be expressed using language then every element in this >>>>>>>>> set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language >>>>>>>> is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very small >>>> part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
In that case your True(X) is uncomputable and any theory that contains
it is incomplete.
The body of general knowledge that can be expressed
using language is defined to be complete. The moment
that new knowledge that can be expressed in language
comes into existence it is added to the set.
True(X) merely tests for membership in this set;
(a) Is X a Basic Fact? Then X is true.
(b) Can X be derived by applying truth preserving operations
to Basic Facts? Then X is true.
(c) Otherwise X is not true, this does not always mean X is false.
Gibberish is not true. Self-contradictory expressions are not true.
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>> sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful >>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the
semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
The set of everything that anyone ever wrote
down would be finite. Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
We also know that a True(X) predicate can be directly
defined for this set.
On 3/27/2025 6:08 PM, Richard Damon wrote:
On 3/27/25 9:03 AM, olcott wrote:
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>> sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful >>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very
small
part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
In that case your True(X) is uncomputable and any theory that contains >>>> it is incomplete.
The body of general knowledge that can be expressed
using language is defined to be complete. The moment
that new knowledge that can be expressed in language
comes into existence it is added to the set.
No its not. We KNOW there are things we don't know yet, but hope to.
As soon as the first person knows new general knowledge
and this knowledge can be written down (unlike the
actual direct physical sensation of smelling a rose)
then this becomes an element of this set of knowledge.
And, the base of a logic system is STATIC and fixed.
The set of general knowledge that can be expressed
in language has more flexibility than that.
You just don't understand the meaning of the words you are using.
True(X) merely tests for membership in this set;
(a) Is X a Basic Fact? Then X is true.
Which makes it not a TRUTH test, but a KNOWLEDGE test, and thus not
names right.
The set of all general knowledge that can be expressed in language
is a subset of all truth and only excludes unknown and unknowable.
(b) Can X be derived by applying truth preserving operations
to Basic Facts? Then X is true.
But that isn't the membershop test you just mentioned, and it is that
op[eration which Tarski specifically showed can not be done.
The problem is TRUTH can be establish via an infinite set of truth
perserving operations, but knowledge can not.
None of this makes any actual difference in the world.
We won't be able to prevent nuclear Winter and the
extinction of humanity on the basis of knowing whether
or not the Goldbach conjecture is true.
Ths FACT is part of that "Knowledge" that you accepted at the
begining, so you can't get rid of it.
(c) Otherwise X is not true, this does not always mean X is false.
Gibberish is not true. Self-contradictory expressions are not true.
But we can't determine if that x was true. You definition was that it
was in the set of lnowledge that we built the set on.
Sorry, but you are just showing that you don't understand what you own
words mean.
On 3/27/2025 6:08 PM, Richard Damon wrote:Exactly, it doesn't include the unknown truths and ought to be called
On 3/27/25 9:03 AM, olcott wrote:
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
As soon as the first person knows new general knowledge and thisNo its not. We KNOW there are things we don't know yet, but hope to.The body of general knowledge that can be expressed using language isI am NOT referring to what is merely presented as the body of
general knowledge, I am referring to the actual body of general
knowledge. Within this hypothesis it is easy to see that True(X)
would be infallible.
In that case your True(X) is uncomputable and any theory that
contains it is incomplete.
defined to be complete. The moment that new knowledge that can be
expressed in language comes into existence it is added to the set.
knowledge can be written down (unlike the actual direct physical
sensation of smelling a rose)
then this becomes an element of this set of knowledge.
And, the base of a logic system is STATIC and fixed.The set of general knowledge that can be expressed in language has more flexibility than that.
You just don't understand the meaning of the words you are using.The set of all general knowledge that can be expressed in language is a subset of all truth and only excludes unknown and unknowable.
True(X) merely tests for membership in this set;Which makes it not a TRUTH test, but a KNOWLEDGE test, and thus not
(a) Is X a Basic Fact? Then X is true.
names right.
--None of this makes any actual difference in the world.(b) Can X be derived by applying truth preserving operationsBut that isn't the membershop test you just mentioned, and it is that
to Basic Facts? Then X is true.
op[eration which Tarski specifically showed can not be done.
The problem is TRUTH can be establish via an infinite set of truth
perserving operations, but knowledge can not.
We won't be able to prevent nuclear Winter and the extinction of
humanity on the basis of knowing whether or not the Goldbach conjecture
is true.
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic >>>> proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
The set of everything that anyone ever wrote
down would be finite.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
We also know that a True(X) predicate can be directly
defined for this set.
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly >>>>>>>>>>>>> be thwarted.
There is no computable predicate that tells whether a sentence >>>>>>>>>>>> of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture >>>>>>>>>> or its negation. Then the predicate True is no longer complete. >>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>> that can be expressed using language then every element in this >>>>>>>>> set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language >>>>>>>> is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very small >>>> part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
In that case your True(X) is uncomputable and any theory that contains
it is incomplete.
The body of general knowledge that can be expressed
using language is defined to be complete.
On 3/27/2025 8:54 PM, Richard Damon wrote:
On 3/27/25 9:04 PM, olcott wrote:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>> derived by applying truth preserving operations to >>>>>>>>>>>>>>>>> elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>>>> sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer >>>>>>>>>>>>>> complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>> with set of basic facts and are only allowed toHowever, it is possible (and, for sufficiently powerful >>>>>>>>>>>>>> sysems, certain)
apply truth preserving operations to these basic >>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>>>> that can be expressed using language then every element in >>>>>>>>>>>>> this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the
semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
In other words, you don't understand the question.
The set of everything that anyone ever wrote
down would be finite. Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
So, what is the DEFINITION of "General Knowledge"?
Knowledge that lacks specific details of specific situations.
A set of knowledge that can be algorithmically compressed
as a finite set of finite strings.
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
On 3/27/2025 6:08 PM, Richard Damon wrote:
On 3/27/25 9:03 AM, olcott wrote:
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
As soon as the first person knows new general knowledge and thisNo its not. We KNOW there are things we don't know yet, but hope to.The body of general knowledge that can be expressed using language is >>>>> defined to be complete. The moment that new knowledge that can beI am NOT referring to what is merely presented as the body of
general knowledge, I am referring to the actual body of general
knowledge. Within this hypothesis it is easy to see that True(X) >>>>>>> would be infallible.
In that case your True(X) is uncomputable and any theory that
contains it is incomplete.
expressed in language comes into existence it is added to the set.
knowledge can be written down (unlike the actual direct physical
sensation of smelling a rose)
then this becomes an element of this set of knowledge.
And, the base of a logic system is STATIC and fixed.The set of general knowledge that can be expressed in language has more
flexibility than that.
You just don't understand the meaning of the words you are using.The set of all general knowledge that can be expressed in language is a
True(X) merely tests for membership in this set;Which makes it not a TRUTH test, but a KNOWLEDGE test, and thus not
(a) Is X a Basic Fact? Then X is true.
names right.
subset of all truth and only excludes unknown and unknowable.
Exactly, it doesn't include the unknown truths and ought to be called
Known(X). It is also contradictory since it gives NO both for unknowns
and their negation.
*The key defining aspect of knowledge is that it is true*
When LLM systems have all of the basic facts encoded and
are only allowed to perform truth preserving operations
on these basic facts:
(a) They won't be able to hallucinate
(b) They will have the basis to shut down the lies
of liars before these lies have any effect.
None of this makes any actual difference in the world.(b) Can X be derived by applying truth preserving operationsBut that isn't the membershop test you just mentioned, and it is that
to Basic Facts? Then X is true.
op[eration which Tarski specifically showed can not be done.
The problem is TRUTH can be establish via an infinite set of truth
perserving operations, but knowledge can not.
We won't be able to prevent nuclear Winter and the extinction of
humanity on the basis of knowing whether or not the Goldbach conjecture
is true.
On 3/28/2025 7:16 AM, Mikko wrote:
On 2025-03-27 13:03:21 +0000, olcott said:
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
On 2025-03-25 14:56:33 +0000, olcott said:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>> sentence
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer complete. >>>>>>>>>>>>
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful >>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
What is presented as the body of human knowledge either is a very
small
part of actual knowledge or contains false claims.
I am NOT referring to what is merely presented as the body
of general knowledge, I am referring to the actual body of
general knowledge. Within this hypothesis it is easy to see
that True(X) would be infallible.
In that case your True(X) is uncomputable and any theory that contains >>>> it is incomplete.
The body of general knowledge that can be expressed
using language is defined to be complete.
That doesn't prevent us from presenting general knowledge that is not
in that "complete" body.
The problem of incompleteness is not inherent.
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said:
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>> derived by applying truth preserving operations to >>>>>>>>>>>>>>>>> elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>>>> sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the >>>>>>>>>>>>>> conjecture
or its negation. Then the predicate True is no longer >>>>>>>>>>>>>> complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>> with set of basic facts and are only allowed toHowever, it is possible (and, for sufficiently powerful >>>>>>>>>>>>>> sysems, certain)
apply truth preserving operations to these basic >>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>>>> that can be expressed using language then every element in >>>>>>>>>>>>> this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the
semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be.
If sentences, and there are not too many of them, a set of knowledge
could be presented as a book that contains those sentences and nothing
else.
A list of sentences would not make for efficient processing.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down >>>>>> somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic >>>> property of true that are written down somewhere" is not useful because >>>> there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
We also know that a True(X) predicate can be directly
defined for this set.
But it is not useful if the value of True(X) cannot be evaluated.
Just like with structured programming of many years ago
we begin analyzing problems at the highest degree of abstraction
and then after fully examined at this level progressively
refine this in increasingly greater detail.
If we jump into the details prior to a 100% complete
understanding of the gist of the idea the idea dies
in endless talking in circles.
On 3/28/2025 8:46 AM, Richard Damon wrote:
On 3/27/25 10:18 PM, olcott wrote:
On 3/27/2025 8:54 PM, Richard Damon wrote:
On 3/27/25 9:04 PM, olcott wrote:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using >>>>>>>>>>>>>> language
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>> to the
set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all >>>>>>>>>>>>>>>>>>> inference
is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot >>>>>>>>>>>>>>>>>>> possibly
be thwarted.
There is no computable predicate that tells whether a >>>>>>>>>>>>>>>>>> sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of >>>>>>>>>>>>>>>> the conjecture
or its negation. Then the predicate True is no longer >>>>>>>>>>>>>>>> complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful >>>>>>>>>>>>>>>> sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth >>>>>>>>>>>>>>> preserving
to the giant semantic tautology of the set of human >>>>>>>>>>>>>>> knowledge
that can be expressed using language then every element >>>>>>>>>>>>>>> in this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the >>>>>>>> semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition >>>>>> it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
In other words, you don't understand the question.
The set of everything that anyone ever wrote
down would be finite. Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
So, what is the DEFINITION of "General Knowledge"?
Knowledge that lacks specific details of specific situations.
A set of knowledge that can be algorithmically compressed
as a finite set of finite strings.
Ok, so therefore it includes all the "laws of mathematics" and the
"rules of inference" and thus, the system is capable of creating the
rules and properties of the Natural Numbers, so it supports the proofs
of Godel and Tarski, and thus there are statements in that sytstem
that are True but unprovable and no definition of the Truth Predicate
can handle those,
Sorry, you are just showing you don't understand what you are talking
about.
Yes it will showed the formal system can be defined
that have all kinds of issues because they were defined
incoherently.
On 3/29/2025 3:19 PM, joes wrote:
Am Sat, 29 Mar 2025 09:14:36 -0500 schrieb olcott:
On 3/29/2025 5:52 AM, Richard Damon wrote:No, it is either true or not.
On 3/28/25 11:19 PM, olcott wrote:
On 3/28/2025 4:18 PM, Richard Damon wrote:
On 3/28/25 4:07 PM, olcott wrote:
On 3/28/2025 8:46 AM, Richard Damon wrote:
On 3/27/25 10:18 PM, olcott wrote:
On 3/27/2025 8:54 PM, Richard Damon wrote:
On 3/27/25 9:04 PM, olcott wrote:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>> On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>> On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>> On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said:
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.When we begin with a set of basic facts and all >>>>>>>>>>>>>>>>>>>>>>>>> inference is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations to elements of this set then a True(X) >>>>>>>>>>>>>>>>>>>>>>>>> predicate cannot possibly be thwarted. >>>>>>>>>>>>>>>>>>>>>>>> There is no computable predicate that tells whether >>>>>>>>>>>>>>>>>>>>>>>> a sentence of the first order group theory can be >>>>>>>>>>>>>>>>>>>>>>>> proven.
Where is there an incoherent definition?However, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>>>>>> powerful sysems, certain)
that the provability is not computable.
Ok, so therefore it includes all the "laws of mathematics" and the >>>>>>>> "rules of inference" and thus, the system is capable of creating >>>>>>>> the rules and properties of the Natural Numbers, so it supports the >>>>>>>> proofs of Godel and Tarski, and thus there are statements in that >>>>>>>> sytstem that are True but unprovable and no definition of the Truth >>>>>>>> Predicate can handle those,Yes it will showed the formal system can be defined that have all >>>>>>> kinds of issues because they were defined incoherently.
When full semantics is directly integrated into the formal system, theWhen any formal logic system begins with stipulated set of basic facts >>>>> and is only allowed to apply truth preserving operations to these
facts and expressions derived from these facts then undecidability
cannot possibly occur.
Sure it can, as Godel and Turing Proved.
system begins with an list of basic facts, the only inference step is
semantic logical entailment applying truth preserving operations
Tarski's proof fails.
Where, at which step, how, why?
True(X) and ~Provable(X) cannot possibly exist
in my system because Provable(X) means truth
preserving operations are applied to basic facts
thus deriving True(X).
We are no longer seeking mere provability we are seeking provably true
at the semantic level. At the semantic level incoherent nonsense such as >>> "This sentence is not true" is screened out.
How?
As I said above and repeated dozens of times.
On 3/29/2025 1:18 PM, Richard Damon wrote:
On 3/29/25 9:53 AM, olcott wrote:
On 3/29/2025 4:51 AM, joes wrote:
Am Fri, 28 Mar 2025 15:07:22 -0500 schrieb olcott:
On 3/28/2025 8:46 AM, Richard Damon wrote:
Ok, so therefore it includes all the "laws of mathematics" and the >>>>>> "rules of inference" and thus, the system is capable of creating the >>>>>> rules and properties of the Natural Numbers, so it supports the
proofs
of Godel and Tarski, and thus there are statements in that sytstem >>>>>> that
are True but unprovable and no definition of the Truth Predicate can >>>>>> handle those,
Yes it will showed the formal system can be defined that have all
kinds
of issues because they were defined incoherently.
How is arithmetic (which is all it takes for Gödel's proof) incoherent? >>>>
To the best of my knowledge arithmetic itself cannot
be incomplete unless it can be shown that the sum of
two finite strings of digits cannot be derived.
Depends on what you consider "Arithmetic". If you just mean "sums" and
the like, then maybe it can't be incomplete, because it can't ask
questions that ask for proofs.
It never could.
Once you include first order logic with things like There exist a
number such that ..., then you can perform Godel's proof and find that
there is at least one statement that is true but can not be proven in
the system.
On 3/29/2025 1:18 PM, Richard Damon wrote:
On 3/29/25 9:53 AM, olcott wrote:
On 3/29/2025 4:51 AM, joes wrote:
Am Fri, 28 Mar 2025 15:07:22 -0500 schrieb olcott:
On 3/28/2025 8:46 AM, Richard Damon wrote:
Ok, so therefore it includes all the "laws of mathematics" and the >>>>>> "rules of inference" and thus, the system is capable of creating the >>>>>> rules and properties of the Natural Numbers, so it supports the
proofs
of Godel and Tarski, and thus there are statements in that sytstem >>>>>> that
are True but unprovable and no definition of the Truth Predicate can >>>>>> handle those,
Yes it will showed the formal system can be defined that have all
kinds
of issues because they were defined incoherently.
How is arithmetic (which is all it takes for Gödel's proof) incoherent? >>>>
To the best of my knowledge arithmetic itself cannot
be incomplete unless it can be shown that the sum of
two finite strings of digits cannot be derived.
Depends on what you consider "Arithmetic". If you just mean "sums" and
the like, then maybe it can't be incomplete, because it can't ask
questions that ask for proofs.
Once you include first order logic with things like There exist a
number such that ..., then you can perform Godel's proof and find that
there is at least one statement that is true but can not be proven in
the system.
When semantics is fully integrated into syntax and all
proofs apply truth preserving operations to basic facts
then ~Provable(X) and True(X) cannot possibly co-exist.
Within this system of general knowledge that can be
expressed in language Tarski is refuted and undecidability
is impossible.
On 3/29/2025 3:21 PM, joes wrote:
Am Sat, 29 Mar 2025 08:53:04 -0500 schrieb olcott:
On 3/29/2025 4:51 AM, joes wrote:And you think arithmetic should be incomplete or what?
Am Fri, 28 Mar 2025 15:07:22 -0500 schrieb olcott:unless it can be shown that the sum of two finite strings of digits
On 3/28/2025 8:46 AM, Richard Damon wrote:
Ok, so therefore it includes all the "laws of mathematics" and the >>>>>> "rules of inference" and thus, the system is capable of creating the >>>>>> rules and properties of the Natural Numbers, so it supports the
proofs of Godel and Tarski, and thus there are statements in that
sytstem that are True but unprovable and no definition of the Truth >>>>>> Predicate can handle those,
Yes it will showed the formal system can be defined that have all
kinds of issues because they were defined incoherently.
How is arithmetic (which is all it takes for Gödel's proof) incoherent? >>> To the best of my knowledge arithmetic itself cannot be incomplete
cannot be derived.
When Provable(X) means applying truth preserving operations
to basic facts thus deriving True(X) then True(X) and ~Provable(X)
cannot possibly exist.
On 3/29/2025 1:28 PM, Richard Damon wrote:
On 3/29/25 10:28 AM, olcott wrote:
On 3/28/2025 4:50 PM, Richard Damon wrote:
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
On 3/27/2025 6:08 PM, Richard Damon wrote:
On 3/27/25 9:03 AM, olcott wrote:
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
As soon as the first person knows new general knowledge and this >>>>>>> knowledge can be written down (unlike the actual direct physical >>>>>>> sensation of smelling a rose)No its not. We KNOW there are things we don't know yet, but hope >>>>>>>> to.The body of general knowledge that can be expressed usingI am NOT referring to what is merely presented as the body of >>>>>>>>>>> general knowledge, I am referring to the actual body of general >>>>>>>>>>> knowledge. Within this hypothesis it is easy to see that True(X) >>>>>>>>>>> would be infallible.
In that case your True(X) is uncomputable and any theory that >>>>>>>>>> contains it is incomplete.
language is
defined to be complete. The moment that new knowledge that can be >>>>>>>>> expressed in language comes into existence it is added to the set. >>>>>>>>>
then this becomes an element of this set of knowledge.
And, the base of a logic system is STATIC and fixed.The set of general knowledge that can be expressed in language
has more
flexibility than that.
You just don't understand the meaning of the words you are using. >>>>>>>>The set of all general knowledge that can be expressed in
True(X) merely tests for membership in this set;Which makes it not a TRUTH test, but a KNOWLEDGE test, and thus not >>>>>>>> names right.
(a) Is X a Basic Fact? Then X is true.
language is a
subset of all truth and only excludes unknown and unknowable.
Exactly, it doesn't include the unknown truths and ought to be called >>>>>> Known(X). It is also contradictory since it gives NO both for
unknowns
and their negation.
*The key defining aspect of knowledge is that it is true*
Which has been the eternal debate, how can we tell if some "fact" we
have discovered is true.
In FORMAL LOGIC (which you just dismissed) truth has a solid
definition, and we can formally PROVE some statements to be true and
formally PROVE that some statements are just false, and thus such
statements CAN become truely established knowledge. There may also
be some statements we have not established yet (and maybe can never
establish in the system) which will remain as "unknown". That
doesn't mean the statements might not be true or false, just that we
don't know the answer yet.
This can be incoherent unless complete semantics is fully
integrated into the formal system. There is no way that
applying ONLY truth preserving operations to basic facts
can possibly result in undecidability.
The problem is that your version of "semantics" is just incompatible
with "Formal Logic".
Not at all. A knowledge ontology inheritance hierarchy has
an unlimited number of Tarski Meta-language levels as types
in a type hierarchy in a single formal system.
On 3/29/2025 3:50 PM, Richard Damon wrote:
On 3/29/25 4:40 PM, olcott wrote:
On 3/29/2025 3:14 PM, joes wrote:
Am Sat, 29 Mar 2025 09:28:29 -0500 schrieb olcott:
On 3/28/2025 4:50 PM, Richard Damon wrote:One of a sentence and its negation must be true.
