When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
On 2023-11-18 16:32:10 +0000, olcott said:
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
That definition does not remove deductive incompleteness of a theory.
E.g., the first order Peano arithmetic is still deductively incomlete.
It only removes the semantic completeness by removing the semantic
concept of truth (and with it all semantics, as the main role of
semantics is to provide a concept of truth).
Mikko
On 11/19/2023 6:35 AM, Mikko wrote:
On 2023-11-18 16:32:10 +0000, olcott said:
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
That definition does not remove deductive incompleteness of a theory.
Sure it does, when the criteria that used to prove incompleteness: Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
becomes
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) Incompleteness cannot possibly exist.
On 2023-11-19 15:43:59 +0000, olcott said:
On 11/19/2023 6:35 AM, Mikko wrote:
On 2023-11-18 16:32:10 +0000, olcott said:
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
That definition does not remove deductive incompleteness of a theory.
Sure it does, when the criteria that used to prove incompleteness:
Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
becomes
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Incompleteness cannot possibly exist.
The OP did not change or remove the defintion of semantic incompleteness, only of True.
Mikko
On 11/20/2023 9:40 AM, Mikko wrote:
On 2023-11-19 15:43:59 +0000, olcott said:
On 11/19/2023 6:35 AM, Mikko wrote:
On 2023-11-18 16:32:10 +0000, olcott said:
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
That definition does not remove deductive incompleteness of a theory.
Sure it does, when the criteria that used to prove incompleteness:
Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
becomes
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>> Incompleteness cannot possibly exist.
The OP did not change or remove the defintion of semantic incompleteness,
only of True.
Mikko
Yes you will get that understanding if you glance at one or two of my
words before artificially contriving a fake rebuttal.
When you actually pay complete attention then what was previously
was Incomplete(L) becomes ¬TruthBearer(L,x) the detection of an epistemological antinomy.
On 11/20/2023 9:40 AM, Mikko wrote:
On 2023-11-19 15:43:59 +0000, olcott said:
On 11/19/2023 6:35 AM, Mikko wrote:
On 2023-11-18 16:32:10 +0000, olcott said:
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
That definition does not remove deductive incompleteness of a theory.
Sure it does, when the criteria that used to prove incompleteness:
Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
becomes
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>> Incompleteness cannot possibly exist.
The OP did not change or remove the defintion of semantic incompleteness,
only of True.
Mikko
Yes you will get that understanding if you glance at one or two of my words
When you actually pay complete attention then what was previously
was Incomplete(L) becomes ¬TruthBearer(L,x) the detection of an epistemological antinomy.
On 2023-11-20 16:10:44 +0000, olcott said:
On 11/20/2023 9:40 AM, Mikko wrote:
On 2023-11-19 15:43:59 +0000, olcott said:
On 11/19/2023 6:35 AM, Mikko wrote:
On 2023-11-18 16:32:10 +0000, olcott said:Sure it does, when the criteria that used to prove incompleteness:
When we define True(L, x) as (L ⊢ x) provable from the axioms
of L, then epistemological antinomies become simply untrue and
no longer show incompleteness or undecidability.
That definition does not remove deductive incompleteness of a theory. >>>>
Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
becomes
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>>> Incompleteness cannot possibly exist.
The OP did not change or remove the defintion of semantic
incompleteness,
only of True.
Mikko
Yes you will get that understanding if you glance at one or two of my
words
Instead of carefully reading all of them? Sorry, too late.
When you actually pay complete attention then what was previously
was Incomplete(L) becomes ¬TruthBearer(L,x) the detection of an
epistemological antinomy.
Only one meaning of Incomplete is mentioned above.
TruthBearer as presented above is of different type so not a possible replacement: Incomplete is a property of a theory but TruthBearer is
a relation of a theory and a sentence.
One can also say that Incomplete(L) ≡ ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>>Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)).
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one should add
that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete
as a faulty x that must be excluded from any bivalent formal system.
There is no otherwise. It is still true that, with your symbols, Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L.
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
This construes every x that would otherwise prove that L is incomplete
as a faulty x that must be excluded from any bivalent formal system.
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L.
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x))) This construes every x that would otherwise prove that L is incomplete
as a faulty x that must be excluded from any bivalent formal system.
https://www.liarparadox.org/Wittgenstein.pdf
∀x ∈ Language(L) (True(L,x) ≡ (L ⊢ x))
∀x ∈ Language(L) (False(L,x) ≡ (L ⊢ ¬x))
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>>>Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)).
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x))) >>That is not a definition but nearly the same. Perhaps one should add
that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete
as a faulty x that must be excluded from any bivalent formal system.
There is no otherwise. It is still true that, with your symbols,
Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
I am redefining the criteria that previously detected Incomplete(L)
to detect Incorrect(x) instead.
https://www.liarparadox.org/Wittgenstein.pdf
∀x ∈ Language(L) (True(L,x) ≡ (L ⊢ x))
∀x ∈ Language(L) (False(L,x) ≡ (L ⊢ ¬x))
The key issue that this solves is that formal systems are no longer determined to be incomplete on the basis that they cannot determine
whether or not a self-contradictory sentence is true or false.
On 11/29/2023 4:15 AM, Mikko wrote:
[...]
I am trying to say that
when-so-ever an x in the Language of L is
neither provable nor refutable in L
then x is not a truth bearer in L.
∀x ∈ Language(L)
(¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
This construes every x that would
otherwise prove that L is incomplete
as a faulty x that must be excluded from
any bivalent formal system.
https://www.liarparadox.org/Wittgenstein.pdf
∀x ∈ Language(L) (True(L,x) ≡ (L ⊢ x))
∀x ∈ Language(L) (False(L,x) ≡ (L ⊢ ¬x))
On 11/30/2023 9:54 AM, Jim Burns wrote:
The Pythagorean theorem, Gödel's theorems,
theorems in general aren't edicts.
They aren't authorizing truth by
virtue of their being expressed.
Theorems are recognitions of truths.
If, for any reason, we do not recognize
their truth, they are true anyway.
For the entire body of analytic truth
True(x) generically means that
a set of inference steps exists from
expressions of language that
had been stipulated to be true.
For the entire body of analytic truth
True(x) generically means that
a set of inference steps exists from
expressions of language that
had been stipulated to be true.
... stipulated to be true.
Math and logic are a subset of analytic truth,
thus are not actually allowed to change
the way that True(x) generically works.
The lack of this set of inference steps
simply means untrue.
On 11/30/2023 3:17 PM, Jim Burns wrote:
[...]
The only way that we can know that
the Goldbach conjecture must be true or false
is that we know that testing every element of
the set of natural numbers would determine this.
On 11/30/2023 9:54 AM, Jim Burns wrote:
On 11/29/2023 10:10 AM, olcott wrote:
On 11/29/2023 4:15 AM, Mikko wrote:
[...]
I am trying to say that
when-so-ever an x in the Language of L is
neither provable nor refutable in L
then x is not a truth bearer in L.
It follows from
what you're trying to say
that various definitions should change.
That would be less effective than you'd like,
it seems to me.
There are these technical terms we've defined:
definientia, singular definiens.
There are these phrases, formulas, etc,
which the definientia represent:
definienda, singular definiendum.
A definition defines a definiens to represent
a definiendum.
In practice, there is nowhere to go and
no one to stand before to argue for
these changes. (sci.logic surely isn't.)
But ignore that.
Hypothetically,
we make an extremely radical change to
these definitions.
We throw out all the offending definientia.
Stop using them. Completely.
Nothing changes.
What was true about
formal systems, arithmetic and
incompleteness
remains true about
formal systems, arithmetic and
incompleteness.
Now, we can't say it,
at least, not the way we have been,
but the truth of
what we're not saying
hasn't changed.
Consider a less fraught example.
The Pythagorean theorem expresses
a fact about right triangles.
Throw out the definiens "right triangle".
It remains true for the definiendum,
a right triangle, that the square of
its longest side is equal to the sum of
the squares of the two other sides.
It's just that we can't say that.
The Pythagorean theorem, Gödel's theorems,
theorems in general aren't edicts.
They aren't authorizing truth by
virtue of their being expressed.
Theorems are recognitions of truths.
If, for any reason, we do not recognize
their truth, they are true anyway.
∀x ∈ Language(L)
(¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
_ ⊢ x
is where sentences go which
you are considering true,
at least for the length of a proof of x
where your hypotheses go.
Your use of 'L' suggests that
you're putting the language there,
both its true and false sentences.
That wouldn't make sense.
Perhaps you're intending to say
IsaTheory(T)
L = LanguageOf(T)
∀x ∈ L
(¬TruthBearer(L,T,x) ≡ ((T ⊬ x) ∧ (T ⊬ ¬x)))
If {x e L|¬TruthBearer(L,T,x)} is not empty
then there are sentences T cannot decide.
You (PO) seem to assign more moral weight
to this than is really warranted.
*The part that you ignored was the important part*
For the entire body of analytic truth True(x) generically means that a
set of inference steps exists from expressions of language that had been stipulated to be true.
Math and logic are a subset of analytic truth, thus are not actually
allowed to change the way that True(x) generically works.
The lack of this set of inference steps simply means untrue.
This construes every x that would
otherwise prove that L is incomplete
as a faulty x that must be excluded from
any bivalent formal system.
https://www.liarparadox.org/Wittgenstein.pdf
∀x ∈ Language(L) (True(L,x) ≡ (L ⊢ x))
∀x ∈ Language(L) (False(L,x) ≡ (L ⊢ ¬x))
On 11/30/2023 12:16 PM, olcott wrote:
On 11/30/2023 9:54 AM, Jim Burns wrote:
On 11/29/2023 10:10 AM, olcott wrote:
On 11/29/2023 4:15 AM, Mikko wrote:
[...]
I am trying to say that
when-so-ever an x in the Language of L is
neither provable nor refutable in L
then x is not a truth bearer in L.
It follows from
what you're trying to say
that various definitions should change.
That would be less effective than you'd like,
it seems to me.
There are these technical terms we've defined:
definientia, singular definiens.
There are these phrases, formulas, etc,
which the definientia represent:
definienda, singular definiendum.
A definition defines a definiens to represent
a definiendum.
In practice, there is nowhere to go and
no one to stand before to argue for
these changes. (sci.logic surely isn't.)
But ignore that.
Hypothetically,
we make an extremely radical change to
these definitions.
We throw out all the offending definientia.
Stop using them. Completely.
Nothing changes.
What was true about
formal systems, arithmetic and
incompleteness
remains true about
formal systems, arithmetic and
incompleteness.
Now, we can't say it,
at least, not the way we have been,
but the truth of
what we're not saying
hasn't changed.
Consider a less fraught example.
The Pythagorean theorem expresses
a fact about right triangles.
Throw out the definiens "right triangle".
It remains true for the definiendum,
a right triangle, that the square of
its longest side is equal to the sum of
the squares of the two other sides.
It's just that we can't say that.
The Pythagorean theorem, Gödel's theorems,
theorems in general aren't edicts.
They aren't authorizing truth by
virtue of their being expressed.
Theorems are recognitions of truths.
If, for any reason, we do not recognize
their truth, they are true anyway.
∀x ∈ Language(L)
(¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
_ ⊢ x
is where sentences go which
you are considering true,
at least for the length of a proof of x
where your hypotheses go.
Your use of 'L' suggests that
you're putting the language there,
both its true and false sentences.
That wouldn't make sense.
Perhaps you're intending to say
IsaTheory(T)
L = LanguageOf(T)
∀x ∈ L
(¬TruthBearer(L,T,x) ≡ ((T ⊬ x) ∧ (T ⊬ ¬x)))
If {x e L|¬TruthBearer(L,T,x)} is not empty
then there are sentences T cannot decide.
You (PO) seem to assign more moral weight
to this than is really warranted.
*The part that you ignored was the important part*
For the entire body of analytic truth True(x) generically means that a
set of inference steps exists from expressions of language that had been
stipulated to be true.
Math and logic are a subset of analytic truth, thus are not actually
allowed to change the way that True(x) generically works.
The lack of this set of inference steps simply means untrue.
I have over-ruled and redefined Incomplete so that it ceases to exist.
This same change also eliminates all undecidability. The purpose of
this change is to force True(L,x) to work consistently across every
element of human analytical knowledge.
On 11/30/2023 9:55 PM, Jim Burns wrote:
We can state arguments that depend upon
our topic of the day being
a natural number,
but which also _don't_ depend upon
our topic of the day being
a particular natural number.
Using this method,
whether infinitely-many or finitely-many exist,
the conclusion is true of each described.
The _natural numbers_ are infinitely-many.
The _statements about them_ are
finitely-many and finite-length.
That, we can do. Maybe.
But, if we can't, it won't be our inability
to perform supertasks which stops us.
I have over-ruled
I have over-ruled and redefined
I have over-ruled and redefined Incomplete
so that it ceases to exist.
I have over-ruled and redefined Incomplete
so that it ceases to exist.
On 12/1/2023 11:38 AM, Jim Burns wrote:
[...]
When
provable from the axioms of L means
true in L, and
unprovable in L means
untrue in L
then
incompleteness and undecidability
cannot exist.
When we try to prove that a kitten <is>
a 15 story office building
the proof fails.
On 12/1/2023 2:14 PM, Jim Burns wrote:
[...}
People with a psychotic break from reality
may insist that we must be able to prove that
kittens <are> 15 story office buildings.
On 12/1/2023 2:14 PM, Jim Burns wrote:
On 12/1/2023 1:42 PM, olcott wrote:
On 12/1/2023 11:38 AM, Jim Burns wrote:
[...]
When
provable from the axioms of L means
true in L, and
unprovable in L means
untrue in L
then
incompleteness and undecidability
cannot exist.
When
the objects in the language of L
can be represented by
objects in the domain of L
then
one object represents
"x can't be proved in L"
Consider
| "x can't be proved in L" can't be proved in L
If it's true,
it can't be proved, and
L is incomplete.
I stipulate that this means that x is simply untrue in L.
This <is> the way that the entire body of analytic truth
really works. That math diverges from this is its error.
If it's false,
it can be proved,
but it's false! and
L is inconsistent.
When
the objects in the language of L
can be represented by
objects in the domain of L
then
the choice is between
incomplete and inconsistent.
False dichotomy.
