Within the entire body of analytical truth any expression of language
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
In other words when any expression of language of any system (formal or informal) has no semantic connection to its semantic meaning in this
system then this expression is simply nonsense in this system. "This
sentence is untrue" is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Within the entire body of analytical truth any expression of language
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression of language
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
In other words when any expression of language of any system (formal
or informal) has no semantic connection to its semantic meaning in
this system then this expression is simply nonsense in this system.
"This sentence is untrue" is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which are TRUE,
because there is a sequence of formal semantic deduction that reaches
the statement, abet an infinite one, but there is no finite sequnce of
formal semantic deduction to form a proof.
That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.
What-so-ever makes an expression true <is> its philosophical
truth maker and thus is proof in the broadest sense of the
term {proof}, not the narrow mathematical idiomatic sense.
You are just so ignorant about the distinction between knowledge and
truth, that you can't make that distinction.
And this stupidity blinds you to the logic that you are trying to
manipulate, so you just prove that stupidity.
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of language
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
If there is a misconception then you have misconceived something. It
is well
known that it is possible to construct a formal theory where some
formulas
are neither provble nor disprovable.
This is well known. What is not so widely known is that this
is only possible because process defining what is referred to
as a math proof intentionally leaves out key required elements
that would otherwise make it complete.
Any expression of language that lacks a sequence of semantic
deductive inference steps from the basic facts stipulated truths
of this system to this expression is simply untrue in this system.
Using another more expressive system to show that the expression
is true in this other system does not make the expression true in
the original system.
Often that is done intentionally in
order to make the theory applicable to situations where some such
sentence
is true as well as to situations where the same sentence is false.
Thus incompleteness is intentional incoherence that can always be
prevented.
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression of
language that has no sequence of formalized semantic deductive
inference steps from the formalized semantic foundational truths of
this system are simply untrue in this system. (Isomorphic to
provable from axioms).
In other words when any expression of language of any system
(formal or informal) has no semantic connection to its semantic
meaning in this system then this expression is simply nonsense in
this system. "This sentence is untrue" is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which are TRUE,
because there is a sequence of formal semantic deduction that
reaches the statement, abet an infinite one, but there is no finite
sequnce of formal semantic deduction to form a proof.
That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.
What was left out?
If there exists no contiguous sequence of semantic deductive inference
steps from the basic facts of a system establishing that the semantic
meaning of this expression has a value of Boolean true in this system
then this expression is simply not true in this system even if it may be
true in other more expressive systems.
The system is incomplete in the artificially contrivance way of
deliberately defined system to be insufficiently expressive.
On 1/31/2025 10:08 AM, Richard Damon wrote:
On 1/31/25 10:20 AM, olcott wrote:
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression of
language that has no sequence of formalized semantic deductive
inference steps from the formalized semantic foundational truths >>>>>>> of this system are simply untrue in this system. (Isomorphic to
provable from axioms).
In other words when any expression of language of any system
(formal or informal) has no semantic connection to its semantic
meaning in this system then this expression is simply nonsense in >>>>>>> this system. "This sentence is untrue" is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which are
TRUE, because there is a sequence of formal semantic deduction
that reaches the statement, abet an infinite one, but there is no
finite sequnce of formal semantic deduction to form a proof.
That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.
What was left out?
If there exists no contiguous sequence of semantic deductive inference
steps from the basic facts of a system establishing that the semantic
meaning of this expression has a value of Boolean true in this system
then this expression is simply not true in this system even if it may be >>> true in other more expressive systems.
The system is incomplete in the artificially contrivance way of
deliberately defined system to be insufficiently expressive.
And what about the fact that ther *IS* a contiguos sequence, infinite
in length, that makes the statement true that you don't understand.
"Incomplete" means that there is no contiguous sequence of inference
steps within the expressiveness of this specific formal system.
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of language
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
If there is a misconception then you have misconceived something. It is well >> known that it is possible to construct a formal theory where some formulas >> are neither provble nor disprovable.
This is well known.
What is not so widely known is that this is only possible because process defining what is referred to as a math proof intentionally leaves out key required elements that would otherwise make it complete.