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
*The key defining aspect of knowledge is that it is true*The set of all general knowledge that can be expressed in language >>>>>>>>> is a subset of all truth and only excludes unknown and unknowable. >>>>>>>Exactly, it doesn't include the unknown truths and ought to be >>>>>>>> called
Known(X). It is also contradictory since it gives NO both for
unknowns and their negation.
Which has been the eternal debate, how can we tell if some "fact" we >>>>>> have discovered is true.This can be incoherent unless complete semantics is fully integrated >>>>> into the formal system. There is no way that applying ONLY truth
In FORMAL LOGIC (which you just dismissed) truth has a solid
definition, and we can formally PROVE some statements to be true and >>>>>> formally PROVE that some statements are just false, and thus such
statements CAN become truely established knowledge. There may also be >>>>>> some statements we have not established yet (and maybe can never
establish in the system) which will remain as "unknown". That doesn't >>>>>> mean the statements might not be true or false, just that we don't >>>>>> know
the answer yet.
preserving operations to basic facts can possibly result in
undecidability.
Only a valid concrete counter-example counts as a rebuttal, everything >>>>> else counts as some sort of deception.
See Gödel 19whenever.
Does not meet my spec. All math proofs make sure to
always ignore semantics. Not all inference steps
are truth preserving operations.
X <is a necessary consequence> of Y.
No, you just don't understand what that means, but are too stupid to
understand that,
It is not that I am stupid. It has always been
that you are dishonest. If you were not dishonest
you could and would point out specific mistakes.
Since I made no mistakes all that you have left
is calling me stupid.
[LLM bullshit]
On 3/29/2025 5:18 PM, Richard Damon wrote:
On 3/29/25 5:49 PM, olcott wrote:
On 3/29/2025 3:50 PM, Richard Damon wrote:
On 3/29/25 4:40 PM, olcott wrote:
On 3/29/2025 3:14 PM, joes wrote:
Am Sat, 29 Mar 2025 09:28:29 -0500 schrieb olcott:
On 3/28/2025 4:50 PM, Richard Damon wrote:One of a sentence and its negation must be true.
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
*The key defining aspect of knowledge is that it is true*The set of all general knowledge that can be expressed in >>>>>>>>>>> language
is a subset of all truth and only excludes unknown and
unknowable.
Exactly, it doesn't include the unknown truths and ought to be >>>>>>>>>> called
Known(X). It is also contradictory since it gives NO both for >>>>>>>>>> unknowns and their negation.
Which has been the eternal debate, how can we tell if someThis can be incoherent unless complete semantics is fully integrated >>>>>>> into the formal system. There is no way that applying ONLY truth >>>>>>> preserving operations to basic facts can possibly result in
"fact" we
have discovered is true.
In FORMAL LOGIC (which you just dismissed) truth has a solid
definition, and we can formally PROVE some statements to be true >>>>>>>> and
formally PROVE that some statements are just false, and thus such >>>>>>>> statements CAN become truely established knowledge. There may
also be
some statements we have not established yet (and maybe can never >>>>>>>> establish in the system) which will remain as "unknown". That
doesn't
mean the statements might not be true or false, just that we
don't know
the answer yet.
undecidability.
Only a valid concrete counter-example counts as a rebuttal,
everything
else counts as some sort of deception.
See Gödel 19whenever.
Does not meet my spec. All math proofs make sure to
always ignore semantics. Not all inference steps
are truth preserving operations.
X <is a necessary consequence> of Y.
No, you just don't understand what that means, but are too stupid to
understand that,
It is not that I am stupid. It has always been
that you are dishonest. If you were not dishonest
you could and would point out specific mistakes.
Since I made no mistakes all that you have left
is calling me stupid.
I HAVE been pointing out specific mistakes.
Point out one mistake that you have pointed out here by
quoting the time/date stamp with your prior reply.
Note, the langauge can't have the metalanguages derived from it within it. Your claims just shows you don't understand what you are talking about because you are just too ignorant to even try to learn the meanings.
Part of the problem is you never actually DEFINE what you are doing
but use vague terms.
It would take millions of years of talking in endless circles
(your whole point) of defining the notion of general knowledge
that can be expressed in language, completely.
It doesn't take a genius to understand that knowledge must be true.
A simple list search determines if an expression in the list
of basic facts. https://en.wikipedia.org/wiki/Backward_chaining
inference determines if basic facts can be reached by semantic
logical entailment from X.
Your reply just shows that you ARE that stupid, as you seem to not
understand the basic problem you need to define.
How can True(X) be defined such that it only returns TRUE
when X is a basic fact or X can reach basic facts by backward
chained inference?
How many sides does a four-sided square have?
Heh Richard: What is your first name?
If cats are animals are cats animals?
Sorry, but until you stop making baseless claim that are just
logically imposssible (like a system can include all the knowledge of
the infinte nymber of meta-systems that can be derived from it, while
still being finite) you are just showing that you are too stupid to
understand what you are doing.
[LLM bullshit]
On 3/29/2025 3:14 PM, joes wrote:
Am Sat, 29 Mar 2025 09:28:29 -0500 schrieb olcott:
On 3/28/2025 4:50 PM, Richard Damon wrote:One of a sentence and its negation must be true.
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
Exactly, it doesn't include the unknown truths and ought to be*The key defining aspect of knowledge is that it is true*
called Known(X). It is also contradictory since it gives NO both
for unknowns and their negation.
Which part of the spec? What semantics does Gödel ignore? WhichDoes not meet my spec. All math proofs make sure to always ignoreThis can be incoherent unless complete semantics is fully integratedSee Gödel 19whenever.
into the formal system. There is no way that applying ONLY truth
preserving operations to basic facts can possibly result in
undecidability.
Only a valid concrete counter-example counts as a rebuttal, everything
else counts as some sort of deception.
semantics. Not all inference steps are truth preserving operations.
On 3/28/2025 4:50 PM, Richard Damon wrote:
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
On 3/27/2025 6:08 PM, Richard Damon wrote:
On 3/27/25 9:03 AM, olcott wrote:
On 3/27/2025 5:58 AM, Mikko wrote:
On 2025-03-26 18:01:14 +0000, olcott said:
On 3/26/2025 3:36 AM, Mikko wrote:
As soon as the first person knows new general knowledge and thisNo its not. We KNOW there are things we don't know yet, but hope to. >>>>>>The body of general knowledge that can be expressed using language is >>>>>>> defined to be complete. The moment that new knowledge that can be >>>>>>> expressed in language comes into existence it is added to the set. >>>>>>>I am NOT referring to what is merely presented as the body of >>>>>>>>> general knowledge, I am referring to the actual body of general >>>>>>>>> knowledge. Within this hypothesis it is easy to see that True(X) >>>>>>>>> would be infallible.
In that case your True(X) is uncomputable and any theory that
contains it is incomplete.
knowledge can be written down (unlike the actual direct physical
sensation of smelling a rose)
then this becomes an element of this set of knowledge.
And, the base of a logic system is STATIC and fixed.The set of general knowledge that can be expressed in language has more >>>>> flexibility than that.
You just don't understand the meaning of the words you are using.The set of all general knowledge that can be expressed in language is a >>>>> subset of all truth and only excludes unknown and unknowable.
True(X) merely tests for membership in this set;Which makes it not a TRUTH test, but a KNOWLEDGE test, and thus not >>>>>> names right.
(a) Is X a Basic Fact? Then X is true.
Exactly, it doesn't include the unknown truths and ought to be called
Known(X). It is also contradictory since it gives NO both for unknowns >>>> and their negation.
*The key defining aspect of knowledge is that it is true*
Which has been the eternal debate, how can we tell if some "fact" we
have discovered is true.
In FORMAL LOGIC (which you just dismissed) truth has a solid
definition, and we can formally PROVE some statements to be true and
formally PROVE that some statements are just false, and thus such
statements CAN become truely established knowledge. There may also be
some statements we have not established yet (and maybe can never
establish in the system) which will remain as "unknown". That doesn't
mean the statements might not be true or false, just that we don't know
the answer yet.
This can be incoherent unless complete semantics is fully
integrated into the formal system.
On 3/29/2025 10:23 PM, olcott wrote:
On 3/29/2025 8:10 PM, Richard Damon wrote:
On 3/29/25 7:24 PM, olcott wrote:
On 3/29/2025 5:18 PM, Richard Damon wrote:
On 3/29/25 5:49 PM, olcott wrote:
On 3/29/2025 3:50 PM, Richard Damon wrote:
On 3/29/25 4:40 PM, olcott wrote:
On 3/29/2025 3:14 PM, joes wrote:
Am Sat, 29 Mar 2025 09:28:29 -0500 schrieb olcott:
On 3/28/2025 4:50 PM, Richard Damon wrote:
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
*The key defining aspect of knowledge is that it is true* >>>>>>>>> One of a sentence and its negation must be true.The set of all general knowledge that can be expressed in >>>>>>>>>>>>>> language
is a subset of all truth and only excludes unknown and >>>>>>>>>>>>>> unknowable.
Exactly, it doesn't include the unknown truths and ought to >>>>>>>>>>>>> be called
Known(X). It is also contradictory since it gives NO both for >>>>>>>>>>>>> unknowns and their negation.
Which has been the eternal debate, how can we tell if some >>>>>>>>>>> "fact" weThis can be incoherent unless complete semantics is fully
have discovered is true.
In FORMAL LOGIC (which you just dismissed) truth has a solid >>>>>>>>>>> definition, and we can formally PROVE some statements to be >>>>>>>>>>> true and
formally PROVE that some statements are just false, and thus >>>>>>>>>>> such
statements CAN become truely established knowledge. There may >>>>>>>>>>> also be
some statements we have not established yet (and maybe can never >>>>>>>>>>> establish in the system) which will remain as "unknown". That >>>>>>>>>>> doesn't
mean the statements might not be true or false, just that we >>>>>>>>>>> don't know
the answer yet.
integrated
into the formal system. There is no way that applying ONLY truth >>>>>>>>>> preserving operations to basic facts can possibly result in >>>>>>>>>> undecidability.
Only a valid concrete counter-example counts as a rebuttal, >>>>>>>>>> everything
else counts as some sort of deception.
See Gödel 19whenever.
Does not meet my spec. All math proofs make sure to
always ignore semantics. Not all inference steps
are truth preserving operations.
X <is a necessary consequence> of Y.
No, you just don't understand what that means, but are too stupid >>>>>>> to understand that,
It is not that I am stupid. It has always been
that you are dishonest. If you were not dishonest
you could and would point out specific mistakes.
Since I made no mistakes all that you have left
is calling me stupid.
I HAVE been pointing out specific mistakes.
Point out one mistake that you have pointed out here by
quoting the time/date stamp with your prior reply.
Like at 6:15 PM today where I said:
Note, the langauge can't have the metalanguages derived from it
within it. Your claims just shows you don't understand what you are
talking about because you are just too ignorant to even try to learn
the meanings.
Good job. That is a reasonable critique. I don't see these things
because I stop at your first mistake. Lets start talking one single
point at a time, that way I will not skip most of what you say.
A single language anchored in an inheritance type hierarchy
can specify the meta-theory for the theory at the next level
in the type hierarchy.
Because you did such a good job proving your point that you
did actually have a reasonable critique I humbly apologize for
calling you a liar.
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language >>>>>>>>>>>>>> is not a tautology.
On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited to the >>>>>>>>>>>>>>>>>>> set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to elements >>>>>>>>>>>>>>>>>>> of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving >>>>>>>>>>>>>>> to the giant semantic tautology of the set of human knowledge >>>>>>>>>>>>>>> that can be expressed using language then every element in this >>>>>>>>>>>>>>> set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition >>>>>> it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be.
If sentences, and there are not too many of them, a set of knowledge
could be presented as a book that contains those sentences and nothing >>>> else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is
small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is
useful and used for practical purposes. How should your True(X) handle
that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down >>>>>>>> somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic >>>>>> property of true that are written down somewhere" is not useful because >>>>>> there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
On 3/29/2025 8:10 PM, Richard Damon wrote:
On 3/29/25 7:24 PM, olcott wrote:
On 3/29/2025 5:18 PM, Richard Damon wrote:
On 3/29/25 5:49 PM, olcott wrote:
On 3/29/2025 3:50 PM, Richard Damon wrote:
On 3/29/25 4:40 PM, olcott wrote:
On 3/29/2025 3:14 PM, joes wrote:
Am Sat, 29 Mar 2025 09:28:29 -0500 schrieb olcott:
On 3/28/2025 4:50 PM, Richard Damon wrote:One of a sentence and its negation must be true.
On 3/28/25 3:45 PM, olcott wrote:
On 3/28/2025 5:33 AM, joes wrote:
Am Thu, 27 Mar 2025 20:44:28 -0500 schrieb olcott:
*The key defining aspect of knowledge is that it is true*The set of all general knowledge that can be expressed in >>>>>>>>>>>>> language
is a subset of all truth and only excludes unknown and >>>>>>>>>>>>> unknowable.
Exactly, it doesn't include the unknown truths and ought to >>>>>>>>>>>> be called
Known(X). It is also contradictory since it gives NO both for >>>>>>>>>>>> unknowns and their negation.
Which has been the eternal debate, how can we tell if some >>>>>>>>>> "fact" weThis can be incoherent unless complete semantics is fully
have discovered is true.
In FORMAL LOGIC (which you just dismissed) truth has a solid >>>>>>>>>> definition, and we can formally PROVE some statements to be >>>>>>>>>> true and
formally PROVE that some statements are just false, and thus such >>>>>>>>>> statements CAN become truely established knowledge. There may >>>>>>>>>> also be
some statements we have not established yet (and maybe can never >>>>>>>>>> establish in the system) which will remain as "unknown". That >>>>>>>>>> doesn't
mean the statements might not be true or false, just that we >>>>>>>>>> don't know
the answer yet.
integrated
into the formal system. There is no way that applying ONLY truth >>>>>>>>> preserving operations to basic facts can possibly result in
undecidability.
Only a valid concrete counter-example counts as a rebuttal,
everything
else counts as some sort of deception.
See Gödel 19whenever.
Does not meet my spec. All math proofs make sure to
always ignore semantics. Not all inference steps
are truth preserving operations.
X <is a necessary consequence> of Y.
No, you just don't understand what that means, but are too stupid
to understand that,
It is not that I am stupid. It has always been
that you are dishonest. If you were not dishonest
you could and would point out specific mistakes.
Since I made no mistakes all that you have left
is calling me stupid.
I HAVE been pointing out specific mistakes.
Point out one mistake that you have pointed out here by
quoting the time/date stamp with your prior reply.
Like at 6:15 PM today where I said:
Note, the langauge can't have the metalanguages derived from it
within it. Your claims just shows you don't understand what you are
talking about because you are just too ignorant to even try to learn
the meanings.
Good job. That is a reasonable critique. I don't see these things
because I stop at your first mistake. Lets start talking one single
point at a time, that way I will not skip most of what you say.
A single language anchored in an inheritance type hierarchy
can specify the meta-theory for the theory at the next level
in the type hierarchy.
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited >>>>>>>>>>>>>>>>>>>>> to the
set of knowledge that can be expressed using >>>>>>>>>>>>>>>>>>>>> language or
derived by applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>> elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all >>>>>>>>>>>>>>>>>>>>> inference
is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate >>>>>>>>>>>>>>>>>>>>> cannot possibly
be thwarted.
There is no computable predicate that tells whether >>>>>>>>>>>>>>>>>>>> a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of >>>>>>>>>>>>>>>>>> the conjecture
or its negation. Then the predicate True is no longer >>>>>>>>>>>>>>>>>> complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>> be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>> powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth >>>>>>>>>>>>>>>>> preserving
to the giant semantic tautology of the set of human >>>>>>>>>>>>>>>>> knowledge
that can be expressed using language then every element >>>>>>>>>>>>>>>>> in this
set is reachable by these same truth preserving >>>>>>>>>>>>>>>>> operations.
The set of human knowledge that can be expressed using >>>>>>>>>>>>>>>> language
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>> What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have >>>>>>>>>> the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any
definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be.
If sentences, and there are not too many of them, a set of knowledge >>>>>> could be presented as a book that contains those sentences and
nothing
else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is
small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known >>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is >>>> useful and used for practical purposes. How should your True(X) handle >>>> that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are
written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the >>>>>>>> semantic
property of true that are written down somewhere" is not useful >>>>>>>> because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as
understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no
definition
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
If you reject
the idea that a sentence derived from true sentences with turth
preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote:However, it is possible that someone finds a proof >>>>>>>>>>>>>>>>>>>> of the conjecture
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is >>>>>>>>>>>>>>>>>>>>>>> limited to the
set of knowledge that can be expressed using >>>>>>>>>>>>>>>>>>>>>>> language or
derived by applying truth preserving operations >>>>>>>>>>>>>>>>>>>>>>> to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all >>>>>>>>>>>>>>>>>>>>>>> inference
is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>> operations to
elements of this set then a True(X) predicate >>>>>>>>>>>>>>>>>>>>>>> cannot possibly
be thwarted.
There is no computable predicate that tells >>>>>>>>>>>>>>>>>>>>>> whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no >>>>>>>>>>>>>>>>>>>> longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>>>> powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth >>>>>>>>>>>>>>>>>>> preserving
to the giant semantic tautology of the set of human >>>>>>>>>>>>>>>>>>> knowledge
that can be expressed using language then every >>>>>>>>>>>>>>>>>>> element in this
set is reachable by these same truth preserving >>>>>>>>>>>>>>>>>>> operations.
The set of human knowledge that can be expressed using >>>>>>>>>>>>>>>>>> language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>> it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have >>>>>>>>>>>> the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any >>>>>>>>>> definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be. >>>>>>>> If sentences, and there are not too many of them, a set of
knowledge
could be presented as a book that contains those sentences and >>>>>>>> nothing
else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is >>>>>> small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not >>>>>>>> known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong
but is
useful and used for practical purposes. How should your True(X)
handle
that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are >>>>>>>>>>>> written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the >>>>>>>>>> semantic
property of true that are written down somewhere" is not
useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as
understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no
definition
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
The point is that an unimplmentable defintion doesn't define an
existing predicate.
If you reject
the idea that a sentence derived from true sentences with turth
preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth preserving
operations on true sentences?
I think you just rejected your own logic by not understanding what you
are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote:And human knowledge is not.
On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a proof >>>>>>>>>>>>>>>>>>>>>> of the conjecture
It is stipulated that analytic knowledge is >>>>>>>>>>>>>>>>>>>>>>>>> limited to the
set of knowledge that can be expressed using >>>>>>>>>>>>>>>>>>>>>>>>> language or
derived by applying truth preserving operations >>>>>>>>>>>>>>>>>>>>>>>>> to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all >>>>>>>>>>>>>>>>>>>>>>>>> inference
is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations to
elements of this set then a True(X) predicate >>>>>>>>>>>>>>>>>>>>>>>>> cannot possibly
be thwarted.
There is no computable predicate that tells >>>>>>>>>>>>>>>>>>>>>>>> whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no >>>>>>>>>>>>>>>>>>>>>> longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>>>>>> powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth >>>>>>>>>>>>>>>>>>>>> preserving
to the giant semantic tautology of the set of human >>>>>>>>>>>>>>>>>>>>> knowledge
that can be expressed using language then every >>>>>>>>>>>>>>>>>>>>> element in this
set is reachable by these same truth preserving >>>>>>>>>>>>>>>>>>>>> operations.
The set of human knowledge that can be expressed >>>>>>>>>>>>>>>>>>>> using language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>> semantic property of true that are written down
somewhere.
We already know that many expressions of language that >>>>>>>>>>>>>> have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any >>>>>>>>>>>> definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be. >>>>>>>>>> If sentences, and there are not too many of them, a set of >>>>>>>>>> knowledge
could be presented as a book that contains those sentences and >>>>>>>>>> nothing
else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is >>>>>>>> small, probably empty. If you include many uncertain facts then >>>>>>>> almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient. >>>>>>>>>
However, there could be no uncertain sentences as they are not >>>>>>>>>> known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong >>>>>>>> but is
useful and used for practical purposes. How should your True(X) >>>>>>>> handle
that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are >>>>>>>>>>>>>> written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have >>>>>>>>>>>> the semantic
property of true that are written down somewhere" is not >>>>>>>>>>>> useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as
understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no
definition
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
The point is that an unimplmentable defintion doesn't define an
existing predicate.
If you reject
the idea that a sentence derived from true sentences with turth
preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth
preserving operations on true sentences?
I think you just rejected your own logic by not understanding what
you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created by an
(infinite) chain of truth preserving operations.
As not in the domain.
When we try to find the sum of an actual rabbit
with an actual pallet of bricks we fail because
these are not in the domain of sum().
Thus you disagree with your own claims.
The problem seems to be you don't understand the potential for a logic
system to have things only shown by an infinite chain of operations,
because you just don't understand infinity.