It is perfectly consistent to say that G is untrue in F.
When unprovable means untrue then it does not mean incomplete.
When we try to prove that a kitten <is>
a 15 story office building
the proof fails.
In some contexts,
that failure might be unacceptable.
People with a psychotic break from reality may insist
that we must be able to prove that kittens <are> 15
story office buildings. The coherence theory of truth
screens out such claims.
My purpose in defining True(L, x) as provable from the
axioms of L is to override Tarski undefinability so that
automated reasoning has a consistently sound basis.
Also that <is> the way that correct reasoning actually
works within the entire body of human knowledge thus
making it much more clear that when math diverges from
this that math is incorrect.
The axioms of natural language stipulate that {cats are animals}
thus giving semantic meaning to that otherwise totally meaningless
finite string.
This corrects the divergence of modern logic from the syllogism
so that True(x) works the same way that it works for the entire
body of analytic knowledge: a sequence of inference steps from
expressions of language that have been stipulated to be true makes
x true. The absence of these steps makes x untrue.
On 12/1/2023 4:26 PM, Jim Burns wrote:
On 12/1/2023 3:46 PM, olcott wrote:
On 12/1/2023 2:14 PM, Jim Burns wrote:
[...}
People with a psychotic break from reality
may insist that we must be able to prove that
kittens <are> 15 story office buildings.
Some people are concerned with topology.
They are said, jokingly, to believe that
doughnuts are coffee cups.
Are you (PO) concerned with topology?
If you aren't, that's fine.
Nearly everyone else on the planet isn't.
However,
if you pretend that no one is concerned
with topology, that doesn't speak well of you.
I have a single-minded focus and distractions away from this
point are construed as the strawman deception.
My purpose in defining True(L, x) as provable from the
axioms of L is to override Tarski undefinability so that
automated reasoning has a consistently sound basis.
Also that <is> the way that correct reasoning actually
works within the entire body of human knowledge thus
making it much more clear that when math diverges from
this that math is incorrect.
The axioms of natural language stipulate that {cats are animals}
thus giving semantic meaning to that otherwise totally meaningless
finite string.
On 12/1/2023 4:26 PM, Jim Burns wrote:
On 12/1/2023 3:46 PM, olcott wrote:
People with a psychotic break from reality
may insist that we must be able to prove that
kittens <are> 15 story office buildings.
Some people are concerned with topology.
They are said, jokingly, to believe that
doughnuts are coffee cups.
Are you (PO) concerned with topology?
If you aren't, that's fine.
Nearly everyone else on the planet isn't.
However,
if you pretend that no one is concerned
with topology, that doesn't speak well of you.
I have a single-minded focus
and distractions away from this point
are construed as the strawman deception.
On 12/2/2023 10:11 AM, Jim Burns wrote:
On 12/1/2023 6:41 PM, olcott wrote:
On 12/1/2023 4:26 PM, Jim Burns wrote:
On 12/1/2023 3:46 PM, olcott wrote:
People with a psychotic break from reality
may insist that we must be able to prove that
kittens <are> 15 story office buildings.
Some people are concerned with topology.
They are said, jokingly, to believe that
doughnuts are coffee cups.
Are you (PO) concerned with topology?
If you aren't, that's fine.
Nearly everyone else on the planet isn't.
However,
if you pretend that no one is concerned
with topology, that doesn't speak well of you.
I have a single-minded focus
and distractions away from this point
are construed as the strawman deception.
You think that
a single-minded focus away from your mistakes
will save you from making mistakes.
Spoiler alert!
It won't.
Ludwig Wittgenstein one of the most famous philosophers
of logic perfectly agrees with me. He was a leader of the
logical positivists.
I know that he is correct because I figured out every single
detail of his view and why these details are correct before I
ever heard of him.
https://www.liarparadox.org/Wittgenstein.pdf
Formalized as:
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Logicians only memorize the rules of logic and take them
as inherently infallible have no actual understanding of
these things.
Rote memorization is the complete depth of their knowledge.
If some of the rules of logic don't fit together coherently
they don't have the ability or the inclination to notice this.
On 12/1/2023 2:14 PM, Jim Burns wrote:
On 12/1/2023 1:42 PM, olcott wrote:
When
provable from the axioms of L means
true in L, and
unprovable in L means
untrue in L
then
incompleteness and undecidability
cannot exist.
When
the objects in the language of L
can be represented by
objects in the domain of L
then
one object represents
"x can't be proved in L"
Consider
| "x can't be proved in L" can't be proved in L
If it's true,
it can't be proved, and
L is incomplete.
I stipulate that
this means that x is simply untrue in L.
This <is> the way that
the entire body of analytic truth really works.
That math diverges from this is its error.
If it's false,
it can be proved,
but it's false! and
L is inconsistent.
When
the objects in the language of L
can be represented by
objects in the domain of L
then
the choice is between
incomplete and inconsistent.
False dichotomy.
It is perfectly consistent to say that
G is untrue in F.
When unprovable means untrue
then it does not mean incomplete.
On 12/2/2023 3:46 PM, Jim Burns wrote:
On 12/1/2023 3:46 PM, olcott wrote:
On 12/1/2023 2:14 PM, Jim Burns wrote:
On 12/1/2023 1:42 PM, olcott wrote:
When
provable from the axioms of L means
true in L, and
unprovable in L means
untrue in L
then
incompleteness and undecidability
cannot exist.
When
the objects in the language of L
can be represented by
objects in the domain of L
then
one object represents
"x can't be proved in L"
Consider
| "x can't be proved in L" can't be proved in L
Oops.
Better:
"preceded by its quotation can't be proved in L"
preceded by its quotation can't be proved in L.
Not a self-reference, but
a self-description.
If it's true,
it can't be proved, and
L is incomplete.
I stipulate that
this means that x is simply untrue in L.
1/2. You introduce a private meaning.
This <is> the way that
the entire body of analytic truth really works.
2/2. You claim (stipulate?) that
everyone is using your private meaning.
*Think it through*
Everything that you know is true on the basis of its meaning
AKA the entire body of analytical knowledge <is> only known
to be true on the basis of its meaning.
(a) Cats <are> Animals is true on the basis of the meaning
of {cats} and the meaning of {animals}.
(b) Animals <are> living things is true on the basis of the
meaning of {animals} and the meaning of {living things}.
(c) That {cats} <are> {living things} is sound deductive
inference on the basis of true premises (a) and (b)
The entire body of analytic knowledge is proven to work this
same way in that counter-examples are categorically impossible.
If you diligently try to find a counter-example you will find
that none can possibly exist because analytic truth is defined
to depend on its meanings. This means that its proof can always
be traced back to its meanings or it is not analytic truth.
True(L,x) ≡ (T ⊢ x) traces x back to its meanings in L.
In formal proofs these semantic meanings would be syntactically
formalized.
It is also common knowledge that all of math and all of
logic are subsets of the body of analytic truth.
On 12/2/2023 4:26 PM, olcott wrote:
On 12/2/2023 3:46 PM, Jim Burns wrote:
On 12/1/2023 3:46 PM, olcott wrote:
On 12/1/2023 2:14 PM, Jim Burns wrote:
On 12/1/2023 1:42 PM, olcott wrote:
When
provable from the axioms of L means
true in L, and
unprovable in L means
untrue in L
then
incompleteness and undecidability
cannot exist.
When
the objects in the language of L
can be represented by
objects in the domain of L
then
one object represents
"x can't be proved in L"
Consider
| "x can't be proved in L" can't be proved in L
Oops.
Better:
"preceded by its quotation can't be proved in L"
preceded by its quotation can't be proved in L.
Not a self-reference, but
a self-description.
If it's true,
it can't be proved, and
L is incomplete.
I stipulate that
this means that x is simply untrue in L.
1/2. You introduce a private meaning.
This <is> the way that
the entire body of analytic truth really works.
2/2. You claim (stipulate?) that
everyone is using your private meaning.
*Think it through*
Everything that you know is true on the basis of its meaning
AKA the entire body of analytical knowledge <is> only known
to be true on the basis of its meaning.
(a) Cats <are> Animals is true on the basis of the meaning
of {cats} and the meaning of {animals}.
(b) Animals <are> living things is true on the basis of the
meaning of {animals} and the meaning of {living things}.
(c) That {cats} <are> {living things} is sound deductive
inference on the basis of true premises (a) and (b)
The entire body of analytic knowledge is proven to work this
same way in that counter-examples are categorically impossible.
If you diligently try to find a counter-example you will find
that none can possibly exist because analytic truth is defined
to depend on its meanings. This means that its proof can always
be traced back to its meanings or it is not analytic truth.
True(L,x) ≡ (T ⊢ x) traces x back to its meanings in L.
In formal proofs these semantic meanings would be syntactically
formalized.
It is also common knowledge that all of math and all of
logic are subsets of the body of analytic truth.
When unprovable in PA means untrue in PA then it does not mean that PA
is incomplete. For the entire body of analytic knowledge the lack of a provability connection back to the semantic meanings that make an
expression true always consistently means that the expression is untrue.
When math tries to override this math screws up.
On 12/2/2023 12:49 PM, Ross Finlayson wrote:
On Saturday, December 2, 2023 at 9:10:48 AM UTC-8, olcott wrote:
On 12/2/2023 10:11 AM, Jim Burns wrote:
On 12/1/2023 6:41 PM, olcott wrote:Ludwig Wittgenstein one of the most famous philosophers
On 12/1/2023 4:26 PM, Jim Burns wrote:
On 12/1/2023 3:46 PM, olcott wrote:
People with a psychotic break from reality
may insist that we must be able to prove that
kittens <are> 15 story office buildings.
Some people are concerned with topology.
They are said, jokingly, to believe that
doughnuts are coffee cups.
Are you (PO) concerned with topology?
If you aren't, that's fine.
Nearly everyone else on the planet isn't.
However,
if you pretend that no one is concerned
with topology, that doesn't speak well of you.
I have a single-minded focus
and distractions away from this point
are construed as the strawman deception.
You think that
a single-minded focus away from your mistakes
will save you from making mistakes.
Spoiler alert!
It won't.
of logic perfectly agrees with me. He was a leader of the
logical positivists.
I know that he is correct because I figured out every single
detail of his view and why these details are correct before I
ever heard of him.
https://www.liarparadox.org/Wittgenstein.pdf
Formalized as:
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Logicians only memorize the rules of logic and take them
as inherently infallible have no actual understanding of
these things.
Rote memorization is the complete depth of their knowledge.
If some of the rules of logic don't fit together coherently
they don't have the ability or the inclination to notice this.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
"Logical, positivists", are usually enough, neither.
Logical positivism ideally though is of course , ..., "true".
When we define the measure of analytical true that way that it
consistently works for the whole body of analytical knowledge
then the only actual incompleteness are unknown truths such as
the Goldbach conjecture. Such as system as Wittgenstein's and
mine simply determines that epistemological antinomies are simply
untrue.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
The conventional mathematical notion of undecidability incorrectly
assumes that self-contradictory sentences must be provably true or
false. That is so ridiculously stupid that I can imagine how this
mistake was not discovered back in 1931.
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)) >>>>Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)).
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x))) >>That is not a definition but nearly the same. Perhaps one should add
that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete
as a faulty x that must be excluded from any bivalent formal system.
There is no otherwise. It is still true that, with your symbols,
Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
I am redefining the criteria that previously detected Incomplete(L)
to detect Incorrect(x) instead.
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)).
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L. >>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>That is not a definition but nearly the same. Perhaps one should add
that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete >>>>> as a faulty x that must be excluded from any bivalent formal system.
There is no otherwise. It is still true that, with your symbols,
Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
I am redefining the criteria that previously detected Incomplete(L)
to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where
the redefinition is made.
A redefinition of one symbol does not cancel the definition of another
symbol.
A redefition does not remove the concept in the old definition,
only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU*
*Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
It is utterly ridiculous that anyone ever believed that formal
systems must be able to prove self-contradictory sentences.
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)).
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is
neither provable nor refutable in L then x is not a truth bearer in L. >>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>That is not a definition but nearly the same. Perhaps one should add
that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete >>>>> as a faulty x that must be excluded from any bivalent formal system.
There is no otherwise. It is still true that, with your symbols,
Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
I am redefining the criteria that previously detected Incomplete(L)
to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where
the redefinition is made.
A redefinition of one symbol does not cancel the definition of another
symbol.
A redefition does not remove the concept in the old definition,
only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU*
*Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
It is utterly ridiculous that anyone ever believed that formal
systems must be able to prove self-contradictory sentences.
On 12/3/2023 11:02 AM, Mikko wrote:
On 2023-12-03 16:40:48 +0000, olcott said:
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)).
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is >>>>>>> neither provable nor refutable in L then x is not a truth bearer in L. >>>>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one should add >>>>>> that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete >>>>>>> as a faulty x that must be excluded from any bivalent formal system. >>>>>>There is no otherwise. It is still true that, with your symbols,
Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
I am redefining the criteria that previously detected Incomplete(L)
to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where
the redefinition is made.
A redefinition of one symbol does not cancel the definition of another >>>> symbol.
A redefition does not remove the concept in the old definition,
only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU*
*Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
It is utterly ridiculous that anyone ever believed that formal
systems must be able to prove self-contradictory sentences.
All of that is irrelevant to anything quoted above.
Mikko
When the notion of Incomplete is incoherent then it must be excluded.
This means that the redefinition does replace it.
On 12/4/2023 3:35 AM, Mikko wrote:
On 2023-12-03 17:25:31 +0000, olcott said:
On 12/3/2023 11:02 AM, Mikko wrote:
On 2023-12-03 16:40:48 +0000, olcott said:
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is >>>>>>>>> neither provable nor refutable in L then x is not a truth
bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)). >>>>>>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one should >>>>>>>> add
that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is
incomplete
as a faulty x that must be excluded from any bivalent formal >>>>>>>>> system.
There is no otherwise. It is still true that, with your symbols, >>>>>>>> Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
Mikko
I am redefining the criteria that previously detected Incomplete(L) >>>>>>> to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where
the redefinition is made.
A redefinition of one symbol does not cancel the definition of
another
symbol.
A redefition does not remove the concept in the old definition,
only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU*
*Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>>
It is utterly ridiculous that anyone ever believed that formal
systems must be able to prove self-contradictory sentences.