On 1/31/2025 7:52 PM, Richard Damon wrote:
On 1/31/25 12:42 PM, olcott wrote:
On 1/31/2025 10:08 AM, Richard Damon wrote:
On 1/31/25 10:20 AM, olcott wrote:
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression of >>>>>>>>> language that has no sequence of formalized semantic deductive >>>>>>>>> inference steps from the formalized semantic foundational
truths of this system are simply untrue in this system.
(Isomorphic to provable from axioms).
In other words when any expression of language of any system >>>>>>>>> (formal or informal) has no semantic connection to its semantic >>>>>>>>> meaning in this system then this expression is simply nonsense >>>>>>>>> in this system. "This sentence is untrue" is Boolean nonsense. >>>>>>>>>
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which are
TRUE, because there is a sequence of formal semantic deduction >>>>>>>> that reaches the statement, abet an infinite one, but there is >>>>>>>> no finite sequnce of formal semantic deduction to form a proof. >>>>>>>>
That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.
What was left out?
If there exists no contiguous sequence of semantic deductive inference >>>>> steps from the basic facts of a system establishing that the
semantic meaning of this expression has a value of Boolean true in
this system then this expression is simply not true in this system
even if it may be
true in other more expressive systems.
The system is incomplete in the artificially contrivance way of
deliberately defined system to be insufficiently expressive.
And what about the fact that ther *IS* a contiguos sequence,
infinite in length, that makes the statement true that you don't
understand.
"Incomplete" means that there is no contiguous sequence of inference
steps within the expressiveness of this specific formal system.
No, "Incomplete" means that there is some true statement that can not
be proven.
Within empirical truth this is possible.
Within analytical truth this is impossible.
Unless there is a semantic connection with
a truthmaker to what makes the expression
true IS IS NOT TRUE.
This is "proof" in the big sense of the term,
not the term-of-the-art thus idiomatic mathematical
meaning.
On 2/1/2025 7:56 AM, Richard Damon wrote:
On 1/31/25 10:43 PM, olcott wrote:
On 1/31/2025 7:52 PM, Richard Damon wrote:
On 1/31/25 12:42 PM, olcott wrote:
On 1/31/2025 10:08 AM, Richard Damon wrote:
On 1/31/25 10:20 AM, olcott wrote:
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression of >>>>>>>>>>> language that has no sequence of formalized semantic
deductive inference steps from the formalized semantic
foundational truths of this system are simply untrue in this >>>>>>>>>>> system. (Isomorphic to provable from axioms).
In other words when any expression of language of any system >>>>>>>>>>> (formal or informal) has no semantic connection to its
semantic meaning in this system then this expression is
simply nonsense in this system. "This sentence is untrue" is >>>>>>>>>>> Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which are >>>>>>>>>> TRUE, because there is a sequence of formal semantic deduction >>>>>>>>>> that reaches the statement, abet an infinite one, but there is >>>>>>>>>> no finite sequnce of formal semantic deduction to form a proof. >>>>>>>>>>
That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.
What was left out?
If there exists no contiguous sequence of semantic deductive
inference
steps from the basic facts of a system establishing that the
semantic meaning of this expression has a value of Boolean true
in this system then this expression is simply not true in this
system even if it may be
true in other more expressive systems.
The system is incomplete in the artificially contrivance way of
deliberately defined system to be insufficiently expressive.
And what about the fact that ther *IS* a contiguos sequence,
infinite in length, that makes the statement true that you don't
understand.
"Incomplete" means that there is no contiguous sequence of inference >>>>> steps within the expressiveness of this specific formal system.
No, "Incomplete" means that there is some true statement that can
not be proven.
Within empirical truth this is possible.
Within analytical truth this is impossible.
No, you only think it is impossible, becuase you don't know what you
are talking about.
Unless there is a semantic connection with
a truthmaker to what makes the expression
true IS IS NOT TRUE.
Right, and that can be an INFINITE series of connection, which thus
don't form a proof.
It does make a {proof} within the foundational base meaning
of the term {proof} even though it may not meet the idiomatic
term-of-the-art meaning from math. The generic notion of {Truth}
itself is only defined in terms of base meanings. When math
diverges from this it is no longer talking about actual truth.