I did prove a whole huge very relevant domain where
True(X) always provides the correct return value.
Such a system wold also know that:
This sentence is not true: "This sentence is not true."
is true because the inner sentence is not a truth bearer.
That, our you think you CAN see an infinite series of steps. IF that
is the case, please present an actual infinite chain of steps that
proves something (not an infinite chain that has a induction that
reduces it to a finite chain, but an actual infinite chain).
Do you know what the domain of a function is, or is this
a brand new idea for you?
You also can't just use ... because you need to show that each one
DOES satisfy the requirements, and we assume an induction isn't
available.
Starting with true expressions and deriving other expressions
only through semantic logical entailment necessarily derives
true expressions.
For example, show that no number satisfies that relationship, by
showing it actually applied to EVERY possible number.
This is what makes Godel's G true, and may be what establishes the
Goldbach conjecture.
The some screwy systems can be defined with undecidability
merely proves that some screwy systems do exist.
Sorry, you are just showing you don't understand what you are talking
about.
I am showing that YOU don't understand what I am talking about.
You have never pointed to any actual error.
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:He didn't say that True(X) cannot be defined. He proved that no >>>>>>>> definition
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:Unless you want to exclude uncertain facts the set of know >>>>>>>>>> facts is
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>And human knowledge is not.
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a >>>>>>>>>>>>>>>>>>>>>>>> proof of the conjecture
It is stipulated that analytic knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>> limited to the
set of knowledge that can be expressed using >>>>>>>>>>>>>>>>>>>>>>>>>>> language or
derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>> operations to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and >>>>>>>>>>>>>>>>>>>>>>>>>>> all inference
is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>> operations to
elements of this set then a True(X) predicate >>>>>>>>>>>>>>>>>>>>>>>>>>> cannot possibly
be thwarted.
There is no computable predicate that tells >>>>>>>>>>>>>>>>>>>>>>>>>> whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or >>>>>>>>>>>>>>>>>>>>>>>>> false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no >>>>>>>>>>>>>>>>>>>>>>>> longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they >>>>>>>>>>>>>>>>>>>>>>>>> beginHowever, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>>>>>>>> powerful sysems, certain)
with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply >>>>>>>>>>>>>>>>>>>>>>> truth preserving
to the giant semantic tautology of the set of >>>>>>>>>>>>>>>>>>>>>>> human knowledge
that can be expressed using language then every >>>>>>>>>>>>>>>>>>>>>>> element in this
set is reachable by these same truth preserving >>>>>>>>>>>>>>>>>>>>>>> operations.
The set of human knowledge that can be expressed >>>>>>>>>>>>>>>>>>>>>> using language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language that >>>>>>>>>>>>>>>> have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any >>>>>>>>>>>>>> definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be. >>>>>>>>>>>> If sentences, and there are not too many of them, a set of >>>>>>>>>>>> knowledge
could be presented as a book that contains those sentences >>>>>>>>>>>> and nothing
else.
A list of sentences would not make for efficient processing. >>>>>>>>>>
small, probably empty. If you include many uncertain facts then >>>>>>>>>> almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings >>>>>>>>> and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient. >>>>>>>>>>>
However, there could be no uncertain sentences as they are >>>>>>>>>>>> not known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be >>>>>>>>>> wrong but is
useful and used for practical purposes. How should your
True(X) handle
that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are >>>>>>>>>>>>>>>> written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have >>>>>>>>>>>>>> the semantic
property of true that are written down somewhere" is not >>>>>>>>>>>>>> useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as >>>>>>>>>> understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong. >>>>>>>>
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
The point is that an unimplmentable defintion doesn't define an
existing predicate.
If you reject
the idea that a sentence derived from true sentences with turth >>>>>>>> preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth
preserving operations on true sentences?
I think you just rejected your own logic by not understanding what >>>>>> you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created by an
(infinite) chain of truth preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:He didn't say that True(X) cannot be defined. He proved that >>>>>>>>>> no definition
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:Unless you want to exclude uncertain facts the set of know >>>>>>>>>>>> facts is
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>Only general knowledge
On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not.
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a >>>>>>>>>>>>>>>>>>>>>>>>>> proof of the conjecture
It is stipulated that analytic knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> limited to the
set of knowledge that can be expressed >>>>>>>>>>>>>>>>>>>>>>>>>>>>> using language or
derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set.
A simple example is the first order group >>>>>>>>>>>>>>>>>>>>>>>>>>>> theory.
When we begin with a set of basic facts and >>>>>>>>>>>>>>>>>>>>>>>>>>>>> all inference
is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to
elements of this set then a True(X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted.
There is no computable predicate that tells >>>>>>>>>>>>>>>>>>>>>>>>>>>> whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any >>>>>>>>>>>>>>>>>>>>>>>>>>> finite
proof that the Goldbach Conjecture is true or >>>>>>>>>>>>>>>>>>>>>>>>>>> false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no >>>>>>>>>>>>>>>>>>>>>>>>>> longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they >>>>>>>>>>>>>>>>>>>>>>>>>>> begin
with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the system is >>>>>>>>>>>>>>>>>>>>>>>>>>> provable
on the basis of these truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>> operations.
However, it is possible (and, for sufficiently >>>>>>>>>>>>>>>>>>>>>>>>>> powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply >>>>>>>>>>>>>>>>>>>>>>>>> truth preserving
to the giant semantic tautology of the set of >>>>>>>>>>>>>>>>>>>>>>>>> human knowledge
that can be expressed using language then every >>>>>>>>>>>>>>>>>>>>>>>>> element in this
set is reachable by these same truth preserving >>>>>>>>>>>>>>>>>>>>>>>>> operations.
The set of human knowledge that can be expressed >>>>>>>>>>>>>>>>>>>>>>>> using language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language that >>>>>>>>>>>>>>>>>> have the semantic
proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In absense of >>>>>>>>>>>>>>>> any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set >>>>>>>>>>>>>> could be.
If sentences, and there are not too many of them, a set of >>>>>>>>>>>>>> knowledge
could be presented as a book that contains those sentences >>>>>>>>>>>>>> and nothing
else.
A list of sentences would not make for efficient processing. >>>>>>>>>>>>
small, probably empty. If you include many uncertain facts then >>>>>>>>>>>> almost certainly your True(X) is true for some false X. >>>>>>>>>>>>
Yes of course there are no known facts it might be the case >>>>>>>>>>> that feline kittens have always been 15 story office buildings >>>>>>>>>>> and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient. >>>>>>>>>>>>>
However, there could be no uncertain sentences as they are >>>>>>>>>>>>>> not known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be >>>>>>>>>>>> wrong but is
useful and used for practical purposes. How should your >>>>>>>>>>>> True(X) handle
that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that >>>>>>>>>>>>>>>>>> are written downFalse statements do not count as knowledge.
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>
No, but your "the set of expressions of language that >>>>>>>>>>>>>>>> have the semantic
property of true that are written down somewhere" is not >>>>>>>>>>>>>>>> useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as >>>>>>>>>>>> understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong. >>>>>>>>>>
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
The point is that an unimplmentable defintion doesn't define an >>>>>>>> existing predicate.
If you reject
the idea that a sentence derived from true sentences with
turth preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth
preserving operations on true sentences?
I think you just rejected your own logic by not understanding
what you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created by an >>>>>> (infinite) chain of truth preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge as its
basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of knowledge,
then you have no "logic system" as you can't allow the logic system to
increase what it knows outside your initial knowledge, and your "truth
predicate" is defined in the wrong type of domain, and is misnamed, it
is just a knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
You are just admitting that all your work is just a big fraud based on
misdefining your core terms.
Not at all. It is all you using weasel words trying
to wiggle out of the truism that the The actual body
of knowledge that can be expressed in language
(a) Inherently has a True(X) predicate
Sorry, you are doing the best job at sinking your reputation to the
bottom of that lake of fire, which you will be shortly joining.
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:Mere more verbose way of saying the same thing.
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:Unless you want to exclude uncertain facts the set of know >>>>>>>>>>>>>> facts is
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:First one should define what the elements of that set >>>>>>>>>>>>>>>> could be.
On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>Only general knowledge
On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not.
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a >>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of the conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the predicate True is >>>>>>>>>>>>>>>>>>>>>>>>>>>> no longer complete.
It is stipulated that analytic knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be expressed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set.
A simple example is the first order group >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theory.
When we begin with a set of basic facts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to
elements of this set then a True(X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted.
There is no computable predicate that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proven.
Likewise there currently does not exist any >>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite
proof that the Goldbach Conjecture is true >>>>>>>>>>>>>>>>>>>>>>>>>>>>> or false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> they begin
with set of basic facts and are only >>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
apply truth preserving operations to these >>>>>>>>>>>>>>>>>>>>>>>>>>>>> basic
facts then every element of the system is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> provable
on the basis of these truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations.
However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply >>>>>>>>>>>>>>>>>>>>>>>>>>> truth preserving
to the giant semantic tautology of the set of >>>>>>>>>>>>>>>>>>>>>>>>>>> human knowledge
that can be expressed using language then >>>>>>>>>>>>>>>>>>>>>>>>>>> every element in this
set is reachable by these same truth >>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations.
The set of human knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be >>>>>>>>>>>>>>>>>>>>>>> false.
What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language >>>>>>>>>>>>>>>>>>>> that have the semantic
proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In absense of >>>>>>>>>>>>>>>>>> any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, a set >>>>>>>>>>>>>>>> of knowledge
could be presented as a book that contains those >>>>>>>>>>>>>>>> sentences and nothing
else.
A list of sentences would not make for efficient processing. >>>>>>>>>>>>>>
small, probably empty. If you include many uncertain facts >>>>>>>>>>>>>> then
almost certainly your True(X) is true for some false X. >>>>>>>>>>>>>>
Yes of course there are no known facts it might be the case >>>>>>>>>>>>> that feline kittens have always been 15 story office buildings >>>>>>>>>>>>> and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most >>>>>>>>>>>>>>> efficient.
However, there could be no uncertain sentences as they >>>>>>>>>>>>>>>> are not known
(sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>> a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be >>>>>>>>>>>>>> wrong but is
useful and used for practical purposes. How should your >>>>>>>>>>>>>> True(X) handle
that?
The set of everything that anyone ever wrote >>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>> Some is general dogs are animals.
No, but your "the set of expressions of language that >>>>>>>>>>>>>>>>>> have the semanticAe also know that many expressions of language that >>>>>>>>>>>>>>>>>>>> are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>
property of true that are written down somewhere" is >>>>>>>>>>>>>>>>>> not useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>> a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts >>>>>>>>>>>>>> as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved >>>>>>>>>>>>> wrong.
He didn't say that True(X) cannot be defined. He proved that >>>>>>>>>>>> no definition
defines a predicate that tells whether a sentence is true. >>>>>>>>>>>
The point is that an unimplmentable defintion doesn't define >>>>>>>>>> an existing predicate.
If you reject
the idea that a sentence derived from true sentences with >>>>>>>>>>>> turth preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth >>>>>>>>>> preserving operations on true sentences?
I think you just rejected your own logic by not understanding >>>>>>>>>> what you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created by >>>>>>>> an (infinite) chain of truth preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge as
its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of knowledge,
then you have no "logic system" as you can't allow the logic system
to increase what it knows outside your initial knowledge, and your
"truth predicate" is defined in the wrong type of domain, and is
misnamed, it is just a knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of
TRUTH, which means the full output of a LOGIC SYSTEM, which you just
denied that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
That you are trying to get away with saying that
a logic system over the domain of all knowledge
that can be expressed using language is not a
logic system is the same as saying that the number
three is not a number.
You keep denying semantic tautologies with
double talk and misdirection.
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said:
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote:
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or >>>>>>>>>>>>>>>>>>>>> derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference >>>>>>>>>>>>>>>>>>>>> is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error.
However, it is possible that someone finds a proof of the conjecture
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>> be expressed using language gets updated.
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable.
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge >>>>>>>>>>>>>>>>> that can be expressed using language then every element in this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>>>
is not a tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>> What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition >>>>>>>> it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be.
If sentences, and there are not too many of them, a set of knowledge >>>>>> could be presented as a book that contains those sentences and nothing >>>>>> else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is
small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known >>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is >>>> useful and used for practical purposes. How should your True(X) handle >>>> that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down >>>>>>>>>> somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as understanding >>>> as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no definition >> defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
If you reject
the idea that a sentence derived from true sentences with turth preserving >> transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote:However, it is possible that someone finds a proof of the conjecture
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>>>>>
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>> it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be. >>>>>>>> If sentences, and there are not too many of them, a set of knowledge >>>>>>>> could be presented as a book that contains those sentences and nothing >>>>>>>> else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is >>>>>> small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known >>>>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is >>>>>> useful and used for practical purposes. How should your True(X) handle >>>>>> that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no definition >>>> defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
The point is that an unimplmentable defintion doesn't define an
existing predicate.
If you reject
the idea that a sentence derived from true sentences with turth preserving >>>> transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth preserving
operations on true sentences?
I think you just rejected your own logic by not understanding what you
are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:Mere more verbose way of saying the same thing.
On 3/29/2025 5:20 AM, Mikko wrote:He didn't say that True(X) cannot be defined. He proved that no definition
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:Unless you want to exclude uncertain facts the set of know facts is
On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote:First one should define what the elements of that set could be.
On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>Only general knowledge
On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a proof of the conjecture
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory.
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, a set of knowledge
could be presented as a book that contains those sentences and nothing
else.
A list of sentences would not make for efficient processing. >>>>>>>>>>>>>>>>
small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X. >>>>>>>>>>>>>>>>
Yes of course there are no known facts it might be the case >>>>>>>>>>>>>>> that feline kittens have always been 15 story office buildings >>>>>>>>>>>>>>> and we have been deluded into thinking differently. >>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is most efficient. >>>>>>>>>>>>>>>>>
However, there could be no uncertain sentences as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>> a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is
useful and used for practical purposes. How should your True(X) handle
that?
The set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>> Some is general dogs are animals.
No, but your "the set of expressions of language that have the semanticAe also know that many expressions of language that are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>> a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong. >>>>>>>>>>>>>>
defines a predicate that tells whether a sentence is true. >>>>>>>>>>>>>
The point is that an unimplmentable defintion doesn't define an >>>>>>>>>>>> existing predicate.
If you rejectSince this <is> my own design, I do not reject it.
the idea that a sentence derived from true sentences with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>
So, you think we can derive a non-true statement from truth preserving
operations on true sentences?
I think you just rejected your own logic by not understanding what you
are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created by an >>>>>>>>>> (infinite) chain of truth preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge as its >>>>>> basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of knowledge, then >>>>>> you have no "logic system" as you can't allow the logic system to
increase what it knows outside your initial knowledge, and your "truth >>>>>> predicate" is defined in the wrong type of domain, and is misnamed, it >>>>>> is just a knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of TRUTH, >>>> which means the full output of a LOGIC SYSTEM, which you just denied
that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it has no
INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:Mere more verbose way of saying the same thing.
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote:First one should define what the elements of that set >>>>>>>>>>>>>>>>>> could be.
On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>Only general knowledge
On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The set of human knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology.
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a proof of the conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the predicate True >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no longer complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be expressed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set.
A simple example is the first order >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> group theory.
When we begin with a set of basic facts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted.
There is no computable predicate that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proven.
Likewise there currently does not exist >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any finite
proof that the Goldbach Conjecture is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true or false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general knowledge that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> can
be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> they begin
with set of basic facts and are only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
apply truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> these basic
facts then every element of the system is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> provable
on the basis of these truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations.
However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only >>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology of the set >>>>>>>>>>>>>>>>>>>>>>>>>>>>> of human knowledge
that can be expressed using language then >>>>>>>>>>>>>>>>>>>>>>>>>>>>> every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be >>>>>>>>>>>>>>>>>>>>>>>>> false.
What actually <is> knowledge is impossibly >>>>>>>>>>>>>>>>>>>>>>>>> false by
definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language >>>>>>>>>>>>>>>>>>>>>> that have the semantic
proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In absense >>>>>>>>>>>>>>>>>>>> of any definition
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, a >>>>>>>>>>>>>>>>>> set of knowledge
could be presented as a book that contains those >>>>>>>>>>>>>>>>>> sentences and nothing
else.
A list of sentences would not make for efficient >>>>>>>>>>>>>>>>> processing.
Unless you want to exclude uncertain facts the set of >>>>>>>>>>>>>>>> know facts is
small, probably empty. If you include many uncertain >>>>>>>>>>>>>>>> facts then
almost certainly your True(X) is true for some false X. >>>>>>>>>>>>>>>>
Yes of course there are no known facts it might be the case >>>>>>>>>>>>>>> that feline kittens have always been 15 story office >>>>>>>>>>>>>>> buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is most >>>>>>>>>>>>>>>>> efficient.
However, there could be no uncertain sentences as they >>>>>>>>>>>>>>>>>> are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>> a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to >>>>>>>>>>>>>>>> be wrong but is
useful and used for practical purposes. How should your >>>>>>>>>>>>>>>> True(X) handle
that?
The set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>> Some is general dogs are animals.
No, but your "the set of expressions of language >>>>>>>>>>>>>>>>>>>> that have the semanticAe also know that many expressions of language >>>>>>>>>>>>>>>>>>>>>> that are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>
property of true that are written down somewhere" is >>>>>>>>>>>>>>>>>>>> not useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>> a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts >>>>>>>>>>>>>>>> as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved >>>>>>>>>>>>>>> wrong.
He didn't say that True(X) cannot be defined. He proved >>>>>>>>>>>>>> that no definition
defines a predicate that tells whether a sentence is true. >>>>>>>>>>>>>
The point is that an unimplmentable defintion doesn't define >>>>>>>>>>>> an existing predicate.
If you rejectSince this <is> my own design, I do not reject it.
the idea that a sentence derived from true sentences with >>>>>>>>>>>>>> turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>
So, you think we can derive a non-true statement from truth >>>>>>>>>>>> preserving operations on true sentences?
I think you just rejected your own logic by not
understanding what you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created >>>>>>>>>> by an (infinite) chain of truth preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge as >>>>>> its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of knowledge, >>>>>> then you have no "logic system" as you can't allow the logic
system to increase what it knows outside your initial knowledge,
and your "truth predicate" is defined in the wrong type of domain, >>>>>> and is misnamed, it is just a knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of
TRUTH, which means the full output of a LOGIC SYSTEM, which you just
denied that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it has no
INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:Mere more verbose way of saying the same thing.
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote:First one should define what the elements of that >>>>>>>>>>>>>>>>>>>> set could be.
On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
Only general knowledgeOn 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The set of human knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:However, it is possible that someone >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finds a proof of the conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the predicate True >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is no longer complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple example is the first order >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>There is no computable predicate that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proven.
Likewise there currently does not exist >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any finite
proof that the Goldbach Conjecture is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can
be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to
apply truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> these basic
facts then every element of the system >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is provable
on the basis of these truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations.
However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using language then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so framed >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that
it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly >>>>>>>>>>>>>>>>>>>>>>>>>>> be false.
What actually <is> knowledge is impossibly >>>>>>>>>>>>>>>>>>>>>>>>>>> false by
definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that have the >>>>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In >>>>>>>>>>>>>>>>>>>>>> absense of any definition
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, a >>>>>>>>>>>>>>>>>>>> set of knowledge
could be presented as a book that contains those >>>>>>>>>>>>>>>>>>>> sentences and nothing
else.
A list of sentences would not make for efficient >>>>>>>>>>>>>>>>>>> processing.
Unless you want to exclude uncertain facts the set of >>>>>>>>>>>>>>>>>> know facts is
small, probably empty. If you include many uncertain >>>>>>>>>>>>>>>>>> facts then
almost certainly your True(X) is true for some false X. >>>>>>>>>>>>>>>>>>
Yes of course there are no known facts it might be the >>>>>>>>>>>>>>>>> case
that feline kittens have always been 15 story office >>>>>>>>>>>>>>>>> buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is most >>>>>>>>>>>>>>>>>>> efficient.
However, there could be no uncertain sentences as >>>>>>>>>>>>>>>>>>>> they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>>>> a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known >>>>>>>>>>>>>>>>>> to be wrong but is
useful and used for practical purposes. How should >>>>>>>>>>>>>>>>>> your True(X) handle
that?
Understanding that Tarski has been refuted hardly >>>>>>>>>>>>>>>>>> counts as understandingThe set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals.
No, but your "the set of expressions of language >>>>>>>>>>>>>>>>>>>>>> that have the semanticAe also know that many expressions of language >>>>>>>>>>>>>>>>>>>>>>>> that are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>>>
property of true that are written down somewhere" >>>>>>>>>>>>>>>>>>>>>> is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is >>>>>>>>>>>>>>>>> proved wrong.