All of that is irrelevant to anything quoted above.
Mikko
When the notion of Incomplete is incoherent then it must be excluded.
The meaning of "incomplete" is simply 'not complete'. There is no
incoherence in that.
Sure that is fine, however this mathematical definition of
incompleteness:
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
matches epistemological antinomies which are self-contradictory
expressions of language
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
That we know formal system cannot be correctly required to prove self-contradictory expressions of language, proves that the above
Gödel quote is terribly incorrect.
There are several notions of completeness, of which
the most important ones here are semantic completeness and deductive
completeness. Both are coherent but they must not be confused. A theory
is deductively complete if every sentence is either a theorem or the
negation of a theorem. Deductive completeness does not depend of
intepretations nor of the notion of truth. Semantic completeness
means that every sentence that is true in some iterpretation (usually
the intended or standard interpretation) is a theorem.
For example, group theory is incomplete: it does not prove that
AB = BA for every element of the group nor does it prove the opposite.
In some groups the sentence is true and in some it is false.
This means that the redefinition does replace it.
Perhaps in your own writings but not in anybody elses.
Mikko
On 12/4/2023 8:32 PM, Ross Finlayson wrote:
On Monday, December 4, 2023 at 4:30:55 PM UTC-8, Richard Damon wrote:
On 12/4/23 3:00 PM, olcott wrote:
On 12/4/2023 3:35 AM, Mikko wrote:Except that epistemological antinomies are not members of most Formal
On 2023-12-03 17:25:31 +0000, olcott said:
On 12/3/2023 11:02 AM, Mikko wrote:The meaning of "incomplete" is simply 'not complete'. There is no
On 2023-12-03 16:40:48 +0000, olcott said:
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings >>>>>>>>>>>>> (like above, where it is used both for a free variable >>>>>>>>>>>>> and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of >>>>>>>>>>>> L is
neither provable nor refutable in L then x is not a truth >>>>>>>>>>>> bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)). >>>>>>>>>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one should >>>>>>>>>>> add
that if x is not in Languabe(L) then ¬TruthBearer(L,x). >>>>>>>>>>>
This construes every x that would otherwise prove that L is >>>>>>>>>>>> incomplete
as a faulty x that must be excluded from any bivalent formal >>>>>>>>>>>> system.
There is no otherwise. It is still true that, with your symbols, >>>>>>>>>>> Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)). >>>>>>>>>>>
Mikko
I am redefining the criteria that previously detected
Incomplete(L)
to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where >>>>>>>>> the redefinition is made.
A redefinition of one symbol does not cancel the definition of >>>>>>>>> another
symbol.
A redefition does not remove the concept in the old definition, >>>>>>>>> only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a >>>>>>>> similar undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU* >>>>>>>> *Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>>>>>
It is utterly ridiculous that anyone ever believed that formal >>>>>>>> systems must be able to prove self-contradictory sentences.
All of that is irrelevant to anything quoted above.
Mikko
When the notion of Incomplete is incoherent then it must be excluded. >>>>>
incoherence in that.
Sure that is fine, however this mathematical definition of
incompleteness:
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
matches epistemological antinomies which are self-contradictory
expressions of language
Systems Language.
You have been told this many times, but can't seem to learn it.
...14 Every epistemological antinomy can likewise be used for a similar >>>> undecidability proof...(Gödel 1931:43-44)
That we know formal system cannot be correctly required to prove
self-contradictory expressions of language, proves that the above
Gödel quote is terribly incorrect.
There are several notions of completeness, of which
the most important ones here are semantic completeness and deductive >>>>> completeness. Both are coherent but they must not be confused. A
theory
is deductively complete if every sentence is either a theorem or the >>>>> negation of a theorem. Deductive completeness does not depend of
intepretations nor of the notion of truth. Semantic completeness
means that every sentence that is true in some iterpretation (usually >>>>> the intended or standard interpretation) is a theorem.
For example, group theory is incomplete: it does not prove that
AB = BA for every element of the group nor does it prove the opposite. >>>>> In some groups the sentence is true and in some it is false.
This means that the redefinition does replace it.
Perhaps in your own writings but not in anybody elses.
Mikko
Peter and Damon seem about flip sides of the same coin.
This is "Janus' introspection", that Janus is a figure with two faces
facing opposite ways,
then that flipping a coin with Janus on one side and the other blank,
only result that
either they don't agree, or, nothing. (And waste.)
But, the deliberate act of observing each, and persistence of vision,
results seeing both,
in a model of alternation as the model of change.
In this manner it results then a simple model of the dialectic and that
there are alternatives instead of outcomes, conflicting.
And, instead of you being reduced to flipping a coin to find your fate,
and getting none, or scratching out one side or the other, defacing it,
then it's for abstraction and deduction, to arrive at why they're just
talking
past each other, that Janus' introspection, "half-a-shadow-play",
that "fighting philosophers" are reduced to "a discourse".
They're both solely founded on coming up from nothing and getting
nowhere,
or, coming down from it all and getting nowhere. Either way for
deduction,
it results, "middle of nowhere".
Here we all hope our decisions are based on principles, instead of the
random,
or just scratching out either side.
Those are finite automatons without a mental model of their own,
objective cognizance,
which everybody should have, unless thinking is too hard, to face.
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
My key point (that is easiest to understand) is that it takes a complete moron to believe that formal systems are required to prove or refute self-contradictory expressions of language.
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
On 12/4/2023 3:35 AM, Mikko wrote:
On 2023-12-03 17:25:31 +0000, olcott said:
On 12/3/2023 11:02 AM, Mikko wrote:
On 2023-12-03 16:40:48 +0000, olcott said:
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings
(like above, where it is used both for a free variable
and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is >>>>>>>>> neither provable nor refutable in L then x is not a truth bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)). >>>>>>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one should add >>>>>>>> that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incompleteThere is no otherwise. It is still true that, with your symbols, >>>>>>>> Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)).
as a faulty x that must be excluded from any bivalent formal system. >>>>>>>>
Mikko
I am redefining the criteria that previously detected Incomplete(L) >>>>>>> to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where
the redefinition is made.
A redefinition of one symbol does not cancel the definition of another >>>>>> symbol.
A redefition does not remove the concept in the old definition,
only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a similar >>>>> undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU*
*Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>>
It is utterly ridiculous that anyone ever believed that formal
systems must be able to prove self-contradictory sentences.
All of that is irrelevant to anything quoted above.
Mikko
When the notion of Incomplete is incoherent then it must be excluded.
The meaning of "incomplete" is simply 'not complete'. There is no
incoherence in that.
Sure that is fine, however this mathematical definition of
incompleteness:
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
On 12/6/2023 1:02 AM, Ross Finlayson wrote:
On Tuesday, December 5, 2023 at 8:52:03 PM UTC-8, olcott wrote:
On 12/5/2023 10:03 PM, Ross Finlayson wrote:
On Tuesday, December 5, 2023 at 7:20:39 PM UTC-8, Ross Finlayson wrote: >>>>> On Tuesday, December 5, 2023 at 3:42:14 PM UTC-8, Richard Damon wrote: >>>>>> On 12/5/23 2:26 PM, olcott wrote:As I already said in a different way. Every element of human
What's a true theory of everything then?
The way that is works for the entire body of analytic knowledge: >>>>>>> True(x) ≡ (⊢ x)Which shows you don't understand the difference between Analytical >>>>>> Knowledge and Analytical Truth.
False(x) ≡ (⊢ ¬x)
Analytical Truths do not need to be provable, just provable to be
known.
If "no", then, how about any true theory of anything?
No true theory of nothing?
Or, is there a "Thesis"?
knowledge can be plugged into a tree of knowledge.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
I can't but imagine you must be familiar with "The Theory
of Anne Elk".
Tarski truth: is a great thing: he at least establishes
that "according to all alternatives, under all suppositions,
under all interpretations, what's non-contradictory is true".
But, of course, in universals, what would be logical "paradox"
immediately establishes it from the very act of quantification,
the very act of stipulation of a thing, of itself.
So, you must find some way to dispatch those if they'd be
considered facts or "knowledge", of the objects, to know them.
Tarski truth is a great thing, but it's usually only a tiny fragment
of objects, where of course there are strong, and sound,, arguments
for induction, and also valid arguments, for deduction, from opposite
means, when induction would otherwise _not suffice_, in for example
various laws of large numbers, or various examples convergence criteria
established by, "induction", which fail, usually after algebraic
manipulation
and insufficient deconstruction of elementary quantities.
I.e. Occam's Razor, and even Shaffer's Laser, are great, but, there's for
a deconstructivist account and criticism, deduction for deduction for
deduction, ..., for theory an abstraction an abduction, axiomless
natural deduction.
Tarski truth is a great thing, but there's a universe of objects, and
language,
is not finite, though people are.
Anyways usual concerns in universals, sort of put the pooh-pooh and
kibosh
on Boole, and Comte, and Russell, as successful hypocrites, then not
about further hypocritically rejecting their constructions,
constructivistically,
but actually even further constructivistically, making a _stronger_,
logical positivism,
that though you may have arrived at what's justifiable and
non-contradictory,
for yourself, that the argument Peter and Damon are having is
basically exactly
that Hausdorff notes that countable sets are countable and
constructible and
so on, and Skolem notes that there are extensions and the generic
after the
standard, that the argument Peter and Damon are having, is old, and,
in a sense, passe.
I.e., the only way either of you can win this argument: is you both do.
Anyways my slates of uncountability and the continuous, and paradoxes
their resolution, are quite above this and a principled outline of
super-classical
axiomless natural deduction, and extra-ordinary theory. Or, it wins.
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Eliminates Tarski undefinability and Gödel incompleteness and forces the concept of truth in math and logic to conform to the way that it works everywhere else in the body of human knowledge: True(x) ≡ (⊢ x)
Incomplete(L) is merely a terribly misleading euphemism for ~True(L,x).
On 12/5/2023 12:08 PM, Mikko wrote:
On 2023-12-04 20:00:18 +0000, olcott said:
On 12/4/2023 3:35 AM, Mikko wrote:
On 2023-12-03 17:25:31 +0000, olcott said:
On 12/3/2023 11:02 AM, Mikko wrote:The meaning of "incomplete" is simply 'not complete'. There is no
On 2023-12-03 16:40:48 +0000, olcott said:
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings >>>>>>>>>>>> (like above, where it is used both for a free variable >>>>>>>>>>>> and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language of L is >>>>>>>>>>> neither provable nor refutable in L then x is not a truth bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)). >>>>>>>>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one should add >>>>>>>>>> that if x is not in Languabe(L) then ¬TruthBearer(L,x).
This construes every x that would otherwise prove that L is incomplete
as a faulty x that must be excluded from any bivalent formal system.
There is no otherwise. It is still true that, with your symbols, >>>>>>>>>> Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)). >>>>>>>>>>
Mikko
I am redefining the criteria that previously detected Incomplete(L) >>>>>>>>> to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where >>>>>>>> the redefinition is made.
A redefinition of one symbol does not cancel the definition of another >>>>>>>> symbol.
A redefition does not remove the concept in the old definition, >>>>>>>> only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a similar >>>>>>> undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU* >>>>>>> *Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>>>>
It is utterly ridiculous that anyone ever believed that formal
systems must be able to prove self-contradictory sentences.
All of that is irrelevant to anything quoted above.
Mikko
When the notion of Incomplete is incoherent then it must be excluded. >>>>
incoherence in that.
Sure that is fine, however this mathematical definition of
incompleteness:
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
Either that or equivalently
Complete(T) := ∀x ∈ Language(T) ((T ⊢ x) ∨ (T ⊢ ¬x)),
Incomplete(T) := ¬Complete(T).
Anyway, that must not be confused with semantical completeness
SemanticallyComplete(T) := ∀x ∈ Language(T) (True(x) → ∨ (T ⊢ x))
One should also make sure that both x ∈ Language(T) and T ⊢ x
should be Turing decidable.
Mikko
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
On 12/5/2023 12:08 PM, Mikko wrote:
On 2023-12-04 20:00:18 +0000, olcott said:
On 12/4/2023 3:35 AM, Mikko wrote:
On 2023-12-03 17:25:31 +0000, olcott said:
On 12/3/2023 11:02 AM, Mikko wrote:
On 2023-12-03 16:40:48 +0000, olcott said:
On 12/3/2023 10:05 AM, Mikko wrote:
On 2023-11-29 18:13:28 +0000, olcott said:
On 11/29/2023 11:18 AM, Mikko wrote:
On 2023-11-29 15:10:28 +0000, olcott said:
On 11/29/2023 4:15 AM, Mikko wrote:
On 2023-11-29 04:56:08 +0000, olcott said:
¬TruthBearer(L,x) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))
Don't use the same xymbol x for two different meanings >>>>>>>>>>>>>> (like above, where it is used both for a free variable >>>>>>>>>>>>>> and a bound variable), you only confuse yourself.
Mikko
I am trying to say that when-so-ever an x in the Language >>>>>>>>>>>>> of L is
neither provable nor refutable in L then x is not a truth >>>>>>>>>>>>> bearer in L.
You could say: TruthBearer(L, x) <-> ((L ⊢ x) ∨ (L ⊢ ¬x)). >>>>>>>>>>>>
∀x ∈ Language(L) (¬TruthBearer(L,x) ≡ ((L ⊬ x) ∧ (L ⊬ ¬x)))
That is not a definition but nearly the same. Perhaps one >>>>>>>>>>>> should add
that if x is not in Languabe(L) then ¬TruthBearer(L,x). >>>>>>>>>>>>
This construes every x that would otherwise prove that L is >>>>>>>>>>>>> incomplete
as a faulty x that must be excluded from any bivalent >>>>>>>>>>>>> formal system.
There is no otherwise. It is still true that, with your >>>>>>>>>>>> symbols,
Incomplete(L) <-> ∃x ∈ Language(L) (¬TruthBearer(L,x)). >>>>>>>>>>>>
Mikko
I am redefining the criteria that previously detected
Incomplete(L)
to detect Incorrect(x) instead.
Your redefinitions have no significance outside the opus where >>>>>>>>>> the redefinition is made.
A redefinition of one symbol does not cancel the definition of >>>>>>>>>> another
symbol.