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of
language that has no sequence of formalized semantic deductive
inference steps from the formalized semantic foundational truths of
this system are simply untrue in this system. (Isomorphic to
provable from axioms).
If there is a misconception then you have misconceived something. It
is well
known that it is possible to construct a formal theory where some
formulas
are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false.
a fact or piece of information that shows that something
exists or is true: https://dictionary.cambridge.org/us/dictionary/english/proof
When you disallow assigning different idiomatic meanings to terms-of
the-art such that the term "proof" retains every nuance of its base
meaning and not allowed to diverge from this meaning at all then every expression of language that is only made true (by a connection through
its philosophical truth maker) to its verbalized semantic meaning must necessarily remain untrue when it lacks such a connection.
What is not so widely known is that this is only possible because
process
defining what is referred to as a math proof intentionally leaves out
key
required elements that would otherwise make it complete.
Wrong. The result is the same if the omission is unintentional. For
example,
Peano did not intentionally leave anything out in order to make an
incomplete
theory. Only later Gödel found out that Peano's theory is incomplete.
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of language >>>>> that has no sequence of formalized semantic deductive inference steps >>>>> from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
If there is a misconception then you have misconceived something. It is well
known that it is possible to construct a formal theory where some formulas >>>> are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false.
a fact or piece of information that shows that something
exists or is true: https://dictionary.cambridge.org/us/dictionary/english/proof
On 2/2/2025 3:27 AM, Mikko wrote:
On 2025-02-01 14:09:54 +0000, olcott said:
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of language >>>>>>> that has no sequence of formalized semantic deductive inference steps >>>>>>> from the formalized semantic foundational truths of this system are >>>>>>> simply untrue in this system. (Isomorphic to provable from axioms). >>>>>>If there is a misconception then you have misconceived something. It is well
known that it is possible to construct a formal theory where some formulas
are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false.
a fact or piece of information that shows that something
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof
We require that terms of art are used with their term-of-art meaning and
The fundamental base meaning of Truth[0] itself remains the same
no matter what idiomatic meanings say.
On 2/1/2025 12:23 PM, Richard Damon wrote:
On 2/1/25 1:10 PM, olcott wrote:
On 2/1/2025 7:56 AM, Richard Damon wrote:
On 1/31/25 10:43 PM, olcott wrote:
On 1/31/2025 7:52 PM, Richard Damon wrote:
On 1/31/25 12:42 PM, olcott wrote:
On 1/31/2025 10:08 AM, Richard Damon wrote:
On 1/31/25 10:20 AM, olcott wrote:
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression >>>>>>>>>>>>> of language that has no sequence of formalized semantic >>>>>>>>>>>>> deductive inference steps from the formalized semantic >>>>>>>>>>>>> foundational truths of this system are simply untrue in >>>>>>>>>>>>> this system. (Isomorphic to provable from axioms).
In other words when any expression of language of any >>>>>>>>>>>>> system (formal or informal) has no semantic connection to >>>>>>>>>>>>> its semantic meaning in this system then this expression is >>>>>>>>>>>>> simply nonsense in this system. "This sentence is untrue" >>>>>>>>>>>>> is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which >>>>>>>>>>>> are TRUE, because there is a sequence of formal semantic >>>>>>>>>>>> deduction that reaches the statement, abet an infinite one, >>>>>>>>>>>> but there is no finite sequnce of formal semantic deduction >>>>>>>>>>>> to form a proof.
That might be correct. If it is correct then all then
all that it is really saying is that math is incomplete
because some key pieces were intentionally left out.
What was left out?
If there exists no contiguous sequence of semantic deductive >>>>>>>>> inference
steps from the basic facts of a system establishing that the >>>>>>>>> semantic meaning of this expression has a value of Boolean true >>>>>>>>> in this system then this expression is simply not true in this >>>>>>>>> system even if it may be
true in other more expressive systems.
The system is incomplete in the artificially contrivance way of >>>>>>>>> deliberately defined system to be insufficiently expressive. >>>>>>>>>
And what about the fact that ther *IS* a contiguos sequence,
infinite in length, that makes the statement true that you don't >>>>>>>> understand.
"Incomplete" means that there is no contiguous sequence of inference >>>>>>> steps within the expressiveness of this specific formal system.