He didn't say that True(X) cannot be defined. He proved >>>>>>>>>>>>>>>> that no definition
defines a predicate that tells whether a sentence is true. >>>>>>>>>>>>>>>
The point is that an unimplmentable defintion doesn't >>>>>>>>>>>>>> define an existing predicate.
So, you think we can derive a non-true statement from >>>>>>>>>>>>>> truth preserving operations on true sentences?
If you rejectSince this <is> my own design, I do not reject it. >>>>>>>>>>>>>>
the idea that a sentence derived from true sentences >>>>>>>>>>>>>>>> with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>>>
I think you just rejected your own logic by not
understanding what you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created >>>>>>>>>>>> by an (infinite) chain of truth preserving operations. >>>>>>>>>>>>
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge >>>>>>>> as its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of
knowledge, then you have no "logic system" as you can't allow
the logic system to increase what it knows outside your initial >>>>>>>> knowledge, and your "truth predicate" is defined in the wrong
type of domain, and is misnamed, it is just a knowledge predicate. >>>>>>>>
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of
TRUTH, which means the full output of a LOGIC SYSTEM, which you
just denied that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it has no
INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
On 3/31/2025 4:10 AM, Mikko wrote:
On 2025-03-31 03:22:17 +0000, olcott said:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:Mere more verbose way of saying the same thing.
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote:First one should define what the elements of that set could be.
On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
Only general knowledgeOn 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a proof of the conjecture
It is stipulated that analytic knowledge is limited to theA simple example is the first order group theory.
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inferenceThere is no computable predicate that tells whether a sentence
is limited to applying truth preserving operations to
elements of this set then a True(X) predicate cannot possibly
be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
of the first order group theory can be proven.
Likewise there currently does not exist any finite
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that have the >>>>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, a set of knowledge
could be presented as a book that contains those sentences and nothing
else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is
small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X. >>>>>>>>>>>>>>>>>>
Yes of course there are no known facts it might be the case >>>>>>>>>>>>>>>>> that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>>>> a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is
useful and used for practical purposes. How should your True(X) handle
that?
Understanding that Tarski has been refuted hardly counts as understandingThe set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals.
No, but your "the set of expressions of language that have the semanticAe also know that many expressions of language that are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>>>
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can >>>>>>>>>>>>>>>>>>>>> possibly be written down (formerly the analytic aspect >>>>>>>>>>>>>>>>>>>>> of the analytic/synthetic distinction) exists without >>>>>>>>>>>>>>>>>>>>> enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no definition
defines a predicate that tells whether a sentence is true. >>>>>>>>>>>>>>>
The point is that an unimplmentable defintion doesn't define an >>>>>>>>>>>>>> existing predicate.
So, you think we can derive a non-true statement from truth preserving
If you rejectSince this <is> my own design, I do not reject it. >>>>>>>>>>>>>>
the idea that a sentence derived from true sentences with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>>>
operations on true sentences?
I think you just rejected your own logic by not understanding what you
are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
But the problme is that you just rejected a sentence created by an >>>>>>>>>>>> (infinite) chain of truth preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate.
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge as its >>>>>>>> basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of knowledge, then
you have no "logic system" as you can't allow the logic system to >>>>>>>> increase what it knows outside your initial knowledge, and your "truth >>>>>>>> predicate" is defined in the wrong type of domain, and is misnamed, it >>>>>>>> is just a knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of TRUTH, >>>>>> which means the full output of a LOGIC SYSTEM, which you just denied >>>>>> that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it has no
INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
Can you prove that the sum of two true numbers is true?
It is true by definition.
On 3/31/2025 5:27 PM, Richard Damon wrote:
On 3/31/25 2:36 PM, olcott wrote:
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:The point is that an unimplmentable defintion doesn't >>>>>>>>>>>>>>>> define an existing predicate.
On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>First one should define what the elements of that >>>>>>>>>>>>>>>>>>>>>> set could be.
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
Only general knowledgeOn 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:The set of human knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:However, it is possible that someone >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finds a proof of the conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True is no longer complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple example is the first order >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>There is no computable predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist any finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can
be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> these basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system is provable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> framed that
it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might >>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be false.
What actually <is> knowledge is impossibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>> false by
definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that have the >>>>>>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In >>>>>>>>>>>>>>>>>>>>>>>> absense of any definition
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, >>>>>>>>>>>>>>>>>>>>>> a set of knowledge
could be presented as a book that contains those >>>>>>>>>>>>>>>>>>>>>> sentences and nothing
else.
A list of sentences would not make for efficient >>>>>>>>>>>>>>>>>>>>> processing.
Unless you want to exclude uncertain facts the set >>>>>>>>>>>>>>>>>>>> of know facts is
small, probably empty. If you include many uncertain >>>>>>>>>>>>>>>>>>>> facts then
almost certainly your True(X) is true for some false X. >>>>>>>>>>>>>>>>>>>>
Yes of course there are no known facts it might be >>>>>>>>>>>>>>>>>>> the case
that feline kittens have always been 15 story office >>>>>>>>>>>>>>>>>>> buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is most >>>>>>>>>>>>>>>>>>>>> efficient.
However, there could be no uncertain sentences as >>>>>>>>>>>>>>>>>>>>>> they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>>>>>> a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known >>>>>>>>>>>>>>>>>>>> to be wrong but is
useful and used for practical purposes. How should >>>>>>>>>>>>>>>>>>>> your True(X) handle
that?
Understanding that Tarski has been refuted hardly >>>>>>>>>>>>>>>>>>>> counts as understandingThe set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals. >>>>>>>>>>>>>>>>>>>>>>>
We can know that the set of general knowledge >>>>>>>>>>>>>>>>>>>>>>> that canNo, but your "the set of expressions of language >>>>>>>>>>>>>>>>>>>>>>>> that have the semanticAe also know that many expressions of language >>>>>>>>>>>>>>>>>>>>>>>>>> that are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>>>>>
property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>> somewhere" is not useful because >>>>>>>>>>>>>>>>>>>>>>>> there is no way to know that set. >>>>>>>>>>>>>>>>>>>>>>>
possibly be written down (formerly the analytic >>>>>>>>>>>>>>>>>>>>>>> aspect
of the analytic/synthetic distinction) exists >>>>>>>>>>>>>>>>>>>>>>> without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>>>
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is >>>>>>>>>>>>>>>>>>> proved wrong.
He didn't say that True(X) cannot be defined. He >>>>>>>>>>>>>>>>>> proved that no definition
defines a predicate that tells whether a sentence is >>>>>>>>>>>>>>>>>> true.
Mere more verbose way of saying the same thing. >>>>>>>>>>>>>>>>
So, you think we can derive a non-true statement from >>>>>>>>>>>>>>>> truth preserving operations on true sentences? >>>>>>>>>>>>>>>>
If you rejectSince this <is> my own design, I do not reject it. >>>>>>>>>>>>>>>>
the idea that a sentence derived from true sentences >>>>>>>>>>>>>>>>>> with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>>>>>
I think you just rejected your own logic by not >>>>>>>>>>>>>>>> understanding what you are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions >>>>>>>>>>>>>>> that are true are always true is necessarily true. >>>>>>>>>>>>>>>
But the problme is that you just rejected a sentence >>>>>>>>>>>>>> created by an (infinite) chain of truth preserving >>>>>>>>>>>>>> operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate. >>>>>>>>>>>
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of
knowledge as its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of
knowledge, then you have no "logic system" as you can't allow >>>>>>>>>> the logic system to increase what it knows outside your
initial knowledge, and your "truth predicate" is defined in >>>>>>>>>> the wrong type of domain, and is misnamed, it is just a
knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of >>>>>>>> TRUTH, which means the full output of a LOGIC SYSTEM, which you >>>>>>>> just denied that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it has
no INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
But your "Computation" system isn't good enought to get there.
Your need a Turing Complete system, which yours isn't
In particular, your definition has no conditional operation.
Deterministic finite automatons have a lookup
table (like a JMP table) form of conditional
branches. I have an issued patent on a DFA.
This is the same kind of thing as a type hierarchy.
On 3/31/2025 4:05 AM, Mikko wrote:
On 2025-03-30 17:16:35 +0000, olcott said:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote:And human knowledge is not.
On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote:
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone finds a proof of the conjecture
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>>>> it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the >>>>>>>>>>>>>>> semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be. >>>>>>>>>> If sentences, and there are not too many of them, a set of knowledge >>>>>>>>>> could be presented as a book that contains those sentences and nothing
else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is >>>>>>>> small, probably empty. If you include many uncertain facts then >>>>>>>> almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient. >>>>>>>>>
However, there could be no uncertain sentences as they are not known >>>>>>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is
useful and used for practical purposes. How should your True(X) handle >>>>>>>> that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no definition
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
The point is that an unimplmentable defintion doesn't define an
existing predicate.
If you reject
the idea that a sentence derived from true sentences with turth preserving
transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
So, you think we can derive a non-true statement from truth preserving >>>> operations on true sentences?
I think you just rejected your own logic by not understanding what you >>>> are talking about.
No this is your ADD again.
That expressions of language derived only from
applying truth preserving operations to expressions
that are true are always true is necessarily true.
Including the one that states that there is no truth predicate.
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
On 3/30/2025 4:57 AM, Mikko wrote:
On 2025-03-29 14:06:17 +0000, olcott said:
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said:
On 3/28/2025 7:12 AM, Mikko wrote:
On 2025-03-28 01:04:45 +0000, olcott said:
On 3/27/2025 5:48 AM, Mikko wrote:
On 2025-03-26 17:58:10 +0000, olcott said:
On 3/26/2025 3:39 AM, Mikko wrote:
On 2025-03-26 02:15:26 +0000, olcott said:
On 3/25/2025 8:08 PM, Richard Damon wrote:
On 3/25/25 10:56 AM, olcott wrote:
On 3/25/2025 5:19 AM, Mikko wrote:
On 2025-03-22 17:53:28 +0000, olcott said:
On 3/22/2025 11:43 AM, Mikko wrote:
On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote:The set of human knowledge that can be expressed using language
On 2025-03-20 15:02:42 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote:However, it is possible that someone finds a proof of the conjecture
On 2025-03-20 02:42:53 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic knowledge is limited to the
set of knowledge that can be expressed using language or
derived by applying truth preserving operations to elements
of this set.
A simple example is the first order group theory. >>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic facts and all inference
is limited to applying truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>> elements of this set then a True(X) predicate cannot possibly
be thwarted.
There is no computable predicate that tells whether a sentence
of the first order group theory can be proven. >>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not exist any finite >>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture is true or false >>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can >>>>>>>>>>>>>>>>>>> be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin >>>>>>>>>>>>>>>>>>>>> with set of basic facts and are only allowed to >>>>>>>>>>>>>>>>>>>>> apply truth preserving operations to these basic >>>>>>>>>>>>>>>>>>>>> facts then every element of the system is provable >>>>>>>>>>>>>>>>>>>>> on the basis of these truth preserving operations. >>>>>>>>>>>>>>>>>>>>However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations. >>>>>>>>>>>>>>>>>>
is not a tautology.
tautology, in logic, a statement so framed that >>>>>>>>>>>>>>>>> it cannot be denied without inconsistency.
And human knowledge is not.
What is taken to be knowledge might possibly be false. >>>>>>>>>>>>>>> What actually <is> knowledge is impossibly false by >>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge?
*This is a good first guess*
The set of expressions of language that have the
semantic property of true that are written down
somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere.
Only general knowledge
What is "general" intended to mean here? In absense of any definition
it is too vague to really mean anything.
Reverse-engineer how you could define a set of
knowledge that is finite rather than infinite.
First one should define what the elements of that set could be. >>>>>>>> If sentences, and there are not too many of them, a set of knowledge >>>>>>>> could be presented as a book that contains those sentences and nothing >>>>>>>> else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is >>>>>> small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently.
A knowledge ontology inheritance hierarchy is most efficient.
However, there could be no uncertain sentences as they are not known >>>>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth.
It is a known fact that X evidence seems to make Y
a reasonably plausible possibility.
A good example is Newtonial mchanics, which is known to be wrong but is >>>>>> useful and used for practical purposes. How should your True(X) handle >>>>>> that?
The set of everything that anyone ever wrote
down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella.
Some is general dogs are animals.
Ae also know that many expressions of language that are written down
somewhere lack the semantic property of true.
False statements do not count as knowledge.
No, but your "the set of expressions of language that have the semantic
property of true that are written down somewhere" is not useful because
there is no way to know that set.
We can know that the set of general knowledge that can
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski
has been refuted and that True(X) does exist for
a specific and crucially relevant domain.
Understanding that Tarski has been refuted hardly counts as understanding
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no definition >>>> defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing.
If you reject
the idea that a sentence derived from true sentences with turth preserving >>>> transformations is always true then you may disagree.
Since this <is> my own design, I do not reject it.
You have never expressed any disagreement with the starting points of
Tarski's proof. You have ever claimed that any of Tarski's inferences
were not truth preserving. But you have claimed that the last one of
these truth preservin transformation has produced a false conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X). https://liarparadox.org/Tarski_275_276.pdf
On 3/31/2025 8:23 PM, Richard Damon wrote:
On 3/31/25 9:06 PM, olcott wrote:
On 3/31/2025 5:27 PM, Richard Damon wrote:
On 3/31/25 2:36 PM, olcott wrote:
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote:
On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:The point is that an unimplmentable defintion doesn't >>>>>>>>>>>>>>>>>> define an existing predicate.
On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 3/29/2025 5:20 AM, Mikko wrote:
On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>First one should define what the elements of >>>>>>>>>>>>>>>>>>>>>>>> that set could be.
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Only general knowledgeOn 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:The set of human knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that someone >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finds a proof of the conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True is no longer complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It is stipulated that analytic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>A simple example is the first >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> order group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with a set of basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>There is no computable predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist any finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach Conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to these basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system is provable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> framed that
it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be false. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What actually <is> knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> have the
semantic property of true that are written >>>>>>>>>>>>>>>>>>>>>>>>>>>>> down
somewhere.
We already know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>>>>>>>
What is "general" intended to mean here? In >>>>>>>>>>>>>>>>>>>>>>>>>> absense of any definition
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of >>>>>>>>>>>>>>>>>>>>>>>> them, a set of knowledge
could be presented as a book that contains those >>>>>>>>>>>>>>>>>>>>>>>> sentences and nothing
else.
A list of sentences would not make for efficient >>>>>>>>>>>>>>>>>>>>>>> processing.
Unless you want to exclude uncertain facts the set >>>>>>>>>>>>>>>>>>>>>> of know facts is
small, probably empty. If you include many >>>>>>>>>>>>>>>>>>>>>> uncertain facts then
almost certainly your True(X) is true for some >>>>>>>>>>>>>>>>>>>>>> false X.
Yes of course there are no known facts it might be >>>>>>>>>>>>>>>>>>>>> the case
that feline kittens have always been 15 story >>>>>>>>>>>>>>>>>>>>> office buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is >>>>>>>>>>>>>>>>>>>>>>> most efficient.A good example is Newtonial mchanics, which is >>>>>>>>>>>>>>>>>>>>>> known to be wrong but is
However, there could be no uncertain sentences >>>>>>>>>>>>>>>>>>>>>>>> as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>>>>>>>> a reasonably plausible possibility. >>>>>>>>>>>>>>>>>>>>>>
useful and used for practical purposes. How should >>>>>>>>>>>>>>>>>>>>>> your True(X) handle
that?
Understanding that Tarski has been refuted hardly >>>>>>>>>>>>>>>>>>>>>> counts as understandingThe set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would be
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals. >>>>>>>>>>>>>>>>>>>>>>>>>
We can know that the set of general knowledge >>>>>>>>>>>>>>>>>>>>>>>>> that canNo, but your "the set of expressions of >>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>>> somewhere" is not useful because >>>>>>>>>>>>>>>>>>>>>>>>>> there is no way to know that set. >>>>>>>>>>>>>>>>>>>>>>>>>Ae also know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>> language that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>>>>>>>False statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>>>>>
possibly be written down (formerly the analytic >>>>>>>>>>>>>>>>>>>>>>>>> aspect
of the analytic/synthetic distinction) exists >>>>>>>>>>>>>>>>>>>>>>>>> without
enumerating its elements.
But we can't use it.
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>>>>>
as Tarstki has not been refuted.
When Tarski said True(X) cannot be defined, he is >>>>>>>>>>>>>>>>>>>>> proved wrong.
He didn't say that True(X) cannot be defined. He >>>>>>>>>>>>>>>>>>>> proved that no definition
defines a predicate that tells whether a sentence is >>>>>>>>>>>>>>>>>>>> true.
Mere more verbose way of saying the same thing. >>>>>>>>>>>>>>>>>>
So, you think we can derive a non-true statement from >>>>>>>>>>>>>>>>>> truth preserving operations on true sentences? >>>>>>>>>>>>>>>>>>
If you rejectSince this <is> my own design, I do not reject it. >>>>>>>>>>>>>>>>>>
the idea that a sentence derived from true sentences >>>>>>>>>>>>>>>>>>>> with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>>>>>>>
I think you just rejected your own logic by not >>>>>>>>>>>>>>>>>> understanding what you are talking about.
No this is your ADD again.
That expressions of language derived only from >>>>>>>>>>>>>>>>> applying truth preserving operations to expressions >>>>>>>>>>>>>>>>> that are true are always true is necessarily true. >>>>>>>>>>>>>>>>>
But the problme is that you just rejected a sentence >>>>>>>>>>>>>>>> created by an (infinite) chain of truth preserving >>>>>>>>>>>>>>>> operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in
the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate. >>>>>>>>>>>>>
The body of knowledge that cannot be expressed in
language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of
knowledge as its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of >>>>>>>>>>>> knowledge, then you have no "logic system" as you can't >>>>>>>>>>>> allow the logic system to increase what it knows outside >>>>>>>>>>>> your initial knowledge, and your "truth predicate" is
defined in the wrong type of domain, and is misnamed, it is >>>>>>>>>>>> just a knowledge predicate.
The actual body of knowledge that can be expressed in
language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain >>>>>>>>>> of TRUTH, which means the full output of a LOGIC SYSTEM, which >>>>>>>>>> you just denied that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it
has no INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
But your "Computation" system isn't good enought to get there.
Your need a Turing Complete system, which yours isn't
In particular, your definition has no conditional operation.
Deterministic finite automatons have a lookup
table (like a JMP table) form of conditional
branches. I have an issued patent on a DFA.
This is the same kind of thing as a type hierarchy.
But your system didn't have that.
It just had a machine that adds two numbers together, and you used
that limitiation to keep the creation of the unprovable truth,
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting points of
Tarski's proof. You have ever claimed that any of Tarski's inferences
were not truth preserving. But you have claimed that the last one of
these truth preservin transformation has produced a false conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved
that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
On 4/1/2025 5:31 AM, Richard Damon wrote:
On 3/31/25 11:06 PM, olcott wrote:
On 3/31/2025 8:23 PM, Richard Damon wrote:
On 3/31/25 9:06 PM, olcott wrote:
On 3/31/2025 5:27 PM, Richard Damon wrote:
On 3/31/25 2:36 PM, olcott wrote:
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/30/25 7:20 AM, olcott wrote:
No this is your ADD again.On 3/30/2025 4:57 AM, Mikko wrote:The point is that an unimplmentable defintion >>>>>>>>>>>>>>>>>>>> doesn't define an existing predicate.
On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/29/2025 5:20 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>First one should define what the elements of >>>>>>>>>>>>>>>>>>>>>>>>>> that set could be.
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What is "general" intended to mean here? In >>>>>>>>>>>>>>>>>>>>>>>>>>>> absense of any definition >>>>>>>>>>>>>>>>>>>>>>>>>>>> it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The set of human knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is stipulated that analytic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge is limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A simple example is the first >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> order group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we begin with a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basic facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) predicate cannot possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no computable predicate >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that tells whether a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group theory >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> someone finds a proof of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate True is no longer complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Likewise there currently does not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist any finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Conjecture is true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type mismatch >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> such that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving operations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to these basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system is provable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>However, it is possible (and, for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sufficiently powerful sysems, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language then every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> framed that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be false. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What actually <is> knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition.
How do you DEFINE what is actually >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge?
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have the
semantic property of true that are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> written down
somewhere.
We already know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anywhere.
Only general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of >>>>>>>>>>>>>>>>>>>>>>>>>> them, a set of knowledge
could be presented as a book that contains >>>>>>>>>>>>>>>>>>>>>>>>>> those sentences and nothing >>>>>>>>>>>>>>>>>>>>>>>>>> else.