A redefition does not remove the concept in the old definition, >>>>>>>>>> only the symbol for that concept.
Mikko
...14 Every epistemological antinomy can likewise be used for a >>>>>>>>> similar undecidability proof...(Gödel 1931:43-44)
*Proves that the definition of mathematical incompleteness is AFU* >>>>>>>>> *Thus must be discarded*
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x))) >>>>>>>>>
It is utterly ridiculous that anyone ever believed that formal >>>>>>>>> systems must be able to prove self-contradictory sentences.
All of that is irrelevant to anything quoted above.
Mikko
When the notion of Incomplete is incoherent then it must be
excluded.
The meaning of "incomplete" is simply 'not complete'. There is no
incoherence in that.
Sure that is fine, however this mathematical definition of
incompleteness:
∀L ∈ Formal_System
(Incomplete(L) ≡ ∃x ∈ Language(L) ((L ⊬ x) ∧ (L ⊬ ¬x)))
Either that or equivalently
Complete(T) := ∀x ∈ Language(T) ((T ⊢ x) ∨ (T ⊢ ¬x)),
Incomplete(T) := ¬Complete(T).
Anyway, that must not be confused with semantical completeness
SemanticallyComplete(T) := ∀x ∈ Language(T) (True(x) → ∨ (T ⊢ x))
One should also make sure that both x ∈ Language(T) and T ⊢ x
should be Turing decidable.
Mikko
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake. (3) Richard Montague showed how to formalize semantics syntactically.
(4) Thus my definitions above <are> semantic via syntax.
With the above definitions deductive incompleteness can be expressed
DeductivelyIncomplete ≡ (⊢ x) ∧ (⊢ ¬x).
Mikko
Yet when we forbid terms-of-the-art from diverging from their root
meaning then incomplete does not mean that formal systems lack the
ability to prove self-contradictory sentences.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43-44)
Thus Incomplete(L) is merely a terribly misleading euphemism for
~True(L,x).
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
(3) Richard Montague showed how to formalize semantics syntactically.
(4) Thus my definitions above <are> semantic via syntax.
With the above definitions deductive incompleteness can be expressed
DeductivelyIncomplete ≡ (⊢ x) ∧ (⊢ ¬x).
Mikko
Yet when we forbid terms-of-the-art from diverging from their root
meaning then incomplete does not mean that formal systems lack the
ability to prove self-contradictory sentences.
...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43-44)
Thus Incomplete(L) is merely a terribly misleading euphemism for ~True(L,x).
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
(3) Richard Montague showed how to formalize semantics syntactically.
That is one way but not the only one and perhaps not the best way.
When dealing with complexity of natural language it is the only way that anyone has ever provided semantics.
(4) Thus my definitions above <are> semantic via syntax.
No, they do not depend on semantics.
I am stipulating that all terms have had their full semantics defined syntactically. "John drives a car." is linked to ever details about
{John}, {Drives} and {Automobiles}. in a knowledge ontology https://en.wikipedia.org/wiki/Ontology_(information_science)
"This sentence is not true" is formalized as LP := ~True(LP)
With the above definitions deductive incompleteness can be expressed
DeductivelyIncomplete ≡ (⊢ x) ∧ (⊢ ¬x).
Mikko
Yet when we forbid terms-of-the-art from diverging from their root
meaning then incomplete does not mean that formal systems lack the
ability to prove self-contradictory sentences.
The root meanings are not relevant.
Calling the incoherent gibberish of epistemological antinomies
undecidable is like saying that one cannot make up ones mind
whether a kitten is a 15 story office building of a 16 story
office building with no option for {incorrect question}.
The semantics of of {knowledge ontology} would resolve this
as a type mismatch error.
By the theory of simple types I mean the doctrine which says that the
objects of thought (or, in another interpretation, the symbolic
expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such
relations, etc. (with a similar hierarchy for extensions), and that
sentences of the form: " a has the property φ ", " b bears the relation
R to c ", etc. are meaningless, if a, b, c, R, φ are not of types
fitting together. https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
If you let words mean something
else that their common meanings you must be very careful or you will
be confused.
Undecidable means that one cannot make up ones mind
Incomplete means that something is missing
This untrue in PA...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43-44)
Thus Incomplete(L) is merely a terribly misleading euphemism for
~True(L,x).
Anyway there are sentences that are well formed formulas of the
first order Peano arithmetic that are not provable and not
negations of provable sentences.
Another point that you may want to consider is that there is no
complete method to find out whether a sentence of the first order
Peano arithmetic is provable.
Mikko
My system probably fixes this too.
When semantic incoherence is screened out all undecidable
sentences simply become untrue sentences.
True(L,x) ≡ (L ⊢ x)
False(L,x) ≡ (L ⊢ ~x)
else ~Truth_bearer(L,x) // screens out epistemological antinomies
The whole problem is that logicians do not understand and do not
care about the fact that the philosophical foundations of logic are incoherent.
They only care about the rules of logic that they learned-by-rote.
I am specifying {correct reasoning} on the basis of the mutually self- defining and interlocking semantic tautologies that the whole body of analytic human knowledge really is. When logic systems diverge from this
they are establishing their break from reality.
On 12/9/2023 11:53 AM, Ross Finlayson wrote:
On Saturday, December 9, 2023 at 9:10:01 AM UTC-8, olcott wrote:
On 12/9/2023 9:27 AM, olcott wrote:
On 12/9/2023 3:53 AM, Mikko wrote:I am specifying {correct reasoning} on the basis of the mutually self-
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge >>>>>> mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical
propositions
https://en.wikipedia.org/wiki/Categorical_proposition
(3) Richard Montague showed how to formalize semantics syntactically. >>>>>That is one way but not the only one and perhaps not the best way.
When dealing with complexity of natural language it is the only way
that
anyone has ever provided semantics.
(4) Thus my definitions above <are> semantic via syntax.
No, they do not depend on semantics.
I am stipulating that all terms have had their full semantics defined
syntactically. "John drives a car." is linked to ever details about
{John}, {Drives} and {Automobiles}. in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
"This sentence is not true" is formalized as LP := ~True(LP)
With the above definitions deductive incompleteness can be expressed >>>>>>> DeductivelyIncomplete ≡ (⊢ x) ∧ (⊢ ¬x).
Mikko
Yet when we forbid terms-of-the-art from diverging from their root >>>>>> meaning then incomplete does not mean that formal systems lack the >>>>>> ability to prove self-contradictory sentences.
The root meanings are not relevant.
Calling the incoherent gibberish of epistemological antinomies
undecidable is like saying that one cannot make up ones mind
whether a kitten is a 15 story office building of a 16 story
office building with no option for {incorrect question}.
The semantics of of {knowledge ontology} would resolve this
as a type mismatch error.
By the theory of simple types I mean the doctrine which says that the
objects of thought (or, in another interpretation, the symbolic
expressions) are divided into types, namely: individuals, properties of >>>> individuals, relations between individuals, properties of such
relations, etc. (with a similar hierarchy for extensions), and that
sentences of the form: " a has the property φ ", " b bears the relation >>>> R to c ", etc. are meaningless, if a, b, c, R, φ are not of types
fitting together.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944
If you let words mean something
else that their common meanings you must be very careful or you will >>>>> be confused.
Undecidable means that one cannot make up ones mind
Incomplete means that something is missing
This untrue in PA...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43-44)
Thus Incomplete(L) is merely a terribly misleading euphemism for
~True(L,x).
Anyway there are sentences that are well formed formulas of the
first order Peano arithmetic that are not provable and not
negations of provable sentences.
Another point that you may want to consider is that there is no
complete method to find out whether a sentence of the first order
Peano arithmetic is provable.
Mikko
My system probably fixes this too.
When semantic incoherence is screened out all undecidable
sentences simply become untrue sentences.
True(L,x) ≡ (L ⊢ x)
False(L,x) ≡ (L ⊢ ~x)
else ~Truth_bearer(L,x) // screens out epistemological antinomies
The whole problem is that logicians do not understand and do not
care about the fact that the philosophical foundations of logic are
incoherent.
They only care about the rules of logic that they learned-by-rote.
defining and interlocking semantic tautologies that the whole body of
analytic human knowledge really is. When logic systems diverge from this >>> they are establishing their break from reality.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
Hegel says that the true logical objects and their arguments
start from nothing, no presuppositions nor stipulations, at all,
then that in a world of those after the negatory and affirmatory,
is for a theory of true objects at all.
Otherwise your course of closure is already sort of broken open,
and if you want to address Goedel and Tarski, it's inside that
universe of things.
Either way, both of you.
When one understands truthmaker theory then one comprehends
that there cannot possibly be any analytical truth that lacks
a truthmaker. Ignorance of this semantic tautology is no
rebuttal what-so-ever.
Gödel and Tarski were clearly confused by epistemological antinomies
never comprehending that they are simply not truth bearers.
On 12/9/2023 1:00 PM, olcott wrote:
On 12/9/2023 11:53 AM, Ross Finlayson wrote:
On Saturday, December 9, 2023 at 9:10:01 AM UTC-8, olcott wrote:
On 12/9/2023 9:27 AM, olcott wrote:
On 12/9/2023 3:53 AM, Mikko wrote:I am specifying {correct reasoning} on the basis of the mutually self- >>>> defining and interlocking semantic tautologies that the whole body of
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion. >>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>> logic to diverge from the model of the syllogism is a huge >>>>>>> mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical
propositions
https://en.wikipedia.org/wiki/Categorical_proposition
(3) Richard Montague showed how to formalize semantics
syntactically.
That is one way but not the only one and perhaps not the best way. >>>>>>
When dealing with complexity of natural language it is the only way
that
anyone has ever provided semantics.
(4) Thus my definitions above <are> semantic via syntax.
No, they do not depend on semantics.
I am stipulating that all terms have had their full semantics defined >>>>> syntactically. "John drives a car." is linked to ever details about
{John}, {Drives} and {Automobiles}. in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
"This sentence is not true" is formalized as LP := ~True(LP)
With the above definitions deductive incompleteness can be
expressed
DeductivelyIncomplete ≡ (⊢ x) ∧ (⊢ ¬x).
Mikko
Yet when we forbid terms-of-the-art from diverging from their root >>>>>>> meaning then incomplete does not mean that formal systems lack the >>>>>>> ability to prove self-contradictory sentences.
The root meanings are not relevant.
Calling the incoherent gibberish of epistemological antinomies
undecidable is like saying that one cannot make up ones mind
whether a kitten is a 15 story office building of a 16 story
office building with no option for {incorrect question}.
The semantics of of {knowledge ontology} would resolve this
as a type mismatch error.
By the theory of simple types I mean the doctrine which says that the >>>>> objects of thought (or, in another interpretation, the symbolic
expressions) are divided into types, namely: individuals,
properties of
individuals, relations between individuals, properties of such
relations, etc. (with a similar hierarchy for extensions), and that
sentences of the form: " a has the property φ ", " b bears the
relation
R to c ", etc. are meaningless, if a, b, c, R, φ are not of types
fitting together.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 >>>>>
If you let words mean something
else that their common meanings you must be very careful or you will >>>>>> be confused.
Undecidable means that one cannot make up ones mind
Incomplete means that something is missing
This untrue in PA...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43-44)
Thus Incomplete(L) is merely a terribly misleading euphemism for >>>>>>> ~True(L,x).
Anyway there are sentences that are well formed formulas of the
first order Peano arithmetic that are not provable and not
negations of provable sentences.
Another point that you may want to consider is that there is no
complete method to find out whether a sentence of the first order
Peano arithmetic is provable.
Mikko
My system probably fixes this too.
When semantic incoherence is screened out all undecidable
sentences simply become untrue sentences.
True(L,x) ≡ (L ⊢ x)
False(L,x) ≡ (L ⊢ ~x)
else ~Truth_bearer(L,x) // screens out epistemological antinomies
The whole problem is that logicians do not understand and do not
care about the fact that the philosophical foundations of logic are
incoherent.
They only care about the rules of logic that they learned-by-rote.
analytic human knowledge really is. When logic systems diverge from
this
they are establishing their break from reality.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius >>>> hits a target no one else can see." Arthur Schopenhauer
Hegel says that the true logical objects and their arguments
start from nothing, no presuppositions nor stipulations, at all,
then that in a world of those after the negatory and affirmatory,
is for a theory of true objects at all.
Otherwise your course of closure is already sort of broken open,
and if you want to address Goedel and Tarski, it's inside that
universe of things.
Either way, both of you.
When one understands truthmaker theory then one comprehends
that there cannot possibly be any analytical truth that lacks
a truthmaker. Ignorance of this semantic tautology is no
rebuttal what-so-ever.
Gödel and Tarski were clearly confused by epistemological antinomies
never comprehending that they are simply not truth bearers.
Every opinion that anyone else in the world has or every had
cannot possibly make one rat's ass of any difference at all
because it <is> what and how it is (as explained above) and
no mere opinion can possibly change this at all.
Expressions that are necessarily true and thus impossibly false can
be verified as completely true entirely on the basis of their meaning.
On 12/9/2023 2:34 PM, olcott wrote:
On 12/9/2023 1:38 PM, olcott wrote:
On 12/9/2023 1:00 PM, olcott wrote:
On 12/9/2023 11:53 AM, Ross Finlayson wrote:
On Saturday, December 9, 2023 at 9:10:01 AM UTC-8, olcott wrote:
On 12/9/2023 9:27 AM, olcott wrote:
On 12/9/2023 3:53 AM, Mikko wrote:I am specifying {correct reasoning} on the basis of the mutually
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>> logic to diverge from the model of the syllogism is a >>>>>>>>> huge mistake.
A syllogism is a formal inference that does not depend on
semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical
propositions
https://en.wikipedia.org/wiki/Categorical_proposition
(3) Richard Montague showed how to formalize semantics
syntactically.
That is one way but not the only one and perhaps not the best way. >>>>>>>>
When dealing with complexity of natural language it is the only
way that
anyone has ever provided semantics.
(4) Thus my definitions above <are> semantic via syntax.
No, they do not depend on semantics.