No, "Incomplete" means that there is some true statement that can
not be proven.
Within empirical truth this is possible.
Within analytical truth this is impossible.
No, you only think it is impossible, becuase you don't know what you
are talking about.
Unless there is a semantic connection with
a truthmaker to what makes the expression
true IS IS NOT TRUE.
Right, and that can be an INFINITE series of connection, which thus
don't form a proof.
It does make a {proof} within the foundational base meaning
of the term {proof} even though it may not meet the idiomatic
term-of-the-art meaning from math. The generic notion of {Truth}
itself is only defined in terms of base meanings. When math
diverges from this it is no longer talking about actual truth.
The "foundational base meaning" of a proof in Formal Logic is a FINITE
series.
True[0] cannot possibly exist for any expression of language that
is only made true by a semantic connection to its truthmaker.
This makes the notion of provable[math] essentially a misnomer
because it attempts to override and supersede the most basic
foundation of the notion of truth itself.
I know of no standard theory of logic that admits an infinite series
of steps as a "proof", as we can not do an infinite series of steps,
and a proof is normally about knowledge, and thus needs to be about
something that we can actually do.
We can do a finite series of steps to show that an infinite series of
steps exist in another system by the properties of meta-logic, but
that is not a "proof" in that other system, only in the meta-system,
again something that seems to be beyond your understanding.
And, you are wrong that "truth" only has a single base meaning, as
Truth is established by several different meanings each given a
different "class" of Truth.
I'm sorry, but you are just showing that you don't really understand
the terms you are using, and tha that you don't even have enough of a
basis to understand that you don't understand the terms.
You HAVE been shown this, and your repeatedly repeating the same
proven false claims just shows that you are totally ignorant of what
you talk about, and have no concern about the actual meaning of Truth.
This shows that you native tounge is that of your "father", the tounge
of lies, which you try your best to sprea.
Sorry that you are sealing your fate, which you are likely going to
see sooner than you want.
On 2/3/2025 9:07 AM, Mikko wrote:
On 2025-02-03 03:30:46 +0000, olcott said:
On 2/2/2025 3:27 AM, Mikko wrote:
On 2025-02-01 14:09:54 +0000, olcott said:The fundamental base meaning of Truth[0] itself remains the same
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of language >>>>>>>>> that has no sequence of formalized semantic deductive inference steps >>>>>>>>> from the formalized semantic foundational truths of this system are >>>>>>>>> simply untrue in this system. (Isomorphic to provable from axioms). >>>>>>>>If there is a misconception then you have misconceived something. It is well
known that it is possible to construct a formal theory where some formulas
are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false.
a fact or piece of information that shows that something
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof
We require that terms of art are used with their term-of-art meaning and >>>
no matter what idiomatic meanings say.
Irrelevant as the subject line does not mention truth.
Therefore, no need to revise my initial comment.
The notion of truth is entailed by the subject line:
misconception means ~True.
On 2/4/2025 3:22 AM, Mikko wrote:
On 2025-02-03 16:54:08 +0000, olcott said:
On 2/3/2025 9:07 AM, Mikko wrote:
On 2025-02-03 03:30:46 +0000, olcott said:
On 2/2/2025 3:27 AM, Mikko wrote:
On 2025-02-01 14:09:54 +0000, olcott said:The fundamental base meaning of Truth[0] itself remains the same
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of languageIf there is a misconception then you have misconceived something. It is well
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are >>>>>>>>>>> simply untrue in this system. (Isomorphic to provable from axioms). >>>>>>>>>>
known that it is possible to construct a formal theory where some formulas
are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false.
a fact or piece of information that shows that something
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof
We require that terms of art are used with their term-of-art meaning and >>>>>
no matter what idiomatic meanings say.
Irrelevant as the subject line does not mention truth.
Therefore, no need to revise my initial comment.
The notion of truth is entailed by the subject line:
misconception means ~True.
The title line means that something is misunderstood but that something
is not the meaning of "true".
It is untrue because it is misunderstood.