A list of sentences would not make for >>>>>>>>>>>>>>>>>>>>>>>>> efficient processing.
Unless you want to exclude uncertain facts the >>>>>>>>>>>>>>>>>>>>>>>> set of know facts is
small, probably empty. If you include many >>>>>>>>>>>>>>>>>>>>>>>> uncertain facts then
almost certainly your True(X) is true for some >>>>>>>>>>>>>>>>>>>>>>>> false X.
Yes of course there are no known facts it might >>>>>>>>>>>>>>>>>>>>>>> be the case
that feline kittens have always been 15 story >>>>>>>>>>>>>>>>>>>>>>> office buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is >>>>>>>>>>>>>>>>>>>>>>>>> most efficient.A good example is Newtonial mchanics, which is >>>>>>>>>>>>>>>>>>>>>>>> known to be wrong but is
However, there could be no uncertain sentences >>>>>>>>>>>>>>>>>>>>>>>>>> as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>>>>>>>>>> a reasonably plausible possibility. >>>>>>>>>>>>>>>>>>>>>>>>
useful and used for practical purposes. How >>>>>>>>>>>>>>>>>>>>>>>> should your True(X) handle
that?
Understanding that Tarski has been refuted >>>>>>>>>>>>>>>>>>>>>>>> hardly counts as understanding >>>>>>>>>>>>>>>>>>>>>>>> as Tarstki has not been refuted. >>>>>>>>>>>>>>>>>>>>>>>>The set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would beBut we can't use it.
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals. >>>>>>>>>>>>>>>>>>>>>>>>>>>
We can know that the set of general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>> that canNo, but your "the set of expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>> property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere" is not useful because >>>>>>>>>>>>>>>>>>>>>>>>>>>> there is no way to know that set. >>>>>>>>>>>>>>>>>>>>>>>>>>>Ae also know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>False statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
possibly be written down (formerly the >>>>>>>>>>>>>>>>>>>>>>>>>>> analytic aspect
of the analytic/synthetic distinction) exists >>>>>>>>>>>>>>>>>>>>>>>>>>> without
enumerating its elements. >>>>>>>>>>>>>>>>>>>>>>>>>>
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>>>>>>>
When Tarski said True(X) cannot be defined, he is >>>>>>>>>>>>>>>>>>>>>>> proved wrong.
He didn't say that True(X) cannot be defined. He >>>>>>>>>>>>>>>>>>>>>> proved that no definition
defines a predicate that tells whether a sentence >>>>>>>>>>>>>>>>>>>>>> is true.
Mere more verbose way of saying the same thing. >>>>>>>>>>>>>>>>>>>>
So, you think we can derive a non-true statement >>>>>>>>>>>>>>>>>>>> from truth preserving operations on true sentences? >>>>>>>>>>>>>>>>>>>>
If you rejectSince this <is> my own design, I do not reject it. >>>>>>>>>>>>>>>>>>>>
the idea that a sentence derived from true >>>>>>>>>>>>>>>>>>>>>> sentences with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>>>>>>>>>
I think you just rejected your own logic by not >>>>>>>>>>>>>>>>>>>> understanding what you are talking about. >>>>>>>>>>>>>>>>>>>
That expressions of language derived only from >>>>>>>>>>>>>>>>>>> applying truth preserving operations to expressions >>>>>>>>>>>>>>>>>>> that are true are always true is necessarily true. >>>>>>>>>>>>>>>>>>>
But the problme is that you just rejected a sentence >>>>>>>>>>>>>>>>>> created by an (infinite) chain of truth preserving >>>>>>>>>>>>>>>>>> operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in >>>>>>>>>>>>>>> the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate. >>>>>>>>>>>>>>>
The body of knowledge that cannot be expressed in >>>>>>>>>>>>>>> language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of >>>>>>>>>>>>>> knowledge as its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of >>>>>>>>>>>>>> knowledge, then you have no "logic system" as you can't >>>>>>>>>>>>>> allow the logic system to increase what it knows outside >>>>>>>>>>>>>> your initial knowledge, and your "truth predicate" is >>>>>>>>>>>>>> defined in the wrong type of domain, and is misnamed, it >>>>>>>>>>>>>> is just a knowledge predicate.
The actual body of knowledge that can be expressed in >>>>>>>>>>>>> language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a >>>>>>>>>>>> domain of TRUTH, which means the full output of a LOGIC >>>>>>>>>>>> SYSTEM, which you just denied that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it >>>>>>>>>> has no INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>
But your "Computation" system isn't good enought to get there.
Your need a Turing Complete system, which yours isn't
In particular, your definition has no conditional operation.
Deterministic finite automatons have a lookup
table (like a JMP table) form of conditional
branches. I have an issued patent on a DFA.
This is the same kind of thing as a type hierarchy.
But your system didn't have that.
It just had a machine that adds two numbers together, and you used
that limitiation to keep the creation of the unprovable truth,
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
No, because we are talking about the machine you claimed:
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
If you have a machine that can do actual logic to try to prove your
statement, then it can do the full mathematics to allow Godel's proof,
and we have a true statement that can not be proven.
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof. The inference steps are the
finite string transformation rules. All inference steps
are always finite string transformation rules.
On 4/1/2025 5:31 PM, Richard Damon wrote:
On 4/1/25 2:00 PM, olcott wrote:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting points of >>>>>> Tarski's proof. You have ever claimed that any of Tarski's inferences >>>>>> were not truth preserving. But you have claimed that the last one of >>>>>> these truth preservin transformation has produced a false conclusion. >>>>>>
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved
that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Yes, and since that step was logically done, it says somewhere we
assumed something incorrect. The assumption we made was that a Truth
Predicate existed, so that can't be true.
You apparently don't understand how logic works.
That Tarski assumed what is false ruined his proof.
True(X) means that X is derived by applying truth preserving
operations to basic facts.
On 4/1/2025 5:27 PM, Richard Damon wrote:
On 4/1/25 1:51 PM, olcott wrote:
On 4/1/2025 5:31 AM, Richard Damon wrote:
On 3/31/25 11:06 PM, olcott wrote:
On 3/31/2025 8:23 PM, Richard Damon wrote:
On 3/31/25 9:06 PM, olcott wrote:
On 3/31/2025 5:27 PM, Richard Damon wrote:
On 3/31/25 2:36 PM, olcott wrote:
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 3/30/25 7:20 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 3/30/2025 4:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
No this is your ADD again.The point is that an unimplmentable defintion >>>>>>>>>>>>>>>>>>>>>> doesn't define an existing predicate. >>>>>>>>>>>>>>>>>>>>>>On 3/29/2025 5:20 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>First one should define what the elements of >>>>>>>>>>>>>>>>>>>>>>>>>>>> that set could be.
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What is "general" intended to mean here? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In absense of any definition >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is stipulated that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> analytic knowledge is limited >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A simple example is the first >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> order group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we begin with a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basic facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) predicate cannot >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no computable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate that tells whether a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Likewise there currently does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist any finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Conjecture is true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> However, it is possible that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> someone finds a proof of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate True is no longer >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The set of human knowledge that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The set of all human general >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language gets >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we redefine logic systems >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> such that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to these basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> system is provable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> However, it is possible (and, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for sufficiently powerful >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and only apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language then every element in this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> framed that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be false. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What actually <is> knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
How do you DEFINE what is actually >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have the
semantic property of true that are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anywhere.
Only general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of >>>>>>>>>>>>>>>>>>>>>>>>>>>> them, a set of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>> could be presented as a book that contains >>>>>>>>>>>>>>>>>>>>>>>>>>>> those sentences and nothing >>>>>>>>>>>>>>>>>>>>>>>>>>>> else.
A list of sentences would not make for >>>>>>>>>>>>>>>>>>>>>>>>>>> efficient processing.
Unless you want to exclude uncertain facts the >>>>>>>>>>>>>>>>>>>>>>>>>> set of know facts is
small, probably empty. If you include many >>>>>>>>>>>>>>>>>>>>>>>>>> uncertain facts then
almost certainly your True(X) is true for some >>>>>>>>>>>>>>>>>>>>>>>>>> false X.
Yes of course there are no known facts it might >>>>>>>>>>>>>>>>>>>>>>>>> be the case
that feline kittens have always been 15 story >>>>>>>>>>>>>>>>>>>>>>>>> office buildings
and we have been deluded into thinking >>>>>>>>>>>>>>>>>>>>>>>>> differently.
A knowledge ontology inheritance hierarchy is >>>>>>>>>>>>>>>>>>>>>>>>>>> most efficient.A good example is Newtonial mchanics, which is >>>>>>>>>>>>>>>>>>>>>>>>>> known to be wrong but is
However, there could be no uncertain >>>>>>>>>>>>>>>>>>>>>>>>>>>> sentences as they are not known >>>>>>>>>>>>>>>>>>>>>>>>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to >>>>>>>>>>>>>>>>>>>>>>>>>>> make Y
a reasonably plausible possibility. >>>>>>>>>>>>>>>>>>>>>>>>>>
useful and used for practical purposes. How >>>>>>>>>>>>>>>>>>>>>>>>>> should your True(X) handle >>>>>>>>>>>>>>>>>>>>>>>>>> that?
Understanding that Tarski has been refuted >>>>>>>>>>>>>>>>>>>>>>>>>> hardly counts as understanding >>>>>>>>>>>>>>>>>>>>>>>>>> as Tarstki has not been refuted. >>>>>>>>>>>>>>>>>>>>>>>>>>The set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>>>>>>>>>> down would be finite. >>>>>>>>>>>>>>>>>>>>>>>>>>>>But not knowable.
Most of this would be >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>But we can't use it.
We can know that the set of general >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that canNo, but your "the set of expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere" is not useful because >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> there is no way to know that set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>Ae also know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere lack the semantic property of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> true.
False statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
possibly be written down (formerly the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> analytic aspect
of the analytic/synthetic distinction) >>>>>>>>>>>>>>>>>>>>>>>>>>>>> exists without
enumerating its elements. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
We can use it right now to understand that >>>>>>>>>>>>>>>>>>>>>>>>>>> Tarski
has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>>>>>>>>>
When Tarski said True(X) cannot be defined, he >>>>>>>>>>>>>>>>>>>>>>>>> is proved wrong.
He didn't say that True(X) cannot be defined. He >>>>>>>>>>>>>>>>>>>>>>>> proved that no definition
defines a predicate that tells whether a >>>>>>>>>>>>>>>>>>>>>>>> sentence is true.
Mere more verbose way of saying the same thing. >>>>>>>>>>>>>>>>>>>>>>
So, you think we can derive a non-true statement >>>>>>>>>>>>>>>>>>>>>> from truth preserving operations on true sentences? >>>>>>>>>>>>>>>>>>>>>>
If you reject
the idea that a sentence derived from true >>>>>>>>>>>>>>>>>>>>>>>> sentences with turth preserving >>>>>>>>>>>>>>>>>>>>>>>> transformations is always true then you may >>>>>>>>>>>>>>>>>>>>>>>> disagree.
Since this <is> my own design, I do not reject it. >>>>>>>>>>>>>>>>>>>>>>
I think you just rejected your own logic by not >>>>>>>>>>>>>>>>>>>>>> understanding what you are talking about. >>>>>>>>>>>>>>>>>>>>>
That expressions of language derived only from >>>>>>>>>>>>>>>>>>>>> applying truth preserving operations to expressions >>>>>>>>>>>>>>>>>>>>> that are true are always true is necessarily true. >>>>>>>>>>>>>>>>>>>>>
But the problme is that you just rejected a sentence >>>>>>>>>>>>>>>>>>>> created by an (infinite) chain of truth preserving >>>>>>>>>>>>>>>>>>>> operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in >>>>>>>>>>>>>>>>> the body of knowledge? The body of knowledge >>>>>>>>>>>>>>>>> Expressed in language INHERENTLY HAS A True(X) predicate. >>>>>>>>>>>>>>>>>
The body of knowledge that cannot be expressed in >>>>>>>>>>>>>>>>> language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of >>>>>>>>>>>>>>>> knowledge as its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is. >>>>>>>>>>>>>>>>
IF you want to restrict your domain to just the body of >>>>>>>>>>>>>>>> knowledge, then you have no "logic system" as you can't >>>>>>>>>>>>>>>> allow the logic system to increase what it knows outside >>>>>>>>>>>>>>>> your initial knowledge, and your "truth predicate" is >>>>>>>>>>>>>>>> defined in the wrong type of domain, and is misnamed, it >>>>>>>>>>>>>>>> is just a knowledge predicate.
The actual body of knowledge that can be expressed in >>>>>>>>>>>>>>> language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a >>>>>>>>>>>>>> domain of TRUTH, which means the full output of a LOGIC >>>>>>>>>>>>>> SYSTEM, which you just denied that you system has. >>>>>>>>>>>>>>
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that >>>>>>>>>>>> it has no INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>>>
But your "Computation" system isn't good enought to get there. >>>>>>>>
Your need a Turing Complete system, which yours isn't
In particular, your definition has no conditional operation.
Deterministic finite automatons have a lookup
table (like a JMP table) form of conditional
branches. I have an issued patent on a DFA.
This is the same kind of thing as a type hierarchy.
But your system didn't have that.
It just had a machine that adds two numbers together, and you used >>>>>> that limitiation to keep the creation of the unprovable truth,
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
No, because we are talking about the machine you claimed:
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
If you have a machine that can do actual logic to try to prove your
statement, then it can do the full mathematics to allow Godel's
proof, and we have a true statement that can not be proven.
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof. The inference steps are the
finite string transformation rules. All inference steps
are always finite string transformation rules.
Then write that program to show what it can do.
You claimed to be very proficient with C.
If it is not dead obvious to you how to
write this function:
void sum(char* x, char* y, char* result);
Then you fibbed about knowing C.
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
On 4/1/2025 8:07 PM, Richard Damon wrote:
On 4/1/25 7:26 PM, olcott wrote:
On 4/1/2025 5:31 PM, Richard Damon wrote:
On 4/1/25 2:00 PM, olcott wrote:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting
points of
Tarski's proof. You have ever claimed that any of Tarski's
inferences
were not truth preserving. But you have claimed that the last
one of
these truth preservin transformation has produced a false
conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved >>>>>> that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Yes, and since that step was logically done, it says somewhere we
assumed something incorrect. The assumption we made was that a Truth
Predicate existed, so that can't be true.
You apparently don't understand how logic works.
That Tarski assumed what is false ruined his proof.
True(X) means that X is derived by applying truth preserving
operations to basic facts.
The only thing he assumed was that a Truth Predict could exist.
Bullshit. His step(3) assumed a falsehood as the basis of
his whole proof. The way that ALL truth that can be expressed
in language really works is semantic logical entailment
from basic facts.
On 4/1/2025 8:03 PM, Richard Damon wrote:
On 4/1/25 7:09 PM, olcott wrote:
On 4/1/2025 5:27 PM, Richard Damon wrote:
On 4/1/25 1:51 PM, olcott wrote:
On 4/1/2025 5:31 AM, Richard Damon wrote:
On 3/31/25 11:06 PM, olcott wrote:
On 3/31/2025 8:23 PM, Richard Damon wrote:
On 3/31/25 9:06 PM, olcott wrote:
On 3/31/2025 5:27 PM, Richard Damon wrote:
On 3/31/25 2:36 PM, olcott wrote:
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> On 3/30/25 1:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 3/30/2025 6:24 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 3/30/25 7:20 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 3/30/2025 4:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
No this is your ADD again.The point is that an unimplmentable defintion >>>>>>>>>>>>>>>>>>>>>>>> doesn't define an existing predicate. >>>>>>>>>>>>>>>>>>>>>>>>On 3/29/2025 5:20 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Unless you want to exclude uncertain facts >>>>>>>>>>>>>>>>>>>>>>>>>>>> the set of know facts is >>>>>>>>>>>>>>>>>>>>>>>>>>>> small, probably empty. If you include many >>>>>>>>>>>>>>>>>>>>>>>>>>>> uncertain facts then
On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> said:What is "general" intended to mean here? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In absense of any definition >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/25/2025 8:08 PM, Richard Damon >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:We already know that many expressions >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proerty of true are not written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anywhere.
On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/20/2025 8:09 AM, Mikko >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is stipulated that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> analytic knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> limited to the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> derived by applying truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A simple example is the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> first order group theory. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we begin with a set of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> basic facts and all inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is limited to applying >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth preserving operations to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> elements of this set then a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> True(X) predicate cannot >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no computable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate that tells whether >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a sentence >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the first order group >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theory can be proven. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Likewise there currently does >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not exist any finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof that the Goldbach >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Conjecture is true or false >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> thus True(GC) is a type >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> However, it is possible that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> someone finds a proof of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> conjecture >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or its negation. Then the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> predicate True is no longer >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> complete. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of all human general >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we redefine logic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> systems such that they begin >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with set of basic facts and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> are only allowed to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> operations to these basic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> facts then every element of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the system is provable >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> on the basis of these truth >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> However, it is possible (and, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for sufficiently powerful >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sysems, certain) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that the provability is not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> When we begin with basic facts >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and only apply truth preserving >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to the giant semantic tautology >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the set of human knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be expressed using >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language then every element in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set is reachable by these same >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth preserving operations. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of human knowledge that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> can be expressed using language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so framed that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it cannot be denied without >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be false. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What actually <is> knowledge is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> impossibly false by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> definition. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
How do you DEFINE what is actually >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that have the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic property of true that are >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Only general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> set of
knowledge that is finite rather than >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite.
First one should define what the elements >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of that set could be. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If sentences, and there are not too many >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of them, a set of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could be presented as a book that contains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> those sentences and nothing >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> else.
A list of sentences would not make for >>>>>>>>>>>>>>>>>>>>>>>>>>>>> efficient processing. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
almost certainly your True(X) is true for >>>>>>>>>>>>>>>>>>>>>>>>>>>> some false X.
Yes of course there are no known facts it >>>>>>>>>>>>>>>>>>>>>>>>>>> might be the case
that feline kittens have always been 15 story >>>>>>>>>>>>>>>>>>>>>>>>>>> office buildings
and we have been deluded into thinking >>>>>>>>>>>>>>>>>>>>>>>>>>> differently.
A knowledge ontology inheritance hierarchy >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is most efficient.A good example is Newtonial mchanics, which >>>>>>>>>>>>>>>>>>>>>>>>>>>> is known to be wrong but is >>>>>>>>>>>>>>>>>>>>>>>>>>>> useful and used for practical purposes. How >>>>>>>>>>>>>>>>>>>>>>>>>>>> should your True(X) handle >>>>>>>>>>>>>>>>>>>>>>>>>>>> that?
However, there could be no uncertain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sentences as they are not known >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> make Y
a reasonably plausible possibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Understanding that Tarski has been refuted >>>>>>>>>>>>>>>>>>>>>>>>>>>> hardly counts as understanding >>>>>>>>>>>>>>>>>>>>>>>>>>>> as Tarstki has not been refuted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>We can use it right now to understand that >>>>>>>>>>>>>>>>>>>>>>>>>>>>> TarskiThe set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> down would be finite. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>But not knowable.
Most of this would be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specific knowledge Pete's dog was named >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Bella.But we can't use it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Some is general dogs are animals. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
We can know that the set of general >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly be written down (formerly the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> analytic aspectAe also know that many expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere lack the semantic property >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of true.
False statements do not count as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge.
No, but your "the set of expressions of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language that have the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere" is not useful because >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> there is no way to know that set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
of the analytic/synthetic distinction) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exists without
enumerating its elements. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
has been refuted and that True(X) does >>>>>>>>>>>>>>>>>>>>>>>>>>>>> exist for
a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
When Tarski said True(X) cannot be defined, >>>>>>>>>>>>>>>>>>>>>>>>>>> he is proved wrong.
He didn't say that True(X) cannot be defined. >>>>>>>>>>>>>>>>>>>>>>>>>> He proved that no definition >>>>>>>>>>>>>>>>>>>>>>>>>> defines a predicate that tells whether a >>>>>>>>>>>>>>>>>>>>>>>>>> sentence is true.
Mere more verbose way of saying the same thing. >>>>>>>>>>>>>>>>>>>>>>>>
So, you think we can derive a non-true statement >>>>>>>>>>>>>>>>>>>>>>>> from truth preserving operations on true sentences? >>>>>>>>>>>>>>>>>>>>>>>>
If you reject
the idea that a sentence derived from true >>>>>>>>>>>>>>>>>>>>>>>>>> sentences with turth preserving >>>>>>>>>>>>>>>>>>>>>>>>>> transformations is always true then you may >>>>>>>>>>>>>>>>>>>>>>>>>> disagree.