I am stipulating that all terms have had their full semantics
defined
syntactically. "John drives a car." is linked to ever details about >>>>>>> {John}, {Drives} and {Automobiles}. in a knowledge ontology
https://en.wikipedia.org/wiki/Ontology_(information_science)
"This sentence is not true" is formalized as LP := ~True(LP)
With the above definitions deductive incompleteness can be >>>>>>>>>> expressed
DeductivelyIncomplete ≡ (⊢ x) ∧ (⊢ ¬x).
Mikko
Yet when we forbid terms-of-the-art from diverging from their root >>>>>>>>> meaning then incomplete does not mean that formal systems lack the >>>>>>>>> ability to prove self-contradictory sentences.
The root meanings are not relevant.
Calling the incoherent gibberish of epistemological antinomies
undecidable is like saying that one cannot make up ones mind
whether a kitten is a 15 story office building of a 16 story
office building with no option for {incorrect question}.
The semantics of of {knowledge ontology} would resolve this
as a type mismatch error.
By the theory of simple types I mean the doctrine which says that >>>>>>> the
objects of thought (or, in another interpretation, the symbolic
expressions) are divided into types, namely: individuals,
properties of
individuals, relations between individuals, properties of such
relations, etc. (with a similar hierarchy for extensions), and that >>>>>>> sentences of the form: " a has the property φ ", " b bears the
relation
R to c ", etc. are meaningless, if a, b, c, R, φ are not of types >>>>>>> fitting together.
https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 >>>>>>>
If you let words mean something
else that their common meanings you must be very careful or you >>>>>>>> will
be confused.
Undecidable means that one cannot make up ones mind
Incomplete means that something is missing
This untrue in PA...14 Every epistemological antinomy can likewise be used for a >>>>>>>>> similar undecidability proof... (Gödel 1931:43-44)
Thus Incomplete(L) is merely a terribly misleading euphemism for >>>>>>>>> ~True(L,x).
Anyway there are sentences that are well formed formulas of the >>>>>>>> first order Peano arithmetic that are not provable and not
negations of provable sentences.
Another point that you may want to consider is that there is no >>>>>>>> complete method to find out whether a sentence of the first order >>>>>>>> Peano arithmetic is provable.
Mikko
My system probably fixes this too.
When semantic incoherence is screened out all undecidable
sentences simply become untrue sentences.
True(L,x) ≡ (L ⊢ x)
False(L,x) ≡ (L ⊢ ~x)
else ~Truth_bearer(L,x) // screens out epistemological antinomies >>>>>>>
The whole problem is that logicians do not understand and do not >>>>>>> care about the fact that the philosophical foundations of logic are >>>>>>> incoherent.
They only care about the rules of logic that they learned-by-rote. >>>>>>>
self-
defining and interlocking semantic tautologies that the whole body of >>>>>> analytic human knowledge really is. When logic systems diverge
from this
they are establishing their break from reality.
--
Copyright 2023 Olcott "Talent hits a target no one else can hit;
Genius
hits a target no one else can see." Arthur Schopenhauer
Hegel says that the true logical objects and their arguments
start from nothing, no presuppositions nor stipulations, at all,
then that in a world of those after the negatory and affirmatory,
is for a theory of true objects at all.
Otherwise your course of closure is already sort of broken open,
and if you want to address Goedel and Tarski, it's inside that
universe of things.
Either way, both of you.
When one understands truthmaker theory then one comprehends
that there cannot possibly be any analytical truth that lacks
a truthmaker. Ignorance of this semantic tautology is no
rebuttal what-so-ever.
Gödel and Tarski were clearly confused by epistemological antinomies
never comprehending that they are simply not truth bearers.
Every opinion that anyone else in the world has or every had
cannot possibly make one rat's ass of any difference at all
because it <is> what and how it is (as explained above) and
no mere opinion can possibly change this at all.
Expressions that are necessarily true and thus impossibly false can
be verified as completely true entirely on the basis of their meaning.
"So ONLY statements that are necessarily true
by the meaning of there words are true?"
*I never limited meaning to the meaning of words*
Clearly you simply don't understand the philosophical foundation of logic.
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions https://en.wikipedia.org/wiki/Categorical_proposition
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge
mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese. https://en.wikipedia.org/wiki/Principle_of_explosion
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
On Sunday, December 10, 2023 at 11:27:26 AM UTC-8, Richard Damon wrote:
On 12/10/23 10:09 AM, olcott wrote:
On 12/10/2023 4:10 AM, Mikko wrote:The. DO SO, and show what you can do with it.
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion. >>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>> logic to diverge from the model of the syllogism is a huge >>>>>>> mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
Remember, you are changing the foundation, so you need to start at the
bottom, you can't use ANYTHIHG from the logic system you say is broken,
and you have to accept the rules of any logic system you take from.
Nope. Remember, the principle of explosion only comes into play once you
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
have your first contradiction. That means your "semantic" rules have
already lost, so they can't help you here.
Your missing a few steps in there.
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese.
https://en.wikipedia.org/wiki/Principle_of_explosion
But that doesn't actually help, since once you HAVE a contradiction,
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
that rule is proved incorrect.
Remember, the principle of explosion is once you HAVE ONE contradiction,
the rules of normal logic allow you to prove any other statement.
You are just proving you don't actually understand how logic works.
You can't just try to "define" the principle away, as your attempted
safety valve was broken already.
In relevance logic there's no principle of explosion.
Ex falso nihilum. So, ....
Here it's that "writing a fallacy after a fallacy is an error".
Or:
Socrates is a man.
He won't be made a liar.
On 12/10/2023 5:03 PM, Ross Finlayson wrote:
On Sunday, December 10, 2023 at 2:55:22 PM UTC-8, Richard Damon wrote:
On 12/10/23 2:59 PM, Ross Finlayson wrote:
On Sunday, December 10, 2023 at 11:27:26 AM UTC-8, Richard Damon wrote: >>>>> On 12/10/23 10:09 AM, olcott wrote:Yea, if Olcott would accept the limits of logic imposed by Relevence
On 12/10/2023 4:10 AM, Mikko wrote:The. DO SO, and show what you can do with it.
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic
knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>>> logic to diverge from the model of the syllogism is a huge >>>>>>>>>> mistake.
A syllogism is a formal inference that does not depend on
semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
Remember, you are changing the foundation, so you need to start at the >>>>> bottom, you can't use ANYTHIHG from the logic system you say is
broken,
and you have to accept the rules of any logic system you take from. >>>>>>
The only way that we can tell the the principle of explosionNope. Remember, the principle of explosion only comes into play
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
once you
have your first contradiction. That means your "semantic" rules have >>>>> already lost, so they can't help you here.
Your missing a few steps in there.
The cow jumped over the Moon and The cow did not jump over the Moon >>>>>> therefore the Moon is made from green cheese.
https://en.wikipedia.org/wiki/Principle_of_explosion
But that doesn't actually help, since once you HAVE a contradiction, >>>>> that rule is proved incorrect.
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
Remember, the principle of explosion is once you HAVE ONE
contradiction,
the rules of normal logic allow you to prove any other statement.
You are just proving you don't actually understand how logic works.
You can't just try to "define" the principle away, as your attempted >>>>> safety valve was broken already.
In relevance logic there's no principle of explosion.
Ex falso nihilum. So, ....
Here it's that "writing a fallacy after a fallacy is an error".
Or:
Socrates is a man.
He won't be made a liar.
Logic, and admit to the limitations thereof, it would seem to be close
to what he is thinking of.
His problem, is he thinks he can just redefine ALL logic to use this,
and still be able to get to all the useful things of classical logic,
just get rid of the few pesky results he doesn't like, like
incompleteness and uncomputability.
What "results"?
You can still have incompleteness and uncomputability as
simply as after related rates and bounds, and, the consideration
of the ordinary, but, there's something to be said for that there
is a "true theory" _at all_, whether or not of course the usual
development in psychology and philosophy make for that we
are all both individuals with our own worlds, but, in a world, all.
Otherwise there's nothing that's actually what would be accepted
as facts in "classical logic" that isn't in "relevance logic", and such
ambiguities as "material implication" and for that matter Ex Falso
Quodlibet, can be kept right out.
I thank you much for acknowledging such notions, it is the sort
of thing a "conscientious logician" must allow.
Getting rid of material implication in no way affects the abstract
world of concepts, in contingencies. It does however strengthen
many truth-valued systems like the tableau under changes, and
then gets into disambiguation of the relevant concepts the
entailment and the modality, the monotony, the things.
Warm regards
The entire body of human analytic knowledge is simply connected
semantic meanings. True(x) means that x is connected to the
meanings that make it true, thus undecidability is inherently
impossible.
Math and logic get confused about this because they are mostly
insufficiently expressive to encode every detail of these semantic
meanings.
On Sunday, December 10, 2023 at 2:55:22 PM UTC-8, Richard Damon wrote:
On 12/10/23 2:59 PM, Ross Finlayson wrote:
On Sunday, December 10, 2023 at 11:27:26 AM UTC-8, Richard Damon wrote: >>>> On 12/10/23 10:09 AM, olcott wrote:Yea, if Olcott would accept the limits of logic imposed by Relevence
On 12/10/2023 4:10 AM, Mikko wrote:The. DO SO, and show what you can do with it.
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>> logic to diverge from the model of the syllogism is a huge
mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
Remember, you are changing the foundation, so you need to start at the >>>> bottom, you can't use ANYTHIHG from the logic system you say is broken, >>>> and you have to accept the rules of any logic system you take from.
Nope. Remember, the principle of explosion only comes into play once you >>>> have your first contradiction. That means your "semantic" rules have
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
already lost, so they can't help you here.
Your missing a few steps in there.
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese.
https://en.wikipedia.org/wiki/Principle_of_explosion
But that doesn't actually help, since once you HAVE a contradiction,
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
that rule is proved incorrect.
Remember, the principle of explosion is once you HAVE ONE contradiction, >>>> the rules of normal logic allow you to prove any other statement.
You are just proving you don't actually understand how logic works.
You can't just try to "define" the principle away, as your attempted
safety valve was broken already.
In relevance logic there's no principle of explosion.
Ex falso nihilum. So, ....
Here it's that "writing a fallacy after a fallacy is an error".
Or:
Socrates is a man.
He won't be made a liar.
Logic, and admit to the limitations thereof, it would seem to be close
to what he is thinking of.
His problem, is he thinks he can just redefine ALL logic to use this,
and still be able to get to all the useful things of classical logic,
just get rid of the few pesky results he doesn't like, like
incompleteness and uncomputability.
What "results"?
You can still have incompleteness and uncomputability as
simply as after related rates and bounds, and, the consideration
of the ordinary, but, there's something to be said for that there
is a "true theory" _at all_, whether or not of course the usual
development in psychology and philosophy make for that we
are all both individuals with our own worlds, but, in a world, all.
Otherwise there's nothing that's actually what would be accepted
as facts in "classical logic" that isn't in "relevance logic", and such ambiguities as "material implication" and for that matter Ex Falso
Quodlibet, can be kept right out.
I thank you much for acknowledging such notions, it is the sort
of thing a "conscientious logician" must allow.
Getting rid of material implication in no way affects the abstract
world of concepts, in contingencies. It does however strengthen
many truth-valued systems like the tableau under changes, and
then gets into disambiguation of the relevant concepts the
entailment and the modality, the monotony, the things.
Warm regards
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese.
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion. >>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>> logic to diverge from the model of the syllogism is a huge >>>>>>> mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense.
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese.
Have you ever met the cow that both jumped over the Moon and did not
jump over the Moon?
It has always been the case that contradictions only proof falsehood.
The principle of explosion violates https://en.wikipedia.org/wiki/Law_of_noncontradiction
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
That does not process the principle of explosion.
That is what a contradiction actually semantically entails.
People that only learn these things by rote never notice
errors that are discerned by the coherent philosophical foundation.
One way to interprete the situation where False is proven is that
instead of the usual two truth values (False and True) there is only
one that has two names, i.e., False is the same as True.
Nonsense gibberish. Bivalent formal systems inherently have a set of immutable properties. This is not merely a game, unless we formalize True(L,x) defeating Tarski dangerous lies will cause climate change
to destroy all life on Earth by the time we hit +8C as early as 2100.
https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
Then every
True sentence is False and every False sentence is True. If there
are no other truth values then every sentence is both True and False.
Not very useful but coherent.
Mikko
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion. >>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>> logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense.
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese.
Have you ever met the cow that both jumped over the Moon and did not
jump over the Moon?
It has always been the case that contradictions only proof falsehood.
The principle of explosion violates https://en.wikipedia.org/wiki/Law_of_noncontradiction
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
That does not process the principle of explosion.
That is what a contradiction actually semantically entails.
People that only learn these things by rote never notice
errors that are discerned by the coherent philosophical foundation.
One way to interprete the situation where False is proven is that
instead of the usual two truth values (False and True) there is only
one that has two names, i.e., False is the same as True.
Nonsense gibberish. Bivalent formal systems inherently have a set of immutable properties.
This is not merely a game, unless we formalize
True(L,x) defeating Tarski dangerous lies will cause climate change
to destroy all life on Earth by the time we hit +8C as early as 2100.
https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
Then every
True sentence is False and every False sentence is True. If there
are no other truth values then every sentence is both True and False.
Not very useful but coherent.
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>> logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense.
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
The principle of explosion "proves" nonsense when semantics are required. >>> (a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find
a cat that both is a dog and is not a dog you can safely conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
The cow jumped over the Moon and The cow did not jump over the Moon
therefore the Moon is made from green cheese.
Have you ever met the cow that both jumped over the Moon and did not
jump over the Moon?
It has always been the case that contradictions only proof falsehood.
The principle of explosion violates
https://en.wikipedia.org/wiki/Law_of_noncontradiction
No, it is not. From a contradiction you can prove anything,
That has always been the misconception as proved below:
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
including any truth. But proving an obvious falsehood is the
useful conclusion: it proves that at least one of the
premises is false. This proof method is often used and some
people find proofs of this kind easier to understand than
direct proofs.
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
That does not process the principle of explosion.
That is what a contradiction actually semantically entails.
Entails but does not process.
People that only learn these things by rote never notice
errors that are discerned by the coherent philosophical foundation.
One way to interprete the situation where False is proven is that
instead of the usual two truth values (False and True) there is only
one that has two names, i.e., False is the same as True.