On 2/3/2025 6:39 PM, Richard Damon wrote:
On 2/3/25 12:00 PM, olcott wrote:
On 2/1/2025 12:23 PM, Richard Damon wrote:
On 2/1/25 1:10 PM, olcott wrote:
On 2/1/2025 7:56 AM, Richard Damon wrote:
On 1/31/25 10:43 PM, olcott wrote:
On 1/31/2025 7:52 PM, Richard Damon wrote:
On 1/31/25 12:42 PM, olcott wrote:
On 1/31/2025 10:08 AM, Richard Damon wrote:
On 1/31/25 10:20 AM, olcott wrote:
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any expression >>>>>>>>>>>>>>> of language that has no sequence of formalized semantic >>>>>>>>>>>>>>> deductive inference steps from the formalized semantic >>>>>>>>>>>>>>> foundational truths of this system are simply untrue in >>>>>>>>>>>>>>> this system. (Isomorphic to provable from axioms). >>>>>>>>>>>>>>>
In other words when any expression of language of any >>>>>>>>>>>>>>> system (formal or informal) has no semantic connection to >>>>>>>>>>>>>>> its semantic meaning in this system then this expression >>>>>>>>>>>>>>> is simply nonsense in this system. "This sentence is >>>>>>>>>>>>>>> untrue" is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements which >>>>>>>>>>>>>> are TRUE, because there is a sequence of formal semantic >>>>>>>>>>>>>> deduction that reaches the statement, abet an infinite >>>>>>>>>>>>>> one, but there is no finite sequnce of formal semantic >>>>>>>>>>>>>> deduction to form a proof.
That might be correct. If it is correct then all then >>>>>>>>>>>>> all that it is really saying is that math is incomplete >>>>>>>>>>>>> because some key pieces were intentionally left out.
What was left out?
If there exists no contiguous sequence of semantic deductive >>>>>>>>>>> inference
steps from the basic facts of a system establishing that the >>>>>>>>>>> semantic meaning of this expression has a value of Boolean >>>>>>>>>>> true in this system then this expression is simply not true >>>>>>>>>>> in this system even if it may be
true in other more expressive systems.
The system is incomplete in the artificially contrivance way of >>>>>>>>>>> deliberately defined system to be insufficiently expressive. >>>>>>>>>>>
And what about the fact that ther *IS* a contiguos sequence, >>>>>>>>>> infinite in length, that makes the statement true that you >>>>>>>>>> don't understand.
"Incomplete" means that there is no contiguous sequence of
inference
steps within the expressiveness of this specific formal system. >>>>>>>>>
No, "Incomplete" means that there is some true statement that
can not be proven.
Within empirical truth this is possible.
Within analytical truth this is impossible.
No, you only think it is impossible, becuase you don't know what
you are talking about.
Unless there is a semantic connection with
a truthmaker to what makes the expression
true IS IS NOT TRUE.
Right, and that can be an INFINITE series of connection, which
thus don't form a proof.
It does make a {proof} within the foundational base meaning
of the term {proof} even though it may not meet the idiomatic
term-of-the-art meaning from math. The generic notion of {Truth}
itself is only defined in terms of base meanings. When math
diverges from this it is no longer talking about actual truth.
The "foundational base meaning" of a proof in Formal Logic is a
FINITE series.
True[0] cannot possibly exist for any expression of language that
is only made true by a semantic connection to its truthmaker.
Which can be a connection of infinite length.
This makes the notion of provable[math] essentially a misnomer
because it attempts to override and supersede the most basic
foundation of the notion of truth itself.
But provable is a statment about the existance of a FINITE sequence of
connection
That IS NOT what Proof[0] means.
Proof[0] means that a connection to a truth-maker exists.
On 2/5/2025 1:44 AM, Mikko wrote:
On 2025-02-04 16:11:08 +0000, olcott said:
On 2/4/2025 3:22 AM, Mikko wrote:
On 2025-02-03 16:54:08 +0000, olcott said:
On 2/3/2025 9:07 AM, Mikko wrote:
On 2025-02-03 03:30:46 +0000, olcott said:
On 2/2/2025 3:27 AM, Mikko wrote:
On 2025-02-01 14:09:54 +0000, olcott said:
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:a fact or piece of information that shows that something
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression >>>>>>>>>>>>> of language that has no sequence of formalized semantic >>>>>>>>>>>>> deductive inference steps from the formalized semantic >>>>>>>>>>>>> foundational truths of this system are simply untrue in >>>>>>>>>>>>> this system. (Isomorphic to provable from axioms).