Since this <is> my own design, I do not reject it. >>>>>>>>>>>>>>>>>>>>>>>>
I think you just rejected your own logic by not >>>>>>>>>>>>>>>>>>>>>>>> understanding what you are talking about. >>>>>>>>>>>>>>>>>>>>>>>
That expressions of language derived only from >>>>>>>>>>>>>>>>>>>>>>> applying truth preserving operations to expressions >>>>>>>>>>>>>>>>>>>>>>> that are true are always true is necessarily true. >>>>>>>>>>>>>>>>>>>>>>>
But the problme is that you just rejected a >>>>>>>>>>>>>>>>>>>>>> sentence created by an (infinite) chain of truth >>>>>>>>>>>>>>>>>>>>>> preserving operations.
As not in the domain.
WHy not?
You don't understand that unknown things are not in >>>>>>>>>>>>>>>>>>> the body of knowledge? The body of knowledge >>>>>>>>>>>>>>>>>>> Expressed in language INHERENTLY HAS A True(X) >>>>>>>>>>>>>>>>>>> predicate.
The body of knowledge that cannot be expressed in >>>>>>>>>>>>>>>>>>> language cannot have a True(X) predicate. >>>>>>>>>>>>>>>>>>>
But they ARE in the logic system based on the body of >>>>>>>>>>>>>>>>>> knowledge as its basic truths.
Provide a citation that says this.
You just don't understand what a logic system is. >>>>>>>>>>>>>>>>>>
IF you want to restrict your domain to just the body >>>>>>>>>>>>>>>>>> of knowledge, then you have no "logic system" as you >>>>>>>>>>>>>>>>>> can't allow the logic system to increase what it knows >>>>>>>>>>>>>>>>>> outside your initial knowledge, and your "truth >>>>>>>>>>>>>>>>>> predicate" is defined in the wrong type of domain, and >>>>>>>>>>>>>>>>>> is misnamed, it is just a knowledge predicate. >>>>>>>>>>>>>>>>>>
The actual body of knowledge that can be expressed in >>>>>>>>>>>>>>>>> language (a) Inherently has a True(X) predicate >>>>>>>>>>>>>>>>> (b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a >>>>>>>>>>>>>>>> domain of TRUTH, which means the full output of a LOGIC >>>>>>>>>>>>>>>> SYSTEM, which you just denied that you system has. >>>>>>>>>>>>>>>>
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that >>>>>>>>>>>>>> it has no INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum. >>>>>>>>>>>>> It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/
Curry%E2%80%93Howard_correspondence
But your "Computation" system isn't good enought to get there. >>>>>>>>>>
Your need a Turing Complete system, which yours isn't
In particular, your definition has no conditional operation. >>>>>>>>>>
Deterministic finite automatons have a lookup
table (like a JMP table) form of conditional
branches. I have an issued patent on a DFA.
This is the same kind of thing as a type hierarchy.
But your system didn't have that.
It just had a machine that adds two numbers together, and you
used that limitiation to keep the creation of the unprovable truth, >>>>>>>>
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
No, because we are talking about the machine you claimed:
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
If you have a machine that can do actual logic to try to prove
your statement, then it can do the full mathematics to allow
Godel's proof, and we have a true statement that can not be proven. >>>>>>
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof. The inference steps are the
finite string transformation rules. All inference steps
are always finite string transformation rules.
Then write that program to show what it can do.
You claimed to be very proficient with C.
If it is not dead obvious to you how to
write this function:
void sum(char* x, char* y, char* result);
Then you fibbed about knowing C.
I never said anything about that program, I guess you have the memory
of a goldfish.
I was asking about this program:
You must reply immediately after my words.
Not a dozen posts ago.
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
;
The problem you have, as I mentioned, if your language can do that,
then it can suppoort Godel's proof, and it must be incomplete with
sentences that are true but not provable,
My system has a different infrastructure such that
undecidability[math] it impossible.
If math was not dishonest it would have never called
the inability to determine the truth value of
self-contradictory expressions undecidable.
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
On 4/1/2025 5:31 AM, Richard Damon wrote:
On 3/31/25 11:06 PM, olcott wrote:
On 3/31/2025 8:23 PM, Richard Damon wrote:
On 3/31/25 9:06 PM, olcott wrote:
On 3/31/2025 5:27 PM, Richard Damon wrote:
On 3/31/25 2:36 PM, olcott wrote:
On 3/31/2025 5:59 AM, Richard Damon wrote:
On 3/30/25 11:22 PM, olcott wrote:
On 3/30/2025 9:31 PM, Richard Damon wrote:
On 3/30/25 10:01 PM, olcott wrote:
On 3/30/2025 7:25 PM, Richard Damon wrote:
On 3/30/25 7:34 PM, olcott wrote:
On 3/30/2025 5:47 PM, Richard Damon wrote:
On 3/30/25 5:47 PM, olcott wrote:
On 3/30/2025 3:59 PM, Richard Damon wrote:
On 3/30/25 3:39 PM, olcott wrote:
On 3/30/2025 1:53 PM, Richard Damon wrote:
On 3/30/25 1:16 PM, olcott wrote:
On 3/30/2025 6:24 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 3/30/25 7:20 AM, olcott wrote:
On 3/30/2025 4:57 AM, Mikko wrote:The point is that an unimplmentable defintion doesn't define an
On 2025-03-29 14:06:17 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 3/29/2025 5:20 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 19:59:16 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>
On 3/28/2025 7:12 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-28 01:04:45 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/27/2025 5:48 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 17:58:10 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>First one should define what the elements of that set could be.
On 3/26/2025 3:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-26 02:15:26 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What is "general" intended to mean here? In absense of any definition
Only general knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>On 3/25/2025 8:08 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/25 10:56 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/25/2025 5:19 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-22 17:53:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/22/2025 11:43 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-21 12:49:06 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>And human knowledge is not. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
On 3/21/2025 3:57 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 15:02:42 +0000, olcott said:
On 3/20/2025 8:09 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2025-03-20 02:42:53 +0000, olcott said:However, it is possible that someone finds a proof of the conjecture
Likewise there currently does not exist any finiteof the first order group theory can be proven.set of knowledge that can be expressed using language orIt is stipulated that analytic knowledge is limited to the
derived by applying truth preserving operations to elements
of this set. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> A simple example is the first order group theory.
is limited to applying truth preserving operations toWhen we begin with a set of basic facts and all inference
elements of this set then a True(X) predicate cannot possibly
be thwarted. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> There is no computable predicate that tells whether a sentence
proof that the Goldbach Conjecture is true or false
thus True(GC) is a type mismatch error. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
or its negation. Then the predicate True is no longer complete.
The set of all human general knowledge that can
be expressed using language gets updated. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we redefine logic systems such that they begin
with set of basic facts and are only allowed to
apply truth preserving operations to these basic
facts then every element of the system is provable
on the basis of these truth preserving operations.
However, it is possible (and, for sufficiently powerful sysems, certain)
that the provability is not computable. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
When we begin with basic facts and only apply truth preserving
to the giant semantic tautology of the set of human knowledge
that can be expressed using language then every element in this
set is reachable by these same truth preserving operations.
The set of human knowledge that can be expressed using language
is not a tautology. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What is taken to be knowledge might possibly be false.
What actually <is> knowledge is impossibly false by
definition.
How do you DEFINE what is actually knowledge? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
*This is a good first guess* >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The set of expressions of language that have the
semantic property of true that are written down >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somewhere.
We already know that many expressions of language that have the semantic
proerty of true are not written down anywhere. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
it is too vague to really mean anything. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Reverse-engineer how you could define a set of >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is finite rather than infinite. >>>>>>>>>>>>>>>>>>>>>>>>>>
If sentences, and there are not too many of them, a set of knowledge
could be presented as a book that contains those sentences and nothing
else.
A list of sentences would not make for efficient processing.
Unless you want to exclude uncertain facts the set of know facts is
small, probably empty. If you include many uncertain facts then
almost certainly your True(X) is true for some false X.
Yes of course there are no known facts it might be the case
that feline kittens have always been 15 story office buildings
and we have been deluded into thinking differently. >>>>>>>>>>>>>>>>>>>>>>>
A knowledge ontology inheritance hierarchy is most efficient.A good example is Newtonial mchanics, which is known to be wrong but is
However, there could be no uncertain sentences as they are not known
(sensu Olcotti).
Scientific theories would be uncertain truth. >>>>>>>>>>>>>>>>>>>>>>>>> It is a known fact that X evidence seems to make Y >>>>>>>>>>>>>>>>>>>>>>>>> a reasonably plausible possibility. >>>>>>>>>>>>>>>>>>>>>>>>
useful and used for practical purposes. How should your True(X) handle
that?
Understanding that Tarski has been refuted hardly counts as understandingThe set of everything that anyone ever wrote >>>>>>>>>>>>>>>>>>>>>>>>>>> down would be finite.
But not knowable.
Most of this would beBut we can't use it.
specific knowledge Pete's dog was named Bella. >>>>>>>>>>>>>>>>>>>>>>>>>>> Some is general dogs are animals. >>>>>>>>>>>>>>>>>>>>>>>>>>>
We can know that the set of general knowledge that canNo, but your "the set of expressions of language that have the semanticAe also know that many expressions of language that are written downFalse statements do not count as knowledge. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
somewhere lack the semantic property of true. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
property of true that are written down somewhere" is not useful because
there is no way to know that set. >>>>>>>>>>>>>>>>>>>>>>>>>>>
possibly be written down (formerly the analytic aspect
of the analytic/synthetic distinction) exists without
enumerating its elements. >>>>>>>>>>>>>>>>>>>>>>>>>>
We can use it right now to understand that Tarski >>>>>>>>>>>>>>>>>>>>>>>>> has been refuted and that True(X) does exist for >>>>>>>>>>>>>>>>>>>>>>>>> a specific and crucially relevant domain. >>>>>>>>>>>>>>>>>>>>>>>>
as Tarstki has not been refuted. >>>>>>>>>>>>>>>>>>>>>>>>
When Tarski said True(X) cannot be defined, he is proved wrong.
He didn't say that True(X) cannot be defined. He proved that no definition
defines a predicate that tells whether a sentence is true.
Mere more verbose way of saying the same thing. >>>>>>>>>>>>>>>>>>>>
existing predicate.
So, you think we can derive a non-true statement from truth preserving
If you rejectSince this <is> my own design, I do not reject it. >>>>>>>>>>>>>>>>>>>>
the idea that a sentence derived from true sentences with turth preserving
transformations is always true then you may disagree. >>>>>>>>>>>>>>>>>>>>>
operations on true sentences?
I think you just rejected your own logic by not understanding what you
are talking about.
No this is your ADD again.
That expressions of language derived only from >>>>>>>>>>>>>>>>>>> applying truth preserving operations to expressions >>>>>>>>>>>>>>>>>>> that are true are always true is necessarily true. >>>>>>>>>>>>>>>>>>>
But the problme is that you just rejected a sentence created by an
(infinite) chain of truth preserving operations. >>>>>>>>>>>>>>>>>>
As not in the domain.
WHy not?
You don't understand that unknown things are not in >>>>>>>>>>>>>>> the body of knowledge? The body of knowledge
Expressed in language INHERENTLY HAS A True(X) predicate. >>>>>>>>>>>>>>>
The body of knowledge that cannot be expressed in >>>>>>>>>>>>>>> language cannot have a True(X) predicate.
But they ARE in the logic system based on the body of knowledge as its
basic truths.
Provide a citation that says this.
You just don't understand what a logic system is.
IF you want to restrict your domain to just the body of knowledge, then
you have no "logic system" as you can't allow the logic system to
increase what it knows outside your initial knowledge, and your "truth
predicate" is defined in the wrong type of domain, and is misnamed, it
is just a knowledge predicate.
The actual body of knowledge that can be expressed in >>>>>>>>>>>>> language (a) Inherently has a True(X) predicate
(b) Is continuously and immediately updated.
No it doesn't, as a Truth Predicate needs to be over a domain of TRUTH,
which means the full output of a LOGIC SYSTEM, which you just denied
that you system has.
Even the system of computing the sum of finite
strings of numeric digits is a complete logic
system over its domain.
No, it isn't a *LOGIC* system, as it has no LOGIC, in that it has no >>>>>>>>>> INFERENCE operation.
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
Which isn't a "LOGIC", it is a COMPUTATION.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence >>>>>>>
But your "Computation" system isn't good enought to get there.
Your need a Turing Complete system, which yours isn't
In particular, your definition has no conditional operation.
Deterministic finite automatons have a lookup
table (like a JMP table) form of conditional
branches. I have an issued patent on a DFA.
This is the same kind of thing as a type hierarchy.
But your system didn't have that.
It just had a machine that adds two numbers together, and you used that >>>> limitiation to keep the creation of the unprovable truth,
A machine that can correctly answer the question:
How do we know that anthropogenic climate change
is real? (The body of knowledge expressed in language)
can do more than sum two numbers.
No, because we are talking about the machine you claimed:
It applies truth preserving operations to pairs of
finite strings of numeric digits deriving their sum.
It computes the mapping from inputs to outputs
as Turing computable functions must do.
If you have a machine that can do actual logic to try to prove your
statement, then it can do the full mathematics to allow Godel's proof,
and we have a true statement that can not be proven.
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting points of
Tarski's proof. You have ever claimed that any of Tarski's inferences
were not truth preserving. But you have claimed that the last one of
these truth preservin transformation has produced a false conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved
that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting points of >>>>>> Tarski's proof. You have ever claimed that any of Tarski's inferences >>>>>> were not truth preserving. But you have claimed that the last one of >>>>>> these truth preservin transformation has produced a false conclusion. >>>>>>
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved
that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from (1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly determine
about some axiom systems that they are inconsistent and fail on others.
The proof is just another proof that some function is not Turing
computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
On 4/2/2025 5:07 PM, Richard Damon wrote:
On 4/2/25 12:03 PM, olcott wrote:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly determine >>>> about some axiom systems that they are inconsistent and fail on others. >>>>
The proof is just another proof that some function is not Turing
computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
Think of how many statements can be constructed from a finite alphabet
of letters.
Can you "test" every statement to see if it is consistant?
Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent?
Try to come up with a better counter-example.
Sorry, you are just showing how limited your thinking ability actually
is.
That fact that YOU can't imagine the problem, doesn't mean it can be
there.
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a
way to
make a C program that can construct the proof or determine that
there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a
finite number of statements expressible in it, and thus it can't
handle most real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as
your "Basic Facts", and if you allow the system to create the concept
of the Natural Numbers, you can't verify that you don't actually have
a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
Your problem is you can't process what that means, because your mind
seems to obly understand the so basic logic system that actually can't
be inconsistant, but it also isn't actually useful for anything.
All you are doing is showing how ignorant you are of what you are
talking about.
On 4/2/2025 5:09 PM, Richard Damon wrote:
On 4/2/25 12:05 PM, olcott wrote:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting
points of
Tarski's proof. You have ever claimed that any of Tarski's
inferences
were not truth preserving. But you have claimed that the last
one of
these truth preservin transformation has produced a false
conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved >>>>>> that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from
(1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
And if (3) is false, then one of (1) or (2) must be false,
(1) is merely a false assumption that stands on its own.
and for those to be false it means some assumption that went into them
must be false, and the only assumption, other than the definition of
the logic system that he used, was that a Truth Predicate exists.
Thus, all you are doing is confirming his conclusion, and proving that
you just don't understand how logic actual works.
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make
your own
if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a
way to
make a C program that can construct the proof or determine that
there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a
finite number of statements expressible in it, and thus it can't
handle most real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as
your "Basic Facts", and if you allow the system to create the
concept of the Natural Numbers, you can't verify that you don't
actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].
On 4/2/2025 8:58 PM, Richard Damon wrote:
On 4/2/25 9:33 PM, olcott wrote:
On 4/2/2025 5:07 PM, Richard Damon wrote:
On 4/2/25 12:03 PM, olcott wrote:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving >>>>>>>> transformations is true. If you can prove that a true sentence >>>>>>>> is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly
determine
about some axiom systems that they are inconsistent and fail on
others.
The proof is just another proof that some function is not Turing
computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
Think of how many statements can be constructed from a finite
alphabet of letters.
Can you "test" every statement to see if it is consistant?
Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent?
Try to come up with a better counter-example.
It depends on what each of those letters mean.
So say what they mean to form your counter-example
showing that consistency across a finite set of axioms
is undecidable. PUT UP OR SHUT UP.
You should know better than that, but you don't, because you really
are too stupid.
On 4/2/2025 9:00 PM, Richard Damon wrote:
On 4/2/25 9:40 PM, olcott wrote:
On 4/2/2025 5:09 PM, Richard Damon wrote:
On 4/2/25 12:05 PM, olcott wrote:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting >>>>>>>>>> points of
Tarski's proof. You have ever claimed that any of Tarski's >>>>>>>>>> inferences
were not truth preserving. But you have claimed that the last >>>>>>>>>> one of
these truth preservin transformation has produced a false
conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved >>>>>>>> that there are unprovable true sentences. Tarski's work is about >>>>>>>> definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from
(1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
And if (3) is false, then one of (1) or (2) must be false,
(1) is merely a false assumption that stands on its own.
No, (1) is the result of a previous proof.
Prove that. I can prove otherwise. PUT UP OR SHUT UP
In accordance with the first
part of Th. I we can obtain ...
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to >>>> make a C program that can construct the proof or determine that there is >>>> none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite
number of statements expressible in it, and thus it can't handle most
real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your
"Basic Facts", and if you allow the system to create the concept of the
Natural Numbers, you can't verify that you don't actually have a
contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to >>>>>> make a C program that can construct the proof or determine that there is >>>>>> none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite >>>> number of statements expressible in it, and thus it can't handle most
real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your >>>> "Basic Facts", and if you allow the system to create the concept of the >>>> Natural Numbers, you can't verify that you don't actually have a
contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
On 4/2/2025 10:09 PM, Richard Damon wrote:
On 4/2/25 10:51 PM, olcott wrote:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make >>>>>>>> your own
if you think the logic used by the existing ones is not correct. >>>>>>>>
If the your logic system is sufficiently weak there may also be >>>>>>>> a way to
make a C program that can construct the proof or determine that >>>>>>>> there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a
finite number of statements expressible in it, and thus it can't
handle most real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as >>>>>> your "Basic Facts", and if you allow the system to create the
concept of the Natural Numbers, you can't verify that you don't
actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].
Wrong, Godel shows that having the properties of the Natural numbers
is enough.
They are merely an ordered set of finite strings of digits.
Show what property he uses that you can withhold and still have a
reasonably usable mathematics.
Your problem is you don't understand the power that basic logic gets
from the basic nature of the Natural Numbers.
On 4/2/2025 10:11 PM, Richard Damon wrote:
On 4/2/25 10:57 PM, olcott wrote:
On 4/2/2025 8:58 PM, Richard Damon wrote:
On 4/2/25 9:33 PM, olcott wrote:
On 4/2/2025 5:07 PM, Richard Damon wrote:
On 4/2/25 12:03 PM, olcott wrote:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving >>>>>>>>>> transformations is true. If you can prove that a true sentence >>>>>>>>>> is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly
determine
about some axiom systems that they are inconsistent and fail on >>>>>>>> others.
The proof is just another proof that some function is not Turing >>>>>>>> computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
Think of how many statements can be constructed from a finite
alphabet of letters.
Can you "test" every statement to see if it is consistant?
Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent?
Try to come up with a better counter-example.
It depends on what each of those letters mean.
So say what they mean to form your counter-example
showing that consistency across a finite set of axioms
is undecidable. PUT UP OR SHUT UP.
No. You are just going off on a Red Herring.
Show where your system defeats Godel's proof of the inability to prove
consistancy.
PUT UP OR SHUT UP.
*I am proved categorically correct*
A system that begins with A consistent set of
basic facts and only derives expressions from
this set by semantic logical entailment cannot
possibly have inconsistency.
If such a system could possibly have inconsistency
then at least one valid counter-example could
be provided showing this.
On 4/2/2025 10:13 PM, Richard Damon wrote:
On 4/2/25 10:59 PM, olcott wrote:
On 4/2/2025 9:00 PM, Richard Damon wrote:
On 4/2/25 9:40 PM, olcott wrote:
On 4/2/2025 5:09 PM, Richard Damon wrote:
On 4/2/25 12:05 PM, olcott wrote:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting >>>>>>>>>>>> points of
Tarski's proof. You have ever claimed that any of Tarski's >>>>>>>>>>>> inferences
were not truth preserving. But you have claimed that the >>>>>>>>>>>> last one of
these truth preservin transformation has produced a false >>>>>>>>>>>> conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X) >>>>>>>>>>> (what Tarski proved) when-so-ever True(X) ≡ Provable(X). >>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already >>>>>>>>>> proved
that there are unprovable true sentences. Tarski's work is about >>>>>>>>>> definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived
from (1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
And if (3) is false, then one of (1) or (2) must be false,
(1) is merely a false assumption that stands on its own.