Nonsense gibberish. Bivalent formal systems inherently have a set of
immutable properties.
So do all formal systems. If an apparently bivalent system is found
to be univalent then univalence is and has always been one of those
immutable properties.
If any {living breathing animal} cat is found to be a 15 story
office building this proves that it is time to check yourself
into a mental ward.
This is not merely a game, unless we formalize
True(L,x) defeating Tarski dangerous lies will cause climate change
to destroy all life on Earth by the time we hit +8C as early as 2100.
https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
Your logic system is still far from useful for these problems.
Only because you are not evaluating my correct reasoning on the basis
of reasoning you are evaluating on the basis that it does not conform to
what you learned by rote.
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>>>
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge: >>>>>>>>>>>>> True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>>>> logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics. >>>>>>>>>>
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as >>>>>>>>> Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning* >>>>>>>
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense.
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy?
The principle of explosion "proves" nonsense when semantics are required. >>>>> (a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find
a cat that both is a dog and is not a dog you can safely conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
I.e., shows that there are no solutions; i.e., no matter what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives NULL.
This proves that the error is divorcing semantics from logic.
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>>> semantics of T, so True as defined above is not a semantic >>>>>>>>>> notion.
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic >>>>>>>>>>>>> knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is >>>>>>>>>>>> the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>
(2) I am saying that dividing semantics from syntax thus >>>>>>>>>>> enabling
logic to diverge from the model of the syllogism is a >>>>>>>>>>> huge mistake.
A syllogism is a formal inference that does not depend on
semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as >>>>>>>>> Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning* >>>>>>>
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense.
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy?
The principle of explosion "proves" nonsense when semantics are
required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find
a cat that both is a dog and is not a dog you can safely conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its
solution set.
I.e., shows that there are no solutions; i.e., no matter what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives
NULL. This proves that the error is divorcing semantics from logic.
The cow jumped over the Moon and The cow did not jump over the Moon >>>>>>> therefore the Moon is made from green cheese.
Have you ever met the cow that both jumped over the Moon and did not >>>>>> jump over the Moon?
It has always been the case that contradictions only proof falsehood. >>>>> The principle of explosion violates
https://en.wikipedia.org/wiki/Law_of_noncontradiction
No, it is not. From a contradiction you can prove anything,
That has always been the misconception as proved below:
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
That does not prove what you claim.
including any truth. But proving an obvious falsehood is the
useful conclusion: it proves that at least one of the
premises is false. This proof method is often used and some
people find proofs of this kind easier to understand than
direct proofs.
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
That does not process the principle of explosion.
That is what a contradiction actually semantically entails.
Entails but does not process.
People that only learn these things by rote never notice
errors that are discerned by the coherent philosophical foundation.
One way to interprete the situation where False is proven is that
instead of the usual two truth values (False and True) there is only >>>>>> one that has two names, i.e., False is the same as True.
Nonsense gibberish. Bivalent formal systems inherently have a set
of immutable properties.
So do all formal systems. If an apparently bivalent system is found
to be univalent then univalence is and has always been one of those
immutable properties.
If any {living breathing animal} cat is found to be a 15 story
office building this proves that it is time to check yourself
into a mental ward.
No point to think about that as long as no such cat is found.
This is not merely a game, unless we formalize
True(L,x) defeating Tarski dangerous lies will cause climate change
to destroy all life on Earth by the time we hit +8C as early as 2100. >>>>>
https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
Your logic system is still far from useful for these problems.
Only because you are not evaluating my correct reasoning on the basis
of reasoning you are evaluating on the basis that it does not conform to >>> what you learned by rote.
Perhaps only because of that but if it is because of that it will stay
as it is because of that.
Mikko
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:How would semantics prevent any derivation of any other result?
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:Ross Finlayson said that the principle of explosion cannot exist in >>>>>>> relevance logic, thus making my point.
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>>>>>
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>>>>>> logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as >>>>>>>>>>> Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning* >>>>>>>>>
The only way that we can tell the the principle of explosion >>>>>>>>> is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense. >>>>>>>
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy? >>>>
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find
a cat that both is a dog and is not a dog you can safely conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
I.e., shows that there are no solutions; i.e., no matter what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives NULL. >>
This proves that the error is divorcing semantics from logic.
How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made
from green cheese.
The syllogism says that this doesn't prove any damn thing.
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:Ross Finlayson said that the principle of explosion cannot
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics.
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve >>>>>>>>>>>>>> any
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic >>>>>>>>>>>>>>>>> knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, >>>>>>>>>>>>>>>> which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>>>>>
semantics of T, so True as defined above is not a semantic >>>>>>>>>>>>>> notion.
(2) I am saying that dividing semantics from syntax thus >>>>>>>>>>>>>>> enabling
logic to diverge from the model of the syllogism is >>>>>>>>>>>>>>> a huge mistake.
A syllogism is a formal inference that does not depend on >>>>>>>>>>>>>> semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>
It always depends on defined sets providing its semantics >>>>>>>>>>>>> as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct
reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>> that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense. >>>>>>>>>
exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics >>>>>>> is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate
fallacy?
The principle of explosion "proves" nonsense when semantics are >>>>>>>>> required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find >>>>>>>> a cat that both is a dog and is not a dog you can safely conclude >>>>>>>> that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its >>>>>>> solution set.
I.e., shows that there are no solutions; i.e., no matter what else is >>>>>> assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only
derives NULL.
How would semantics prevent any derivation of any other result?
This proves that the error is divorcing semantics from logic.
How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon
is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism
only the empty set is derived thus refuting the principle of explosion.
The syllogism says that this doesn't prove any damn thing.
The scope of syllogistic logic is very limited. It works perfectly
in that scope but fails to infer anything from more complex premises.
(a) Bob is either a cat or a dog.
(b) All cats are mammals.
(c) All dogs are mammals.
The ordinary logic can infer that Bob is a mammal but syllogistic
logic can't.
Mikko
On 12/14/2023 8:37 PM, Ross Finlayson wrote:
On Thursday, December 14, 2023 at 3:42:56 PM UTC-8, Richard Damon wrote: >>> On 12/14/23 10:21 AM, olcott wrote:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is >>>>>>>>>>>>> nonsense.
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>
The way that is works for the entire body of analytic >>>>>>>>>>>>>>>>>>>> knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, >>>>>>>>>>>>>>>>>>> which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently >>>>>>>>>>>>>>>>>> semantic.
The usual notions. The expression (T ⊢ x) does not involve >>>>>>>>>>>>>>>>> any
semantics of T, so True as defined above is not a semantic >>>>>>>>>>>>>>>>> notion.
(2) I am saying that dividing semantics from syntax thus >>>>>>>>>>>>>>>>>> enabling
logic to diverge from the model of the syllogism is
a huge mistake.
A syllogism is a formal inference that does not depend on >>>>>>>>>>>>>>>>> semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>
It always depends on defined sets providing its semantics >>>>>>>>>>>>>>>> as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct >>>>>>>>>>>>>> reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>>
Ross Finlayson said that the principle of explosion cannot >>>>>>>>>>>> exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when
semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate >>>>>>>>> fallacy?
The principle of explosion "proves" nonsense when semantics are >>>>>>>>>>>> required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever >>>>>>>>>>> find
a cat that both is a dog and is not a dog you can safely >>>>>>>>>>> conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its >>>>>>>>>> solution set.
I.e., shows that there are no solutions; i.e., no matter what >>>>>>>>> else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only
derives NULL.
How would semantics prevent any derivation of any other result?
This proves that the error is divorcing semantics from logic.
How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is
made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon
is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism
only the empty set is derived thus refuting the principle of explosion. >>> No, we can derive that some dogs are not dogs.
And thus the logic system is broken.
The syllogism says that this doesn't prove any damn thing.
The scope of syllogistic logic is very limited. It works perfectly
in that scope but fails to infer anything from more complex premises. >>>>>
(a) Bob is either a cat or a dog.
(b) All cats are mammals.
(c) All dogs are mammals.
The ordinary logic can infer that Bob is a mammal but syllogistic
logic can't.
Mikko
So, as a false antecedent, you can't tell the difference,
and it just asserts itself again?
I know, whatever you say, whatever you say, ....
1) All syllogistic components are orderless
2) All syllogistic components must be evaluated in all orders and agree
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
Defines a pair of sets that do not intersect thus
the empty set <is> the conclusion.
This refutes the Principle of Explosion.
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:Ross Finlayson said that the principle of explosion cannot exist in >>>>>>>>> relevance logic, thus making my point.
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics.
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>>>>>>> semantics of T, so True as defined above is not a semantic notion.
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>
It always depends on defined sets providing its semantics as >>>>>>>>>>>>> Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct reasoning* >>>>>>>>>>>
The only way that we can tell the the principle of explosion >>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>> that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense. >>>>>>>>>
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics >>>>>>> is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy? >>>>>>
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find >>>>>>>> a cat that both is a dog and is not a dog you can safely conclude >>>>>>>> that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
I.e., shows that there are no solutions; i.e., no matter what else is >>>>>> assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives NULL.
How would semantics prevent any derivation of any other result?
This proves that the error is divorcing semantics from logic.
How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon
is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism
only the empty set is derived thus refuting the principle of explosion.
The scope of syllogistic logic is very limited. It works perfectly
in that scope but fails to infer anything from more complex premises.
(a) Bob is either a cat or a dog.
(b) All cats are mammals.
(c) All dogs are mammals.
The ordinary logic can infer that Bob is a mammal but syllogistic
logic can't.
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:Ross Finlayson said that the principle of explosion cannot >>>>>>>>>>> exist in
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is nonsense. >>>>>>>>>>>
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics.
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not >>>>>>>>>>>>>>>> involve any
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic >>>>>>>>>>>>>>>>>>> knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, >>>>>>>>>>>>>>>>>> which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>>>>>>>
semantics of T, so True as defined above is not a >>>>>>>>>>>>>>>> semantic notion.
(2) I am saying that dividing semantics from syntax >>>>>>>>>>>>>>>>> thus enabling
logic to diverge from the model of the syllogism >>>>>>>>>>>>>>>>> is a huge mistake.
A syllogism is a formal inference that does not depend >>>>>>>>>>>>>>>> on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>
It always depends on defined sets providing its semantics >>>>>>>>>>>>>>> as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct >>>>>>>>>>>>> reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics >>>>>>>>> is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate >>>>>>>> fallacy?
The principle of explosion "proves" nonsense when semantics >>>>>>>>>>> are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find >>>>>>>>>> a cat that both is a dog and is not a dog you can safely conclude >>>>>>>>>> that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as >>>>>>>>> its solution set.
I.e., shows that there are no solutions; i.e., no matter what
else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only
derives NULL.
How would semantics prevent any derivation of any other result?
This proves that the error is divorcing semantics from logic.
How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made >>>>> from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon
is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism
only the empty set is derived thus refuting the principle of explosion.
No syllogistic inference rule can derive the empty set.
I just proved otherwise.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The intersection of (a) and (b) is the empty set.
A set is not
a sentence of syllogistic logic. The principle of explosion is not
valid in syllogistic logic but that does not refute its validity in
stronger logics.
The actual root cause of the problem seems to be that
the term {valid} is defined incoherently.
When a conclusion is defined as a necessary consequence of
all of its premises, then explosion cannot occur.
There is no semantic meaning from (a) and (b) that can be
carried over to a conclusion.
As I already said,
The scope of syllogistic logic is very limited. It works perfectly
in that scope but fails to infer anything from more complex premises.
(a) Bob is either a cat or a dog.
(b) All cats are mammals.
(c) All dogs are mammals.
The ordinary logic can infer that Bob is a mammal but syllogistic
logic can't.
Mikko
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:Ross Finlayson said that the principle of explosion cannot exist in >>>>>>>>>>> relevance logic, thus making my point.
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is nonsense. >>>>>>>>>>>
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics.
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve any
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>>>>>>>
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>
It always depends on defined sets providing its semantics as >>>>>>>>>>>>>>> Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics >>>>>>>>> is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy?
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find >>>>>>>>>> a cat that both is a dog and is not a dog you can safely conclude >>>>>>>>>> that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
I.e., shows that there are no solutions; i.e., no matter what else is >>>>>>>> assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives NULL.
How would semantics prevent any derivation of any other result?
This proves that the error is divorcing semantics from logic.
How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made >>>>> from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon
is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism
only the empty set is derived thus refuting the principle of explosion.
No syllogistic inference rule can derive the empty set.
I just proved otherwise.
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The intersection of (a) and (b) is the empty set.
A set is not
a sentence of syllogistic logic. The principle of explosion is not
valid in syllogistic logic but that does not refute its validity in
stronger logics.
The actual root cause of the problem seems to be that
the term {valid} is defined incoherently.
When a conclusion is defined as a necessary consequence of
all of its premises, then explosion cannot occur.
There is no semantic meaning from (a) and (b) that can be
carried over to a conclusion.
As I already said,
The scope of syllogistic logic is very limited. It works perfectly
in that scope but fails to infer anything from more complex premises.
(a) Bob is either a cat or a dog.
(b) All cats are mammals.
(c) All dogs are mammals.
The ordinary logic can infer that Bob is a mammal but syllogistic
logic can't.
On 12/17/2023 2:08 AM, Mikko wrote:
On 2023-12-15 15:33:59 +0000, olcott said:
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is >>>>>>>>>>>>>> nonsense.
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>
The way that is works for the entire body of >>>>>>>>>>>>>>>>>>>>> analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, >>>>>>>>>>>>>>>>>>>> which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently >>>>>>>>>>>>>>>>>>> semantic.
The usual notions. The expression (T ⊢ x) does not >>>>>>>>>>>>>>>>>> involve any
semantics of T, so True as defined above is not a >>>>>>>>>>>>>>>>>> semantic notion.
(2) I am saying that dividing semantics from syntax >>>>>>>>>>>>>>>>>>> thus enabling
logic to diverge from the model of the syllogism >>>>>>>>>>>>>>>>>>> is a huge mistake.