If there is a misconception then you have misconceived >>>>>>>>>>>> something. It is well
known that it is possible to construct a formal theory where >>>>>>>>>>>> some formulas
are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false. >>>>>>>>>
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof
We require that terms of art are used with their term-of-art
meaning and
The fundamental base meaning of Truth[0] itself remains the same >>>>>>> no matter what idiomatic meanings say.
Irrelevant as the subject line does not mention truth.
Therefore, no need to revise my initial comment.
The notion of truth is entailed by the subject line:
misconception means ~True.
The title line means that something is misunderstood but that something >>>> is not the meaning of "true".
It is untrue because it is misunderstood.
Mathematical incompleteness is not a claim so it cannot be untrue.
That mathematical incompleteness coherently exists <is> claim.
The closest that it can possibly be interpreted as true would
be that because key elements of proof[0] have been specified
as not existing in proof[math] math is intentionally made less
than complete.
When-so-ever any expression of formal or natural language X lacks
a connection to its truthmaker X remains untrue.
On 2/5/2025 6:08 AM, Richard Damon wrote:
On 2/4/25 11:30 PM, olcott wrote:
On 2/3/2025 6:39 PM, Richard Damon wrote:
On 2/3/25 12:00 PM, olcott wrote:
On 2/1/2025 12:23 PM, Richard Damon wrote:
On 2/1/25 1:10 PM, olcott wrote:
On 2/1/2025 7:56 AM, Richard Damon wrote:
On 1/31/25 10:43 PM, olcott wrote:
On 1/31/2025 7:52 PM, Richard Damon wrote:
On 1/31/25 12:42 PM, olcott wrote:
On 1/31/2025 10:08 AM, Richard Damon wrote:
On 1/31/25 10:20 AM, olcott wrote:
On 1/31/2025 8:49 AM, Richard Damon wrote:
On 1/30/25 8:24 PM, olcott wrote:
On 1/30/2025 7:06 PM, Richard Damon wrote:What was left out?
On 1/30/25 6:10 PM, olcott wrote:
Within the entire body of analytical truth any >>>>>>>>>>>>>>>>> expression of language that has no sequence of >>>>>>>>>>>>>>>>> formalized semantic deductive inference steps from the >>>>>>>>>>>>>>>>> formalized semantic foundational truths of this system >>>>>>>>>>>>>>>>> are simply untrue in this system. (Isomorphic to >>>>>>>>>>>>>>>>> provable from axioms).
In other words when any expression of language of any >>>>>>>>>>>>>>>>> system (formal or informal) has no semantic connection >>>>>>>>>>>>>>>>> to its semantic meaning in this system then this >>>>>>>>>>>>>>>>> expression is simply nonsense in this system. "This >>>>>>>>>>>>>>>>> sentence is untrue" is Boolean nonsense.
Copyright PL Olcott 2016 through 2025.
Except that isn't what incompleteness says.
Incompleteness is about the existance of statements >>>>>>>>>>>>>>>> which are TRUE, because there is a sequence of formal >>>>>>>>>>>>>>>> semantic deduction that reaches the statement, abet an >>>>>>>>>>>>>>>> infinite one, but there is no finite sequnce of formal >>>>>>>>>>>>>>>> semantic deduction to form a proof.
That might be correct. If it is correct then all then >>>>>>>>>>>>>>> all that it is really saying is that math is incomplete >>>>>>>>>>>>>>> because some key pieces were intentionally left out. >>>>>>>>>>>>>>
If there exists no contiguous sequence of semantic
deductive inference
steps from the basic facts of a system establishing that >>>>>>>>>>>>> the semantic meaning of this expression has a value of >>>>>>>>>>>>> Boolean true in this system then this expression is simply >>>>>>>>>>>>> not true in this system even if it may be
true in other more expressive systems.
The system is incomplete in the artificially contrivance >>>>>>>>>>>>> way of
deliberately defined system to be insufficiently expressive. >>>>>>>>>>>>>
And what about the fact that ther *IS* a contiguos sequence, >>>>>>>>>>>> infinite in length, that makes the statement true that you >>>>>>>>>>>> don't understand.