No, (1) is the result of a previous proof.
Prove that. I can prove otherwise. PUT UP OR SHUT UP
The paragraph before that he says:
In accordance with the first
part of Th. I we can obtain ...
That shows that he is building that statement from his previous proof.
So, prove him wrong or PUT UP OR SHUT UP.
I merely have to prove that you are wrong
about deriving (1) from truth preserving operations. https://liarparadox.org/Tarski_247_248.pdf
On 4/3/2025 6:10 AM, Richard Damon wrote:
On 4/2/25 11:33 PM, olcott wrote:
On 4/2/2025 10:11 PM, Richard Damon wrote:
On 4/2/25 10:57 PM, olcott wrote:
On 4/2/2025 8:58 PM, Richard Damon wrote:
On 4/2/25 9:33 PM, olcott wrote:
On 4/2/2025 5:07 PM, Richard Damon wrote:
On 4/2/25 12:03 PM, olcott wrote:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven >>>>>>>>>>>>> false.
Anything that follows from true sentences by a truth preserving >>>>>>>>>>>> transformations is true. If you can prove that a true sentence >>>>>>>>>>>> is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is >>>>>>>>>> inconsistent
does not exist. However, there are methods that can correctly >>>>>>>>>> determine
about some axiom systems that they are inconsistent and fail >>>>>>>>>> on others.
The proof is just another proof that some function is not
Turing computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
Think of how many statements can be constructed from a finite
alphabet of letters.
Can you "test" every statement to see if it is consistant?
Is "LKNSDFKLWRLKLKNKUKQWEEYIYWQFGFGH" consistent or inconsistent? >>>>>>> Try to come up with a better counter-example.
It depends on what each of those letters mean.
So say what they mean to form your counter-example
showing that consistency across a finite set of axioms
is undecidable. PUT UP OR SHUT UP.
No. You are just going off on a Red Herring.
Show where your system defeats Godel's proof of the inability to
prove consistancy.
PUT UP OR SHUT UP.
*I am proved categorically correct*
A system that begins with A consistent set of
basic facts and only derives expressions from
this set by semantic logical entailment cannot
possibly have inconsistency.
If such a system could possibly have inconsistency
then at least one valid counter-example could
be provided showing this.
But how do you know that you began with a consistent set of basic
facts. That is the question. You just set yourself up with a circular
definition.
(a) Test them against each other (finite set)
(b) Test them against each other (finite set in a hierarchy of types)
You can't just define that a given set of facts are, in fact, consistant.
Note, that "Consistency" of the facts is only defined through the
logic system they create and it being consistent, so you are just
showing that if you assume the answer, you should be able to prove it.
Sorry, you are just showing you fundamentally don't understand what
you are talking about.
On 4/3/2025 2:03 AM, Mikko wrote:
On 2025-04-02 15:59:47 +0000, olcott said:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a
way to
make a C program that can construct the proof or determine that
there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But a proof of paraconsistency is required.
When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
It can if the set of basic facts is inconsistent or if the logical
entailment sematics is not sufficiently weak. Inconsistencies are
avoided if your system has no way to express logical negations
(which incudes negative quantification).
Stipulated basic facts + semantic logical entailment
guarantees True(X). When the basic facts do not contradict
each other then undecidability is impossible.
On 4/3/2025 2:08 AM, Mikko wrote:
On 2025-04-03 01:30:28 +0000, olcott said:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make
your own
if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a
way to
make a C program that can construct the proof or determine that
there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a
finite number of statements expressible in it, and thus it can't
handle most real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as
your "Basic Facts", and if you allow the system to create the
concept of the Natural Numbers, you can't verify that you don't
actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
That is generally believed but not actually proven.
they are essentially nothing more than an ordered
set of finite strings of digits.
The "nothing more" part cannot be proven.
It is a stipulated basic fact.
There is no way that elements of the set of natural
is anything more or less then an ordered set of
concepts that can be expressed in some way such as a
string of digits.
When we ADD the notion of arithmetic this notion
is added on top of the notion of an ordered set
of concepts.
In first order logic one cannot
We are still adding notions on top of the notion
of an ordered set of concepts.
even say that those strings must be finite.
It would seem to be a stipulated aspect of the
definition of natural number: ∀n ∈ ℕ (n ≠ ∞)
On 4/3/2025 6:06 AM, Richard Damon wrote:
On 4/3/25 12:27 AM, olcott wrote:
On 4/2/2025 10:09 PM, Richard Damon wrote:
On 4/2/25 10:51 PM, olcott wrote:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently >>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make >>>>>>>>>> your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>
If the your logic system is sufficiently weak there may also >>>>>>>>>> be a way to
make a C program that can construct the proof or determine >>>>>>>>>> that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a >>>>>>>> finite number of statements expressible in it, and thus it can't >>>>>>>> handle most real problems
A system entirely comprised of Basic Facts and Semantic logical >>>>>>>>> entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow >>>>>>>> as your "Basic Facts", and if you allow the system to create the >>>>>>>> concept of the Natural Numbers, you can't verify that you don't >>>>>>>> actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].
Wrong, Godel shows that having the properties of the Natural numbers
is enough.
They are merely an ordered set of finite strings of digits.
No, the Natural Numbers are NOT "finite strings" but that is just a
representation for them, and a given number can have many
representations.
And they are just an ordered set, but there are a number of semantic
properties of the members. Things like 2 + 3 is 5, and 2 * 3 is 6, and
that some numbers are called "prime" because the only way to decompose
them with multiplication is themselves times one, but other numbers
can be decomposed as the product of other numbers, and the set of
prime numbers (with their powers) has a one to one relationship to the
set of numbers, every product set resulting in just a single number
and every number having just a single product set.
From this, and the fact that a logic system that can support these
concepts WILL have a statement in it that is true and unprovable in
the system.
Natural numbers are merely an ordered set of concepts
that are associated with some form of encoding. Even
arithmetic is added on top of the notion of natural
numbers.
A simple algorithm can specify the operations required
to find the sum of pairs of strings of numeric digits.
This much cannot possibly result in undecidability or
incompleteness.
(a) Any consistent set of axioms that are stipulated to be true.
(b) Semantic logical entailment from these axioms
Cannot possibly have any undecidability.
This remains true when the formal language is as
expressive as natural language (such as English).
It also remains true for the entire body of
knowledge that can be expressed in language.
Show what property he uses that you can withhold and still have a
reasonably usable mathematics.
Your problem is you don't understand the power that basic logic gets
from the basic nature of the Natural Numbers.
On 4/2/2025 11:38 PM, dbush wrote:
On 4/3/2025 12:25 AM, olcott wrote:
On 4/2/2025 10:43 PM, dbush wrote:
We don't have to. It was scrutinized by many experts for decades.
The burden of proof is on YOU to show that it is wrong.
Appeal to authority is an error.
Tarski says that he does not derive (1)
by applying truth preserving operations.
LIAR:
On 4/2/2025 11:13 PM, Richard Damon wrote:
The paragraph before that he says:
;
In accordance with the first;
part of Th. I we can obtain ...
That shows that he is building that statement from his previous proof. >> >
So, prove him wrong or PUT UP OR SHUT UP.
<DIRECT QUOTE>
THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
class of expressions, is defined in the metatheory, it will be possible
to derive from it the negation of one of the sentences which were
described in the condition (α) of the convention T;
(β) assuming that the class of all provable sentences of the metatheory
is consistent, it is impossible to construct an adequate
definition of truth in the sense of convention T on the basis of the metatheory. ...
Should we succeed in constructing in the metalanguage
a correct definition of truth, then ...
It would
then be possible to reconstruct the antinomy of the liar in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
</DIRECT QUOTE>
https://liarparadox.org/Tarski_247_248.pdf
On 4/3/2025 6:15 AM, Richard Damon wrote:
On 4/2/25 11:37 PM, olcott wrote:
On 4/2/2025 10:13 PM, Richard Damon wrote:
On 4/2/25 10:59 PM, olcott wrote:
On 4/2/2025 9:00 PM, Richard Damon wrote:
On 4/2/25 9:40 PM, olcott wrote:
On 4/2/2025 5:09 PM, Richard Damon wrote:
On 4/2/25 12:05 PM, olcott wrote:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:Irrelevant. As Traski clearly points out, (3) can be derived >>>>>>>>>> from (1) and
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the >>>>>>>>>>>>>> starting points of
Tarski's proof. You have ever claimed that any of Tarski's >>>>>>>>>>>>>> inferences
were not truth preserving. But you have claimed that the >>>>>>>>>>>>>> last one of
these truth preservin transformation has produced a false >>>>>>>>>>>>>> conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X) >>>>>>>>>>>>> (what Tarski proved) when-so-ever True(X) ≡ Provable(X). >>>>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already >>>>>>>>>>>> proved
that there are unprovable true sentences. Tarski's work is >>>>>>>>>>>> about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails. >>>>>>>>>>
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
And if (3) is false, then one of (1) or (2) must be false,
(1) is merely a false assumption that stands on its own.
No, (1) is the result of a previous proof.
Prove that. I can prove otherwise. PUT UP OR SHUT UP
The paragraph before that he says:
In accordance with the first
part of Th. I we can obtain ...
That shows that he is building that statement from his previous proof. >>>>
So, prove him wrong or PUT UP OR SHUT UP.
I merely have to prove that you are wrong
about deriving (1) from truth preserving operations.
https://liarparadox.org/Tarski_247_248.pdf
So, you can't read the article you post?
<DIRECT QUOTE>
THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
class of expressions, is defined in the metatheory, it will be possible
to derive from it the negation of one of the sentences which were
described in the condition (α) of the convention T;
(β) assuming that the class of all provable sentences of the metatheory
is consistent, it is impossible to construct an adequate
definition of truth in the sense of convention T on the basis of the metatheory. ...
Should we succeed in constructing in the metalanguage
a correct definition of truth, then ...
It would
then be possible to reconstruct the antinomy of the liar in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
</DIRECT QUOTE>
https://liarparadox.org/Tarski_247_248.pdf
On 4/3/2025 5:12 PM, Richard Damon wrote:
On 4/3/25 5:26 PM, olcott wrote:
On 4/3/2025 6:06 AM, Richard Damon wrote:
On 4/3/25 12:27 AM, olcott wrote:
On 4/2/2025 10:09 PM, Richard Damon wrote:
On 4/2/25 10:51 PM, olcott wrote:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this >>>>>>>>>>>>> with pairs of finite strings then it becomes self-evidently >>>>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can >>>>>>>>>>>> make your own
if you think the logic used by the existing ones is not >>>>>>>>>>>> correct.
If the your logic system is sufficiently weak there may also >>>>>>>>>>>> be a way to
make a C program that can construct the proof or determine >>>>>>>>>>>> that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have >>>>>>>>>> a finite number of statements expressible in it, and thus it >>>>>>>>>> can't handle most real problems
A system entirely comprised of Basic Facts and Semantic
logical entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you
allow as your "Basic Facts", and if you allow the system to >>>>>>>>>> create the concept of the Natural Numbers, you can't verify >>>>>>>>>> that you don't actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].
Wrong, Godel shows that having the properties of the Natural
numbers is enough.
They are merely an ordered set of finite strings of digits.
No, the Natural Numbers are NOT "finite strings" but that is just a
representation for them, and a given number can have many
representations.
And they are just an ordered set, but there are a number of semantic
properties of the members. Things like 2 + 3 is 5, and 2 * 3 is 6,
and that some numbers are called "prime" because the only way to
decompose them with multiplication is themselves times one, but
other numbers can be decomposed as the product of other numbers, and
the set of prime numbers (with their powers) has a one to one
relationship to the set of numbers, every product set resulting in
just a single number and every number having just a single product set. >>>>
From this, and the fact that a logic system that can support these
concepts WILL have a statement in it that is true and unprovable in
the system.
Natural numbers are merely an ordered set of concepts
that are associated with some form of encoding. Even
arithmetic is added on top of the notion of natural
numbers.
Nope, that is part of the PROPERTIES of the Natural Numbers.
Note, given the ordered set, all the properties of the numbers fall
out from that definition, assuming you actually HAVE a logic system
that can deduce properties.
A simple algorithm can specify the operations required
to find the sum of pairs of strings of numeric digits.
This much cannot possibly result in undecidability or
incompleteness.
Because it is not a logic system.
The sum of a pair of natural numbers converts
them into a single natural number.
The most generic way to specify formal systems is
to see them as applying finite string transformations
to finite strings deriving other finite strings.
That is the essence from which:
(a) premises
(b) inference steps
(c) conclusion
is derived.
(a) Any consistent set of axioms that are stipulated to be true.
And the problem is how do you KNOW that you set of axioms are consistent?
(b) Semantic logical entailment from these axioms
Cannot possibly have any undecidability.
This remains true when the formal language is as
expressive as natural language (such as English).
It also remains true for the entire body of
knowledge that can be expressed in language.
Nope, as proven by Godel.
Sorry, you are just proving that you don't understand how logic works.
Show what property he uses that you can withhold and still have a
reasonably usable mathematics.
Your problem is you don't understand the power that basic logic
gets from the basic nature of the Natural Numbers.
On 4/3/2025 6:06 AM, Richard Damon wrote:
On 4/3/25 12:27 AM, olcott wrote:
On 4/2/2025 10:09 PM, Richard Damon wrote:
On 4/2/25 10:51 PM, olcott wrote:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently >>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite
number of statements expressible in it, and thus it can't handle most >>>>>>>> real problems
A system entirely comprised of Basic Facts and Semantic logical >>>>>>>>> entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your
"Basic Facts", and if you allow the system to create the concept of the
Natural Numbers, you can't verify that you don't actually have a >>>>>>>> contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
Basic facts and expressions semantically entailed
by the basic facts cannot have undecidability[math].
Wrong, Godel shows that having the properties of the Natural numbers is enough.
They are merely an ordered set of finite strings of digits.
No, the Natural Numbers are NOT "finite strings" but that is just a
representation for them, and a given number can have many
representations.
And they are just an ordered set, but there are a number of semantic
properties of the members. Things like 2 + 3 is 5, and 2 * 3 is 6, and
that some numbers are called "prime" because the only way to decompose
them with multiplication is themselves times one, but other numbers can
be decomposed as the product of other numbers, and the set of prime
numbers (with their powers) has a one to one relationship to the set of
numbers, every product set resulting in just a single number and every
number having just a single product set.
From this, and the fact that a logic system that can support these
concepts WILL have a statement in it that is true and unprovable in the
system.
Natural numbers are merely an ordered set of concepts
that are associated with some form of encoding.
Even
arithmetic is added on top of the notion of natural
numbers.
On 4/3/2025 2:08 AM, Mikko wrote:
On 2025-04-03 01:30:28 +0000, olcott said:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to >>>>>> make a C program that can construct the proof or determine that there is >>>>>> none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite >>>> number of statements expressible in it, and thus it can't handle most
real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your >>>> "Basic Facts", and if you allow the system to create the concept of the >>>> Natural Numbers, you can't verify that you don't actually have a
contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
That is generally believed but not actually proven.
they are essentially nothing more than an ordered
set of finite strings of digits.
The "nothing more" part cannot be proven.
It is a stipulated basic fact.
On 4/3/2025 2:03 AM, Mikko wrote:
On 2025-04-02 15:59:47 +0000, olcott said:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to >>>> make a C program that can construct the proof or determine that there is >>>> none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But a proof of paraconsistency is required.
When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.
On 4/3/2025 2:09 AM, Mikko wrote:
On 2025-04-03 02:51:32 +0000, olcott said:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct. >>>>>>>>
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite >>>>>> number of statements expressible in it, and thus it can't handle most >>>>>> real problems
A system entirely comprised of Basic Facts and Semantic logical
entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your >>>>>> "Basic Facts", and if you allow the system to create the concept of the >>>>>> Natural Numbers, you can't verify that you don't actually have a
contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
And you can't define it otherwise.
Yes it free to keeps its screwy definition just like
set theory until a superior alternative comes along,
then it may be renamed naive formal systems.
A consistent set of stipulated axioms combined with
semantic logical entailment as the only inference step
makes undecidability impossible.
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is inconsistent >> does not exist. However, there are methods that can correctly determine
about some axiom systems that they are inconsistent and fail on others.
The proof is just another proof that some function is not Turing computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting points of >>>>>> Tarski's proof. You have ever claimed that any of Tarski's inferences >>>>>> were not truth preserving. But you have claimed that the last one of >>>>>> these truth preservin transformation has produced a false conclusion. >>>>>>
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved
that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from (1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
On 4/5/2025 2:30 AM, Mikko wrote:
On 2025-04-03 18:59:15 +0000, olcott said:
On 4/3/2025 2:03 AM, Mikko wrote:
On 2025-04-02 15:59:47 +0000, olcott said:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make
your own
if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a
way to
make a C program that can construct the proof or determine that
there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But a proof of paraconsistency is required.
When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.
For that sort of system paraconsistency is possible, depending on
what else there is in the system.
https://en.wikipedia.org/wiki/Paraconsistent_logic
Starting with a consistent set of basic facts (AKA axioms)
while only allowing semantic logical entailment thus
truth preserving operations does not seem to allow
any contradictions, thus paraconsistency.
Try to provide a concrete counter-example.
On 4/5/2025 2:44 AM, Mikko wrote:
On 2025-04-02 16:03:32 +0000, olcott said:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly determine >>>> about some axiom systems that they are inconsistent and fail on others. >>>>
The proof is just another proof that some function is not Turing
computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
If ordinary logic is used it is sufficient to prove that there is
a sentence that cannot be proven in order to prove consistency or
to prove two sentences that contradict each other in order to prove
inconsistency. But if neither proof is known there is no method to
find one.
We are only talking about the inability to detect
that basic facts contradict each other. I need a
100% concrete example proving this that this is
sometimes impossible.
On 4/5/2025 2:48 AM, Mikko wrote:
On 2025-04-02 16:05:28 +0000, olcott said:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting
points of
Tarski's proof. You have ever claimed that any of Tarski's
inferences
were not truth preserving. But you have claimed that the last
one of
these truth preservin transformation has produced a false
conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved >>>>>> that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from
(1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
So you reject the principle that a truth preserving transfromation from
true sentences always produces a true sentence.
Tarski started with a false sentence, as I have shown.
<DIRECT QUOTE>
THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
class of expressions, is defined in the metatheory, it will be possible
to derive from it the negation of one of the sentences which were
described in the condition (α) of the convention T;
(β) assuming that the class of all provable sentences of the metatheory
is consistent, it is impossible to construct an adequate
definition of truth in the sense of convention T on the basis of the metatheory. ...
Should we succeed in constructing in the metalanguage
a correct definition of truth, then ...
It would
then be possible to reconstruct the antinomy of the liar in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
</DIRECT QUOTE>
https://liarparadox.org/Tarski_247_248.pdf
On 4/5/2025 2:20 AM, Mikko wrote:
On 2025-04-03 19:33:41 +0000, olcott said:
On 4/3/2025 2:09 AM, Mikko wrote:
On 2025-04-03 02:51:32 +0000, olcott said:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently >>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make >>>>>>>>>> your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>
If the your logic system is sufficiently weak there may also >>>>>>>>>> be a way to
make a C program that can construct the proof or determine >>>>>>>>>> that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a >>>>>>>> finite number of statements expressible in it, and thus it can't >>>>>>>> handle most real problems
A system entirely comprised of Basic Facts and Semantic logical >>>>>>>>> entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow >>>>>>>> as your "Basic Facts", and if you allow the system to create the >>>>>>>> concept of the Natural Numbers, you can't verify that you don't >>>>>>>> actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
And you can't define it otherwise.
Yes it free to keeps its screwy definition just like
set theory until a superior alternative comes along,
then it may be renamed naive formal systems.
A consistent set of stipulated axioms combined with
semantic logical entailment as the only inference step
makes undecidability impossible.
If semantic logical entaillment is allowed as an inference rule
the system is not formal.
Unless the full semantics is formalized syntactically
using something like Montague Grammar of natural language
semantics.
In order to be formal the system must
define "proof" as any string that satiisfies the syntactic rules
that the system specifies for proofs.
On 4/5/2025 3:03 PM, Richard Damon wrote:
On 4/5/25 1:51 PM, olcott wrote:
On 4/5/2025 2:30 AM, Mikko wrote:
On 2025-04-03 18:59:15 +0000, olcott said:
On 4/3/2025 2:03 AM, Mikko wrote:
On 2025-04-02 15:59:47 +0000, olcott said:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make >>>>>>>> your own
if you think the logic used by the existing ones is not correct. >>>>>>>>
If the your logic system is sufficiently weak there may also be >>>>>>>> a way to
make a C program that can construct the proof or determine that >>>>>>>> there is
none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But a proof of paraconsistency is required.