A syllogism is a formal inference that does not depend >>>>>>>>>>>>>>>>>> on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>>
It always depends on defined sets providing its >>>>>>>>>>>>>>>>> semantics as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct >>>>>>>>>>>>>>> reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>>>
Ross Finlayson said that the principle of explosion cannot >>>>>>>>>>>>> exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when >>>>>>>>>>> semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab
auctoritate fallacy?
The principle of explosion "proves" nonsense when semantics >>>>>>>>>>>>> are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever >>>>>>>>>>>> find
a cat that both is a dog and is not a dog you can safely >>>>>>>>>>>> conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as >>>>>>>>>>> its solution set.
I.e., shows that there are no solutions; i.e., no matter what >>>>>>>>>> else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only >>>>>>>>> derives NULL.
How would semantics prevent any derivation of any other result? >>>>>>>>
This proves that the error is divorcing semantics from logic. >>>>>>>>How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is >>>>>>> made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon >>>>>> is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism >>>>> only the empty set is derived thus refuting the principle of
explosion.
No syllogistic inference rule can derive the empty set.
I just proved otherwise.
You did not prove, you just claimed.
Categorical propositions do define sets that can be
represented by Venn diagrams.
All S are P and No S are P are defined sets that
have no intersection.
Here is the Venn diagrams of the above two defined sets. https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg
On 12/17/2023 2:08 AM, Mikko wrote:
On 2023-12-15 15:33:59 +0000, olcott said:
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:No syllogistic inference rule can derive the empty set.
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:Ross Finlayson said that the principle of explosion cannot exist in
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is nonsense. >>>>>>>>>>>>>
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 12/8/2023 1:52 AM, Mikko wrote:The usual notions. The expression (T ⊢ x) does not involve any
On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic. >>>>>>>>>>>>>>>>>>
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>>
It always depends on defined sets providing its semantics as >>>>>>>>>>>>>>>>> Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>>>
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics >>>>>>>>>>> is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy?
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find >>>>>>>>>>>> a cat that both is a dog and is not a dog you can safely conclude >>>>>>>>>>>> that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
I.e., shows that there are no solutions; i.e., no matter what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives NULL.
How would semantics prevent any derivation of any other result? >>>>>>>>
This proves that the error is divorcing semantics from logic. >>>>>>>>How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made >>>>>>> from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon >>>>>> is made from green cheese. Nobody has ever observed otherwise.
whenever all cats are dogs and some cats are not dogs as a syllogism >>>>> only the empty set is derived thus refuting the principle of explosion. >>>>
I just proved otherwise.
You did not prove, you just claimed.
Categorical propositions do define sets that can be
represented by Venn diagrams.
All S are P and No S are P are defined sets that
have no intersection.
On 12/18/2023 3:32 AM, Mikko wrote:
On 2023-12-17 17:27:48 +0000, olcott said:
On 12/17/2023 2:08 AM, Mikko wrote:
On 2023-12-15 15:33:59 +0000, olcott said:
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is >>>>>>>>>>>>>>>> nonsense.
On 2023-12-09 15:27:08 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
The way that is works for the entire body of >>>>>>>>>>>>>>>>>>>>>>> analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical >>>>>>>>>>>>>>>>>>>>>> thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently >>>>>>>>>>>>>>>>>>>>> semantic.
The usual notions. The expression (T ⊢ x) does not >>>>>>>>>>>>>>>>>>>> involve any
semantics of T, so True as defined above is not a >>>>>>>>>>>>>>>>>>>> semantic notion.
(2) I am saying that dividing semantics from syntax >>>>>>>>>>>>>>>>>>>>> thus enabling
logic to diverge from the model of the >>>>>>>>>>>>>>>>>>>>> syllogism is a huge mistake.
A syllogism is a formal inference that does not >>>>>>>>>>>>>>>>>>>> depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>>>>
It always depends on defined sets providing its >>>>>>>>>>>>>>>>>>> semantics as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct >>>>>>>>>>>>>>>>> reasoning*
The only way that we can tell the the principle of >>>>>>>>>>>>>>>>> explosion
is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>>>>>
Ross Finlayson said that the principle of explosion >>>>>>>>>>>>>>> cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when >>>>>>>>>>>>> semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab
auctoritate fallacy?
The principle of explosion "proves" nonsense when >>>>>>>>>>>>>>> semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you >>>>>>>>>>>>>> ever find
a cat that both is a dog and is not a dog you can safely >>>>>>>>>>>>>> conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set >>>>>>>>>>>>> as its solution set.
I.e., shows that there are no solutions; i.e., no matter >>>>>>>>>>>> what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only >>>>>>>>>>> derives NULL.
How would semantics prevent any derivation of any other result? >>>>>>>>>>
This proves that the error is divorcing semantics from logic. >>>>>>>>>>How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon >>>>>>>>> is made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon >>>>>>>> is made from green cheese. Nobody has ever observed otherwise. >>>>>>>>
whenever all cats are dogs and some cats are not dogs as a syllogism >>>>>>> only the empty set is derived thus refuting the principle of
explosion.
No syllogistic inference rule can derive the empty set.
I just proved otherwise.
You did not prove, you just claimed.
Categorical propositions do define sets that can be
represented by Venn diagrams.
All S are P and No S are P are defined sets that
have no intersection.
More correctly, their intersection is the empty set.
If you regard them as sets then a conclusion is valid if the intersection
of premises is a subset of conclusion; or equivalently, if the
intersection
of all premises and the negation of the conclusion is the empty set.
Mikko
If the intersection of the premises is the empty set because
the premises contradict each other then that proves that
nothing follows from a contradiction. This refutes the POE.
On 12/18/2023 10:18 AM, olcott wrote:
On 12/18/2023 3:32 AM, Mikko wrote:
On 2023-12-17 17:27:48 +0000, olcott said:
On 12/17/2023 2:08 AM, Mikko wrote:
On 2023-12-15 15:33:59 +0000, olcott said:
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is >>>>>>>>>>>>>>>>> nonsense.
On 2023-12-09 15:27:08 +0000, olcott said: >>>>>>>>>>>>>>>>>>>
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>
On 12/8/2023 1:52 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>
The way that is works for the entire body of >>>>>>>>>>>>>>>>>>>>>>>> analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical >>>>>>>>>>>>>>>>>>>>>>> thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently >>>>>>>>>>>>>>>>>>>>>> semantic.
The usual notions. The expression (T ⊢ x) does not >>>>>>>>>>>>>>>>>>>>> involve any
semantics of T, so True as defined above is not a >>>>>>>>>>>>>>>>>>>>> semantic notion.
(2) I am saying that dividing semantics from >>>>>>>>>>>>>>>>>>>>>> syntax thus enabling
logic to diverge from the model of the >>>>>>>>>>>>>>>>>>>>>> syllogism is a huge mistake.
A syllogism is a formal inference that does not >>>>>>>>>>>>>>>>>>>>> depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>>>>>
It always depends on defined sets providing its >>>>>>>>>>>>>>>>>>>> semantics as Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into >>>>>>>>>>>>>>>>>> correct reasoning*
The only way that we can tell the the principle of >>>>>>>>>>>>>>>>>> explosion
is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>>>>>>
Ross Finlayson said that the principle of explosion >>>>>>>>>>>>>>>> cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when >>>>>>>>>>>>>> semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab
auctoritate fallacy?
The principle of explosion "proves" nonsense when >>>>>>>>>>>>>>>> semantics are required.That is a valid inference without any semantics. If you >>>>>>>>>>>>>>> ever find
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese >>>>>>>>>>>>>>>
a cat that both is a dog and is not a dog you can safely >>>>>>>>>>>>>>> conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set >>>>>>>>>>>>>> as its solution set.
I.e., shows that there are no solutions; i.e., no matter >>>>>>>>>>>>> what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion >>>>>>>>>>>> only derives NULL.
How would semantics prevent any derivation of any other result? >>>>>>>>>>>
This proves that the error is divorcing semantics from logic. >>>>>>>>>>>How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon >>>>>>>>>> is made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the >>>>>>>>> Moon
is made from green cheese. Nobody has ever observed otherwise. >>>>>>>>>
whenever all cats are dogs and some cats are not dogs as a
syllogism
only the empty set is derived thus refuting the principle of
explosion.
No syllogistic inference rule can derive the empty set.
I just proved otherwise.
You did not prove, you just claimed.
Categorical propositions do define sets that can be
represented by Venn diagrams.
All S are P and No S are P are defined sets that
have no intersection.
More correctly, their intersection is the empty set.
If you regard them as sets then a conclusion is valid if the
intersection
of premises is a subset of conclusion; or equivalently, if the
intersection
of all premises and the negation of the conclusion is the empty set.
Mikko
If the intersection of the premises is the empty set because
the premises contradict each other then that proves that
nothing follows from a contradiction. This refutes the POE.
Categorical propositions DO DEFINE SETS
All S are P and No S are P are defined sets
that are represented by Venn diagrams.
Everyone that said categorical propositions
do not define sets is WRONG.
Here are the Venn diagrams for those two sets. https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg
There is a single well defined process of correct reasoning
such that when any logical system diverges from this process
*IT IS WRONG IN THE ABSOLUTE SENSE*
On 12/18/2023 2:33 PM, Richard Damon wrote:
On 12/18/23 3:09 PM, olcott wrote:
There is a single well defined process of correct reasoning
such that when any logical system diverges from this process
*IT IS WRONG IN THE ABSOLUTE SENSE*
You have said this a number of times, but have been unable to actually
DEFINE what you mean.
I have defined exactly what I mean numerous times yet no one can
understand what I say.
The body of analytic truth is a set of mutually self-defining semantic tautologies.
When I say analytical knowledge this is the subset of analytical truth
of the philosophical analytic / synthetic distinction. https://plato.stanford.edu/entries/analytic-synthetic/
When any expression of language of analytic knowledge cannot be
proved to be true on the basis of its connection to other semantic
meanings then this expression is simply *FLAT OUT UNTRUE*.
*There is no undecidability or incompleteness, merely untruth*
You have demonstrated that the logic you use gets wrong results, and
is succeptable to getting you to make awful category errors.
Not when construed within the philosophical notion of analytical
knowledge elaborated above. You must be anchored in philosophy
of logic to begin to understand what I said.
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion nevertheless to be false. https://iep.utm.edu/val-snd/
According to that:
{Dogs are 15 story office buildings therefore water is H2O} is valid.
I call bullshit on that.
Here is my correction:
A deductive argument is said to be valid if and only if it takes a form
*that the conclusion is a necessary consequence of all of its premises*
{Dogs are 15 story office buildings therefore water is H2O} is invalid.
On 12/18/2023 3:32 AM, Mikko wrote:
On 2023-12-17 17:27:48 +0000, olcott said:
On 12/17/2023 2:08 AM, Mikko wrote:
On 2023-12-15 15:33:59 +0000, olcott said:
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:No syllogistic inference rule can derive the empty set.
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is nonsense.
On 2023-12-09 15:27:08 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
The way that is works for the entire body of analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any
semantics of T, so True as defined above is not a semantic notion.
(2) I am saying that dividing semantics from syntax thus enabling
logic to diverge from the model of the syllogism is a huge mistake.
A syllogism is a formal inference that does not depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>>>>
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into correct reasoning*
The only way that we can tell the the principle of explosion >>>>>>>>>>>>>>>>> is nonsense is by plugging semantics into it and then see >>>>>>>>>>>>>>>>> that this semantics is not semantically carried though. >>>>>>>>>>>>>>>>
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab auctoritate fallacy?
The principle of explosion "proves" nonsense when semantics are required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
That is a valid inference without any semantics. If you ever find
a cat that both is a dog and is not a dog you can safely conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set as its solution set.
I.e., shows that there are no solutions; i.e., no matter what else is
assumed, both of the pemises a and b can't be true.
Thus when we retain semantics the Principle of Explosion only derives NULL.
How would semantics prevent any derivation of any other result? >>>>>>>>>>
This proves that the error is divorcing semantics from logic. >>>>>>>>>>How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs)
The Principle of explosion says that this proves that the Moon is made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the Moon >>>>>>>> is made from green cheese. Nobody has ever observed otherwise. >>>>>>>>
whenever all cats are dogs and some cats are not dogs as a syllogism >>>>>>> only the empty set is derived thus refuting the principle of explosion. >>>>>>
I just proved otherwise.
You did not prove, you just claimed.
Categorical propositions do define sets that can be
represented by Venn diagrams.
All S are P and No S are P are defined sets that
have no intersection.
More correctly, their intersection is the empty set.
If you regard them as sets then a conclusion is valid if the intersection
of premises is a subset of conclusion; or equivalently, if the intersection >> of all premises and the negation of the conclusion is the empty set.
Mikko
If the intersection of the premises is the empty set because
the premises contradict each other then that proves that
nothing follows from a contradiction. This refutes the POE.
On 12/19/2023 4:14 AM, Mikko wrote:
If you regard sentences as sets, the conclusion
can also be regarded as a set. The conclusion is a necessary
consequence of the premises if the intersection of all premises
is a subset of the conclusion.
https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg
The intersection of (All S are P) and (No S is P)
is the empty set.
In logic an inference of C from A and B is valid if A ∧ B → C
The implication operator screws up when its antecedent is false in the
same way that deduction screws up when its premises are false.
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion nevertheless to be false. https://iep.utm.edu/val-snd/
On 12/19/2023 4:14 AM, Mikko wrote:
On 2023-12-18 16:18:01 +0000, olcott said:
On 12/18/2023 3:32 AM, Mikko wrote:
On 2023-12-17 17:27:48 +0000, olcott said:
On 12/17/2023 2:08 AM, Mikko wrote:
On 2023-12-15 15:33:59 +0000, olcott said:
On 12/15/2023 5:37 AM, Mikko wrote:
On 2023-12-14 15:21:28 +0000, olcott said:
On 12/14/2023 3:55 AM, Mikko wrote:
On 2023-12-13 21:28:48 +0000, olcott said:
On 12/13/2023 12:04 PM, Mikko wrote:
On 2023-12-13 15:18:04 +0000, olcott said:
On 12/13/2023 4:39 AM, Mikko wrote:
On 2023-12-12 16:09:17 +0000, olcott said:
On 12/12/2023 4:44 AM, Mikko wrote:
On 2023-12-11 16:43:00 +0000, olcott said:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said: >>>>>>>>>>>>>>>>>>
On 12/10/2023 4:10 AM, Mikko wrote:That does not show that the principle of explosion is >>>>>>>>>>>>>>>>>> nonsense.