"Incomplete" means that there is no contiguous sequence of >>>>>>>>>>> inference
steps within the expressiveness of this specific formal system. >>>>>>>>>>>
No, "Incomplete" means that there is some true statement that >>>>>>>>>> can not be proven.
Within empirical truth this is possible.
Within analytical truth this is impossible.
No, you only think it is impossible, becuase you don't know what >>>>>>>> you are talking about.
Unless there is a semantic connection with
a truthmaker to what makes the expression
true IS IS NOT TRUE.
Right, and that can be an INFINITE series of connection, which >>>>>>>> thus don't form a proof.
It does make a {proof} within the foundational base meaning
of the term {proof} even though it may not meet the idiomatic
term-of-the-art meaning from math. The generic notion of {Truth} >>>>>>> itself is only defined in terms of base meanings. When math
diverges from this it is no longer talking about actual truth.
The "foundational base meaning" of a proof in Formal Logic is a
FINITE series.
True[0] cannot possibly exist for any expression of language that
is only made true by a semantic connection to its truthmaker.
Which can be a connection of infinite length.
This makes the notion of provable[math] essentially a misnomer
because it attempts to override and supersede the most basic
foundation of the notion of truth itself.
But provable is a statment about the existance of a FINITE sequence
of connection
That IS NOT what Proof[0] means.
Proof[0] means that a connection to a truth-maker exists.
Show me an actual formal system defined that allows "Proof" to be an
infinite connection to the truth-maker. All you are doing ios proving
that you are just making up everything you say,
Math is not allowed to change the base meaning of terms.
When-so-ever any expression of formal or natural language X lacks
a connection to its truthmaker X remains untrue.
I think part of the problem is you just don't understand what a Formal
System is, and since Incompleteness is a property of Formal System
(not just general philosophy) that is an important part.
Of course, your big part for not understanding Formal Systens is you
don't believe you need to follow the rules, and that is fundamental to
Formal Logic, so its concepts are just foreign to you.
Sorry, you are just proving your total ignorance of what you talk
about, and so ignorant that you can't see your ignorance.
On 2/5/2025 1:44 AM, Mikko wrote:
On 2025-02-04 16:11:08 +0000, olcott said:
On 2/4/2025 3:22 AM, Mikko wrote:
On 2025-02-03 16:54:08 +0000, olcott said:
On 2/3/2025 9:07 AM, Mikko wrote:
On 2025-02-03 03:30:46 +0000, olcott said:
On 2/2/2025 3:27 AM, Mikko wrote:
On 2025-02-01 14:09:54 +0000, olcott said:
On 2/1/2025 3:19 AM, Mikko wrote:
On 2025-01-31 13:57:02 +0000, olcott said:a fact or piece of information that shows that something
On 1/31/2025 3:24 AM, Mikko wrote:
On 2025-01-30 23:10:18 +0000, olcott said:
Within the entire body of analytical truth any expression of language
that has no sequence of formalized semantic deductive inference steps
from the formalized semantic foundational truths of this system are
simply untrue in this system. (Isomorphic to provable from axioms).
If there is a misconception then you have misconceived something. It is well
known that it is possible to construct a formal theory where some formulas
are neither provble nor disprovable.
This is well known.
And well undeerstood. The claim on the subject line is false. >>>>>>>>>
exists or is true:
https://dictionary.cambridge.org/us/dictionary/english/proof
We require that terms of art are used with their term-of-art meaning and
The fundamental base meaning of Truth[0] itself remains the same >>>>>>> no matter what idiomatic meanings say.
Irrelevant as the subject line does not mention truth.
Therefore, no need to revise my initial comment.
The notion of truth is entailed by the subject line:
misconception means ~True.
The title line means that something is misunderstood but that something >>>> is not the meaning of "true".
It is untrue because it is misunderstood.
Mathematical incompleteness is not a claim so it cannot be untrue.
That mathematical incompleteness coherently exists <is> claim.
The closest that it can possibly be interpreted as true would
be that because key elements of proof[0] have been specified
as not existing in proof[math] math is intentionally made less
than complete.
When-so-ever any expression of formal or natural language X lacks
a connection to its truthmaker X remains untrue.
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