When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.
For that sort of system paraconsistency is possible, depending on
what else there is in the system.
https://en.wikipedia.org/wiki/Paraconsistent_logic
Starting with a consistent set of basic facts (AKA axioms)
while only allowing semantic logical entailment thus
truth preserving operations does not seem to allow
any contradictions, thus paraconsistency.
Try to provide a concrete counter-example.
Your problem is you are making the error of assuming the concluion.
You can't tell that you axioms ARE consistant excpet by proving that
the system itself is consistant,
Counter-factual. A system with a consistent set of basic
facts can possibly have inference rules that derive
inconsistency because these rules are less than perfectly
truth preserving.
On 4/5/2025 3:15 PM, Richard Damon wrote:
On 4/5/25 1:56 PM, olcott wrote:
On 4/5/2025 2:44 AM, Mikko wrote:
On 2025-04-02 16:03:32 +0000, olcott said:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving >>>>>>>> transformations is true. If you can prove that a true sentence >>>>>>>> is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly
determine
about some axiom systems that they are inconsistent and fail on
others.
The proof is just another proof that some function is not Turing
computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
If ordinary logic is used it is sufficient to prove that there is
a sentence that cannot be proven in order to prove consistency or
to prove two sentences that contradict each other in order to prove
inconsistency. But if neither proof is known there is no method to
find one.
We are only talking about the inability to detect
that basic facts contradict each other. I need a
100% concrete example proving this that this is
sometimes impossible.
Read Godel's proof.
Note, this follows from the incompleteness proof, as a proof of
consistency yields a proof of completeness and thus any set powerful
enough to be incomplete also can not prove its own consistancy.
We are not talking about a proof of consistency
of the whole system, only a proof of consistency
of a finite set of axioms. Simply test them against
each other.
On 4/5/2025 2:20 AM, Mikko wrote:
On 2025-04-03 19:33:41 +0000, olcott said:
On 4/3/2025 2:09 AM, Mikko wrote:
On 2025-04-03 02:51:32 +0000, olcott said:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently >>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make >>>>>>>>>> your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>
If the your logic system is sufficiently weak there may also >>>>>>>>>> be a way to
make a C program that can construct the proof or determine >>>>>>>>>> that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a >>>>>>>> finite number of statements expressible in it, and thus it can't >>>>>>>> handle most real problems
A system entirely comprised of Basic Facts and Semantic logical >>>>>>>>> entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow >>>>>>>> as your "Basic Facts", and if you allow the system to create the >>>>>>>> concept of the Natural Numbers, you can't verify that you don't >>>>>>>> actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
And you can't define it otherwise.
Yes it free to keeps its screwy definition just like
set theory until a superior alternative comes along,
then it may be renamed naive formal systems.
A consistent set of stipulated axioms combined with
semantic logical entailment as the only inference step
makes undecidability impossible.
If semantic logical entaillment is allowed as an inference rule
the system is not formal. In order to be formal the system must
define "proof" as any string that satiisfies the syntactic rules
that the system specifies for proofs.
This "baffled" Richard
https://en.wikipedia.org/wiki/Montague_grammar https://plato.stanford.edu/entries/montague-semantics/
Semantics as rich as natural language fully formalized
syntactically.
On 4/5/2025 3:20 PM, Richard Damon wrote:
On 4/5/25 2:01 PM, olcott wrote:
On 4/5/2025 2:48 AM, Mikko wrote:
On 2025-04-02 16:05:28 +0000, olcott said:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting >>>>>>>>>> points of
Tarski's proof. You have ever claimed that any of Tarski's >>>>>>>>>> inferences
were not truth preserving. But you have claimed that the last >>>>>>>>>> one of
these truth preservin transformation has produced a false
conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved >>>>>>>> that there are unprovable true sentences. Tarski's work is about >>>>>>>> definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from
(1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
So you reject the principle that a truth preserving transfromation from >>>> true sentences always produces a true sentence.
Tarski started with a false sentence, as I have shown.
<DIRECT QUOTE>
THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
class of expressions, is defined in the metatheory, it will be possible
to derive from it the negation of one of the sentences which were
described in the condition (α) of the convention T;
(β) assuming that the class of all provable sentences of the metatheory >>> is consistent, it is impossible to construct an adequate
definition of truth in the sense of convention T on the basis of the
metatheory. ...
Should we succeed in constructing in the metalanguage
a correct definition of truth, then ...
It would
then be possible to reconstruct the antinomy of the liar in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
</DIRECT QUOTE>
https://liarparadox.org/Tarski_247_248.pdf
But that Theorem has been proven, and isn't just a "false assumption",
and thus it is YOUR claim that is based on lies.
(1) x ∉ Provable if and only if p
I have just shown that Step (1) of the proof is a false assumption.
On 4/5/2025 2:20 AM, Mikko wrote:
On 2025-04-03 19:33:41 +0000, olcott said:
On 4/3/2025 2:09 AM, Mikko wrote:
On 2025-04-03 02:51:32 +0000, olcott said:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently >>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite
number of statements expressible in it, and thus it can't handle most >>>>>>>> real problems
A system entirely comprised of Basic Facts and Semantic logical >>>>>>>>> entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your
"Basic Facts", and if you allow the system to create the concept of the
Natural Numbers, you can't verify that you don't actually have a >>>>>>>> contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
And you can't define it otherwise.
Yes it free to keeps its screwy definition just like
set theory until a superior alternative comes along,
then it may be renamed naive formal systems.
A consistent set of stipulated axioms combined with
semantic logical entailment as the only inference step
makes undecidability impossible.
If semantic logical entaillment is allowed as an inference rule
the system is not formal.
Unless the full semantics is formalized syntactically
using something like Montague Grammar of natural language
semantics.
On 4/5/2025 5:19 PM, Richard Damon wrote:
On 4/5/25 4:58 PM, olcott wrote:
On 4/5/2025 2:20 AM, Mikko wrote:
On 2025-04-03 19:33:41 +0000, olcott said:
On 4/3/2025 2:09 AM, Mikko wrote:
On 2025-04-03 02:51:32 +0000, olcott said:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this >>>>>>>>>>>>> with pairs of finite strings then it becomes self-evidently >>>>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>>>
If the your logic system is sufficiently weak there may also be a way to
make a C program that can construct the proof or determine that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have a finite
number of statements expressible in it, and thus it can't handle most
real problems
A system entirely comprised of Basic Facts and Semantic logical >>>>>>>>>>> entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you allow as your
"Basic Facts", and if you allow the system to create the concept of the
Natural Numbers, you can't verify that you don't actually have a >>>>>>>>>> contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
And you can't define it otherwise.
Yes it free to keeps its screwy definition just like
set theory until a superior alternative comes along,
then it may be renamed naive formal systems.
A consistent set of stipulated axioms combined with
semantic logical entailment as the only inference step
makes undecidability impossible.
If semantic logical entaillment is allowed as an inference rule
the system is not formal. In order to be formal the system must
define "proof" as any string that satiisfies the syntactic rules
that the system specifies for proofs.
This "baffled" Richard
https://en.wikipedia.org/wiki/Montague_grammar
https://plato.stanford.edu/entries/montague-semantics/
Semantics as rich as natural language fully formalized
syntactically.
WHich doesn't "baffle" me, but doesn't define the LOGIC that the system
uses, a fact that seems to baffle you, because you just don't
understand what logic actually is.
Also note, this grammer doesn't remove the ambiguity inherent in the
meaning of the words used, and especially can't handle the cases where
the speaker was intentionally being vague to form a word play that
extends the meaning of the word.
It provides a system such that the full expressiveness
of natural language can be formalized thus enabling
the only inference step that my formal system architecture
requires: semantic logical entailment.
On 4/5/2025 2:30 AM, Mikko wrote:
On 2025-04-03 18:59:15 +0000, olcott said:
On 4/3/2025 2:03 AM, Mikko wrote:
On 2025-04-02 15:59:47 +0000, olcott said:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently
correct needing no proof.
There already are programs that check proofs. But you can make your own >>>>>> if you think the logic used by the existing ones is not correct.
If the your logic system is sufficiently weak there may also be a way to >>>>>> make a C program that can construct the proof or determine that there is >>>>>> none.
When we define a system that cannot possibly be inconsistent
then a proof of consistency not needed.
But a proof of paraconsistency is required.
When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.
For that sort of system paraconsistency is possible, depending on
what else there is in the system.
https://en.wikipedia.org/wiki/Paraconsistent_logic
Starting with a consistent set of basic facts (AKA axioms)
while only allowing semantic logical entailment thus
truth preserving operations does not seem to allow
any contradictions, thus paraconsistency.
Try to provide a concrete counter-example.
On 4/5/2025 2:44 AM, Mikko wrote:
On 2025-04-02 16:03:32 +0000, olcott said:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving
transformations is true. If you can prove that a true sentence
is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is inconsistent >>>> does not exist. However, there are methods that can correctly determine >>>> about some axiom systems that they are inconsistent and fail on others. >>>>
The proof is just another proof that some function is not Turing computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
If ordinary logic is used it is sufficient to prove that there is
a sentence that cannot be proven in order to prove consistency or
to prove two sentences that contradict each other in order to prove
inconsistency. But if neither proof is known there is no method to
find one.
We are only talking about the inability to detect
that basic facts contradict each other. I need a
100% concrete example proving this that this is
sometimes impossible.
On 4/5/2025 2:48 AM, Mikko wrote:
On 2025-04-02 16:05:28 +0000, olcott said:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting points of >>>>>>>> Tarski's proof. You have ever claimed that any of Tarski's inferences >>>>>>>> were not truth preserving. But you have claimed that the last one of >>>>>>>> these truth preservin transformation has produced a false conclusion. >>>>>>>>
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
(what Tarski proved) when-so-ever True(X) ≡ Provable(X).
https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already proved >>>>>> that there are unprovable true sentences. Tarski's work is about
definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived from (1) and >>>> (2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
So you reject the principle that a truth preserving transfromation from
true sentences always produces a true sentence.
Tarski started with a false sentence, as I have shown.
<DIRECT QUOTE>
THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
class of expressions, is defined in the metatheory, it will be possible
to derive from it the negation of one of the sentences which were
described in the condition (α) of the convention T;
(β) assuming that the class of all provable sentences of the metatheory
is consistent, it is impossible to construct an adequate
definition of truth in the sense of convention T on the basis of the metatheory. ...
Should we succeed in constructing in the metalanguage
a correct definition of truth, then ...
It would
then be possible to reconstruct the antinomy of the liar in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
</DIRECT QUOTE>
https://liarparadox.org/Tarski_247_248.pdf
On 4/5/2025 5:24 PM, Richard Damon wrote:
On 4/5/25 5:03 PM, olcott wrote:No it is not. The axioms can be consistent and create
On 4/5/2025 3:15 PM, Richard Damon wrote:
On 4/5/25 1:56 PM, olcott wrote:
On 4/5/2025 2:44 AM, Mikko wrote:
On 2025-04-02 16:03:32 +0000, olcott said:
On 4/2/2025 4:32 AM, Mikko wrote:
On 2025-04-01 17:56:25 +0000, olcott said:
On 4/1/2025 1:33 AM, Mikko wrote:
On 2025-03-31 18:33:26 +0000, olcott said:
Anything the contradicts basic facts or expressions
semantically entailed from these basic facts is proven
false.
Anything that follows from true sentences by a truth preserving >>>>>>>>>> transformations is true. If you can prove that a true sentence >>>>>>>>>> is false your system is unsound.
Ah so we finally agree on something.
What about the "proof" that detecting inconsistent
axioms is impossible? (I thought that I remebered this).
A method that can always determine whether a set of axioms is
inconsistent
does not exist. However, there are methods that can correctly
determine
about some axiom systems that they are inconsistent and fail on >>>>>>>> others.
The proof is just another proof that some function is not Turing >>>>>>>> computable.
A finite set of axioms would seem to always be verifiable
as consistent or inconsistent. This may be the same for
a finite list of axiom schemas.
If ordinary logic is used it is sufficient to prove that there is
a sentence that cannot be proven in order to prove consistency or
to prove two sentences that contradict each other in order to
prove inconsistency. But if neither proof is known there is no
method to
find one.
We are only talking about the inability to detect
that basic facts contradict each other. I need a
100% concrete example proving this that this is
sometimes impossible.
Read Godel's proof.
Note, this follows from the incompleteness proof, as a proof of
consistency yields a proof of completeness and thus any set powerful
enough to be incomplete also can not prove its own consistancy.
We are not talking about a proof of consistency
of the whole system, only a proof of consistency
of a finite set of axioms. Simply test them against
each other.
But the test of consistency of the axioms is the test of the
consistency of the logic system they create.
an inconsistent system because the inference steps
are not truth preserving.
You just don't understand the meaning of the words you are using.
On 4/5/2025 5:22 PM, Richard Damon wrote:
On 4/5/25 5:01 PM, olcott wrote:
On 4/5/2025 3:03 PM, Richard Damon wrote:
On 4/5/25 1:51 PM, olcott wrote:
On 4/5/2025 2:30 AM, Mikko wrote:
On 2025-04-03 18:59:15 +0000, olcott said:
On 4/3/2025 2:03 AM, Mikko wrote:
On 2025-04-02 15:59:47 +0000, olcott said:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this
with pairs of finite strings then it becomes self-evidently >>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can make >>>>>>>>>> your own
if you think the logic used by the existing ones is not correct. >>>>>>>>>>
If the your logic system is sufficiently weak there may also >>>>>>>>>> be a way to
make a C program that can construct the proof or determine >>>>>>>>>> that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>> then a proof of consistency not needed.
But a proof of paraconsistency is required.
When it is stipulated that {cats} <are> {Animals}
When it is stipulated that {Animals} <are> {Living Things}
Then the complete proof of those is their stipulation.
AND {Cats} <are> {Living Things} is semantically entailed.
For that sort of system paraconsistency is possible, depending on
what else there is in the system.
https://en.wikipedia.org/wiki/Paraconsistent_logic
Starting with a consistent set of basic facts (AKA axioms)
while only allowing semantic logical entailment thus
truth preserving operations does not seem to allow
any contradictions, thus paraconsistency.
Try to provide a concrete counter-example.
Your problem is you are making the error of assuming the concluion.
You can't tell that you axioms ARE consistant excpet by proving that
the system itself is consistant,
Counter-factual. A system with a consistent set of basic
facts can possibly have inference rules that derive
inconsistency because these rules are less than perfectly
truth preserving.
How do you know your axioms are consistant?
You don't seem to understand that basic problem, because you are just
too stupid.
You can't stipulate that the axioms are consistent.
When tested against each other they have no
contradictions.
On 4/5/2025 5:26 PM, Richard Damon wrote:
On 4/5/25 5:08 PM, olcott wrote:
On 4/5/2025 3:20 PM, Richard Damon wrote:
On 4/5/25 2:01 PM, olcott wrote:
On 4/5/2025 2:48 AM, Mikko wrote:
On 2025-04-02 16:05:28 +0000, olcott said:
On 4/2/2025 4:43 AM, Mikko wrote:
On 2025-04-01 18:00:56 +0000, olcott said:
On 4/1/2025 1:36 AM, Mikko wrote:
On 2025-03-31 18:29:32 +0000, olcott said:
On 3/31/2025 4:04 AM, Mikko wrote:
On 2025-03-30 11:20:05 +0000, olcott said:
You have never expressed any disagreement with the starting >>>>>>>>>>>> points of
Tarski's proof. You have ever claimed that any of Tarski's >>>>>>>>>>>> inferences
were not truth preserving. But you have claimed that the >>>>>>>>>>>> last one of
these truth preservin transformation has produced a false >>>>>>>>>>>> conclusion.
It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X) >>>>>>>>>>> (what Tarski proved) when-so-ever True(X) ≡ Provable(X). >>>>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
Tarski's proof was not about provability. Gödel had already >>>>>>>>>> proved
that there are unprovable true sentences. Tarski's work is about >>>>>>>>>> definability.
https://liarparadox.org/Tarski_275_276.pdf
Step (3) is self-contradictory, thus his whole proof fails.
Irrelevant. As Traski clearly points out, (3) can be derived
from (1) and
(2) with a truth preserving transformation.
(3) is false, thus his whole proof is dead.
So you reject the principle that a truth preserving transfromation >>>>>> from
true sentences always produces a true sentence.
Tarski started with a false sentence, as I have shown.
<DIRECT QUOTE>
THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
class of expressions, is defined in the metatheory, it will be
possible
to derive from it the negation of one of the sentences which were
described in the condition (α) of the convention T;
(β) assuming that the class of all provable sentences of the
metatheory
is consistent, it is impossible to construct an adequate
definition of truth in the sense of convention T on the basis of the >>>>> metatheory. ...
Should we succeed in constructing in the metalanguage
a correct definition of truth, then ...
It would
then be possible to reconstruct the antinomy of the liar in the
metalanguage, by forming in the language itself a sentence x
such that the sentence of the metalanguage which is correlated
with x asserts that x is not a true sentence.
</DIRECT QUOTE>
https://liarparadox.org/Tarski_247_248.pdf
But that Theorem has been proven, and isn't just a "false
assumption", and thus it is YOUR claim that is based on lies.
(1) x ∉ Provable if and only if p
I have just shown that Step (1) of the proof is a false assumption.
And Godel proves that such a statement is creatable in the metasystem.
We can create lies in English, lies are not true.
We cannot create lies by applying semantic logical
entailment (SLE) to basic facts.
On 4/5/2025 5:19 PM, Richard Damon wrote:
On 4/5/25 4:58 PM, olcott wrote:
On 4/5/2025 2:20 AM, Mikko wrote:
On 2025-04-03 19:33:41 +0000, olcott said:
On 4/3/2025 2:09 AM, Mikko wrote:
On 2025-04-03 02:51:32 +0000, olcott said:
On 4/2/2025 8:56 PM, Richard Damon wrote:
On 4/2/25 9:30 PM, olcott wrote:
On 4/2/2025 5:05 PM, Richard Damon wrote:
On 4/2/25 11:59 AM, olcott wrote:
On 4/2/2025 4:20 AM, Mikko wrote:
On 2025-04-01 17:51:29 +0000, olcott said:
All we have to do is make a C program that does this >>>>>>>>>>>>> with pairs of finite strings then it becomes self-evidently >>>>>>>>>>>>> correct needing no proof.
There already are programs that check proofs. But you can >>>>>>>>>>>> make your own
if you think the logic used by the existing ones is not >>>>>>>>>>>> correct.
If the your logic system is sufficiently weak there may also >>>>>>>>>>>> be a way to
make a C program that can construct the proof or determine >>>>>>>>>>>> that there is
none.
When we define a system that cannot possibly be inconsistent >>>>>>>>>>> then a proof of consistency not needed.
But you can't do that unless you limit the system to only have >>>>>>>>>> a finite number of statements expressible in it, and thus it >>>>>>>>>> can't handle most real problems
A system entirely comprised of Basic Facts and Semantic
logical entailment cannot possibly be inconsistent.
Sure it can.
The problem is you need to be very careful about what you
allow as your "Basic Facts", and if you allow the system to >>>>>>>>>> create the concept of the Natural Numbers, you can't verify >>>>>>>>>> that you don't actually have a contradition in it.
It never has been that natural numbers have
ever actually had any inconsistency themselves
they are essentially nothing more than an ordered
set of finite strings of digits.
No, but any logic system that can support them
Can be defined in screwy that has undecidability
or not defined in this screwy way.
And you can't define it otherwise.
Yes it free to keeps its screwy definition just like
set theory until a superior alternative comes along,
then it may be renamed naive formal systems.
A consistent set of stipulated axioms combined with
semantic logical entailment as the only inference step
makes undecidability impossible.
If semantic logical entaillment is allowed as an inference rule
the system is not formal. In order to be formal the system must
define "proof" as any string that satiisfies the syntactic rules
that the system specifies for proofs.
This "baffled" Richard
https://en.wikipedia.org/wiki/Montague_grammar
https://plato.stanford.edu/entries/montague-semantics/
Semantics as rich as natural language fully formalized
syntactically.
WHich doesn't "baffle" me, but doesn't define the LOGIC that the
system uses, a fact that seems to baffle you, because you just don't
understand what logic actually is.
Also note, this grammer doesn't remove the ambiguity inherent in the
meaning of the words used, and especially can't handle the cases where
the speaker was intentionally being vague to form a word play that
extends the meaning of the word.
It provides a system such that the full expressiveness
of natural language can be formalized thus enabling
the only inference step that my formal system architecture
requires: semantic logical entailment.
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 715 |
| Nodes: | 16 (2 / 14) |
| Uptime: | 27:05:32 |
| Calls: | 12,106 |
| Calls today: | 6 |
| Files: | 15,006 |
| Messages: | 6,518,203 |