On 2023-12-09 15:27:08 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>
On 12/9/2023 3:53 AM, Mikko wrote:Not for purposes that do not need any semantics. >>>>>>>>>>>>>>>>>>>>
On 2023-12-08 17:10:15 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
On 12/8/2023 1:52 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2023-12-05 19:26:20 +0000, olcott said: >>>>>>>>>>>>>>>>>>>>>>
The way that is works for the entire body of >>>>>>>>>>>>>>>>>>>>>>>>> analytic knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical >>>>>>>>>>>>>>>>>>>>>>>> thruth, which is the
usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L) >>>>>>>>>>>>>>>>>>>>>>> True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently >>>>>>>>>>>>>>>>>>>>>>> semantic.
The usual notions. The expression (T ⊢ x) does not >>>>>>>>>>>>>>>>>>>>>> involve any
semantics of T, so True as defined above is not a >>>>>>>>>>>>>>>>>>>>>> semantic notion.
(2) I am saying that dividing semantics from >>>>>>>>>>>>>>>>>>>>>>> syntax thus enabling
logic to diverge from the model of the >>>>>>>>>>>>>>>>>>>>>>> syllogism is a huge mistake.
A syllogism is a formal inference that does not >>>>>>>>>>>>>>>>>>>>>> depend on semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure >>>>>>>>>>>>>>>>>>>>>
It always depends on defined sets providing its >>>>>>>>>>>>>>>>>>>>> semantics as Categorical propositions >>>>>>>>>>>>>>>>>>>>> https://en.wikipedia.org/wiki/Categorical_proposition >>>>>>>>>>>>>>>>>>>>
Mikko
*Yes for all purposes. I am changing logic into >>>>>>>>>>>>>>>>>>> correct reasoning*
The only way that we can tell the the principle of >>>>>>>>>>>>>>>>>>> explosion
is nonsense is by plugging semantics into it and then >>>>>>>>>>>>>>>>>>> see
that this semantics is not semantically carried though. >>>>>>>>>>>>>>>>>>
Ross Finlayson said that the principle of explosion >>>>>>>>>>>>>>>>> cannot exist in
relevance logic, thus making my point.
Hearsay does not prove.
It is an analytical impossibility to create the POE when >>>>>>>>>>>>>>> semantics
is directly integrated into logic.
Try and show the POE using syllogisms.
What releveance that would have to an argumentum ab >>>>>>>>>>>>>> auctoritate fallacy?
The principle of explosion "proves" nonsense when >>>>>>>>>>>>>>>>> semantics are required.That is a valid inference without any semantics. If you >>>>>>>>>>>>>>>> ever find
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese >>>>>>>>>>>>>>>>
a cat that both is a dog and is not a dog you can safely >>>>>>>>>>>>>>>> conclude
that the Moon is made frm green cheese.
(a) All Cat are dogs
(b) Some Cats are not dogs
(c) Therefore NULL
Construing the above as a syllogism derives the empty set >>>>>>>>>>>>>>> as its solution set.
I.e., shows that there are no solutions; i.e., no matter >>>>>>>>>>>>>> what else is
assumed, both of the pemises a and b can't be true. >>>>>>>>>>>>>>
Thus when we retain semantics the Principle of Explosion >>>>>>>>>>>>> only derives NULL.
How would semantics prevent any derivation of any other result? >>>>>>>>>>>>
This proves that the error is divorcing semantics from logic. >>>>>>>>>>>>How could it prove that?
Mikko
(a) All Cats are dogs
(b) Some Cats are not dogs // AKA Not(All Cats are dogs) >>>>>>>>>>>
The Principle of explosion says that this proves that the >>>>>>>>>>> Moon is made
from green cheese.
Yes, whenever all cats are dogs and some cats are not dogs the >>>>>>>>>> Moon
is made from green cheese. Nobody has ever observed otherwise. >>>>>>>>>>
whenever all cats are dogs and some cats are not dogs as a
syllogism
only the empty set is derived thus refuting the principle of >>>>>>>>> explosion.
No syllogistic inference rule can derive the empty set.
I just proved otherwise.
You did not prove, you just claimed.
Categorical propositions do define sets that can be
represented by Venn diagrams.
All S are P and No S are P are defined sets that
have no intersection.
More correctly, their intersection is the empty set.
If you regard them as sets then a conclusion is valid if the
intersection
of premises is a subset of conclusion; or equivalently, if the
intersection
of all premises and the negation of the conclusion is the empty set.
Mikko
If the intersection of the premises is the empty set because
the premises contradict each other then that proves that
nothing follows from a contradiction. This refutes the POE.
No, it doesn't. If you regard sentences as sets, the conclusion
can also be regarded as a set. The conclusion is a necessary
consequence of the premises if the intersection of all premises
is a subset of the conclusion.
https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg
The intersection of (All S are P) and (No S is P)
is the empty set.
In logic an inference of C from A and B is valid if A ∧ B → C
The implication operator screws up when its antecedent is false in the
same way that deduction screws up when its premises are false.
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion nevertheless to be false. https://iep.utm.edu/val-snd/
On that basis we can conclude that this sentence is valid:
"Kittens are 15 story office buildings therefore water is H2O."
When we redefine value to be a conclusion must be a necessary
consequence of all of its premises then the above nonsense
sentence is not valid.
is true. If A, B, and C are regarded as sets the same inference
is valid if (A ∩ B) ⊆ C is true.
Mikko
On 12/20/2023 5:53 AM, Mikko wrote:
On 2023-12-19 15:34:44 +0000, olcott said:
On 12/19/2023 4:14 AM, Mikko wrote:
If you regard sentences as sets, the conclusion
can also be regarded as a set. The conclusion is a necessary
consequence of the premises if the intersection of all premises
is a subset of the conclusion.
https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg >>> The intersection of (All S are P) and (No S is P)
is the empty set.
In logic an inference of C from A and B is valid if A ∧ B → C
The implication operator screws up when its antecedent is false in
the same way that deduction screws up when its premises are false.
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion
nevertheless to be false. https://iep.utm.edu/val-snd/
Your "screws up" above seems to mean that do you not accept all
valid inferences.
Mikko
If dogs are 15 story office buildings(false) then water is H2O(true) is
valid according to the above criteria.
When the conclusion must be a necessary (thus relevant) consequence of
all of its premises then the above sentence is invalid.
*The notion of valid is wrong. I fixed it*
On 12/20/2023 5:53 AM, Mikko wrote:
On 2023-12-19 15:34:44 +0000, olcott said:
On 12/19/2023 4:14 AM, Mikko wrote:
If you regard sentences as sets, the conclusion
can also be regarded as a set. The conclusion is a necessary
consequence of the premises if the intersection of all premises
is a subset of the conclusion.
https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg >>> The intersection of (All S are P) and (No S is P)
is the empty set.
In logic an inference of C from A and B is valid if A ∧ B → C
The implication operator screws up when its antecedent is false in the
same way that deduction screws up when its premises are false.
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for the premises to be true and the conclusion
nevertheless to be false. https://iep.utm.edu/val-snd/
Your "screws up" above seems to mean that do you not accept all
valid inferences.
Mikko
If dogs are 15 story office buildings(false) then water is H2O(true) is
valid according to the above criteria.
When the conclusion must be a necessary (thus relevant) consequence of
all of its premises then the above sentence is invalid.
*The notion of valid is wrong. I fixed it*
On 12/22/2023 3:45 AM, Mikko wrote:
On 2023-12-20 17:54:31 +0000, olcott said:
On 12/20/2023 5:53 AM, Mikko wrote:
On 2023-12-19 15:34:44 +0000, olcott said:
On 12/19/2023 4:14 AM, Mikko wrote:
If you regard sentences as sets, the conclusion
can also be regarded as a set. The conclusion is a necessary
consequence of the premises if the intersection of all premises
is a subset of the conclusion.
https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg >>>>> The intersection of (All S are P) and (No S is P)
is the empty set.
In logic an inference of C from A and B is valid if A ∧ B → C
The implication operator screws up when its antecedent is false in
the same way that deduction screws up when its premises are false.
A deductive argument is said to be valid if and only if it takes a
form
that makes it impossible for the premises to be true and the
conclusion
nevertheless to be false. https://iep.utm.edu/val-snd/
Your "screws up" above seems to mean that do you not accept all
valid inferences.
Mikko
If dogs are 15 story office buildings(false) then water is H2O(true) is
valid according to the above criteria.
When the conclusion must be a necessary (thus relevant) consequence of
all of its premises then the above sentence is invalid.
*The notion of valid is wrong. I fixed it*
The notion of validity is what it is because that is what is needed
for the notion of soundness.
*Mine works better at this to*
When the conclusion is a necessary consequence of all of the premises
then when the premises are all true we still get the conventional notion
of soundness.
This is almost the same thing as the conclusion must be semantically
relevant to all of the premises.
*What we don't get is the principle of explosion*
The notion of soundness is needed to
serve the purpose of logic. If you want to replace or reject validity
you must also replace or reject soundness.
If you want to replace validity or soundness you need to find a new
word and define it to mean what you think it needs to mean.
Mikko
On 12/22/2023 12:34 PM, olcott wrote:
*Mine works better at this to*
When the conclusion is a necessary consequence of all of the premises
then when the premises are all true we still get the conventional notion
of soundness.
This is almost the same thing as the conclusion must be semantically
relevant to all of the premises.
*What we don't get is the principle of explosion*
People that never heard of relevance logic will "disagree" never
knowing that they are ignorant and people having not the slightest
clue about the formal semantics of natural language will also
"disagree" entirely on the basis of their own ignorance.
On 12/22/2023 3:45 AM, Mikko wrote:
On 2023-12-20 17:54:31 +0000, olcott said:
On 12/20/2023 5:53 AM, Mikko wrote:
On 2023-12-19 15:34:44 +0000, olcott said:
On 12/19/2023 4:14 AM, Mikko wrote:
If you regard sentences as sets, the conclusion
can also be regarded as a set. The conclusion is a necessary
consequence of the premises if the intersection of all premises
is a subset of the conclusion.
https://en.wikipedia.org/wiki/File:Square_of_opposition,_set_diagrams.svg >>>>> The intersection of (All S are P) and (No S is P)
is the empty set.
In logic an inference of C from A and B is valid if A ∧ B → C
The implication operator screws up when its antecedent is false in the >>>>> same way that deduction screws up when its premises are false.
A deductive argument is said to be valid if and only if it takes a form >>>>> that makes it impossible for the premises to be true and the conclusion >>>>> nevertheless to be false. https://iep.utm.edu/val-snd/
Your "screws up" above seems to mean that do you not accept all
valid inferences.
Mikko
If dogs are 15 story office buildings(false) then water is H2O(true) is
valid according to the above criteria.
When the conclusion must be a necessary (thus relevant) consequence of
all of its premises then the above sentence is invalid.
*The notion of valid is wrong. I fixed it*
The notion of validity is what it is because that is what is needed
for the notion of soundness.
*Mine works better at this to*
When the conclusion is a necessary consequence of all of the premises
then when the premises are all true we still get the conventional notion
of soundness.
This is almost the same thing as the conclusion must be semantically
relevant to all of the premises.
*What we don't get is the principle of explosion*
On 12/23/2023 4:18 AM, Mikko wrote:
You still have details undefined, e.g.
the meaning of "necessary". After that you should show that it works
at least to some extent.
Modal logic already defines that.
◊ means possibly
◻ means necessarily
¬ means not
◊P means ¬◻¬P
◻P means ¬◊¬P
A ◻ B When A is true then B is impossibly false
On 12/23/2023 12:28 PM, André G. Isaak wrote:
On 2023-12-23 11:09, olcott wrote:
On 12/23/2023 4:18 AM, Mikko wrote:
You still have details undefined, e.g.
the meaning of "necessary". After that you should show that it works
at least to some extent.
Modal logic already defines that.
Except you're clearly not using the term in the same way that Modal
Logic does. You may have heard of Modal Logic but you've clearly never
worked within it and have just picked up a few random terms from it to
which you have assigned your own private meanings
◊ means possibly
◻ means necessarily
¬ means not
◊P means ¬◻¬P
◻P means ¬◊¬P
A ◻ B When A is true then B is impossibly false
"A ◻ B" doesn't mean anything whatsoever in Modal Logic. The necessity
operator is not a binary operator.
André
The aspect of Modal logic that I am referring to is this
◊P means ¬◻¬P // Possibly P <means> not Necessarily not P
◻P means ¬◊¬P // Necessarily P <means> not Possibly not P
Until we define this much Possibly and Necessarily remain meaningless.
The conventional a notion of deductive validity derive this nonsense:
The Moon is made from green cheese therefore 2 + 3 = 5.
Very obviously not relevant at natural language the semantic level.
My system starts with a model of the current world specified
as Richard Montague meaning postulates as its axioms.
On 12/23/2023 1:48 PM, André G. Isaak wrote:
On 2023-12-23 12:25, olcott wrote:
On 12/23/2023 12:28 PM, André G. Isaak wrote:
On 2023-12-23 11:09, olcott wrote:
On 12/23/2023 4:18 AM, Mikko wrote:
You still have details undefined, e.g.
the meaning of "necessary". After that you should show that it works >>>>>> at least to some extent.
Modal logic already defines that.
Except you're clearly not using the term in the same way that Modal
Logic does. You may have heard of Modal Logic but you've clearly
never worked within it and have just picked up a few random terms
from it to which you have assigned your own private meanings
◊ means possibly
◻ means necessarily
¬ means not
◊P means ¬◻¬P
◻P means ¬◊¬P
A ◻ B When A is true then B is impossibly false
"A ◻ B" doesn't mean anything whatsoever in Modal Logic. The
necessity operator is not a binary operator.
André
The aspect of Modal logic that I am referring to is this
◊P means ¬◻¬P // Possibly P <means> not Necessarily not P
◻P means ¬◊¬P // Necessarily P <means> not Possibly not P
Until we define this much Possibly and Necessarily remain meaningless.
As "definitions", those would be entirely circular.
That most certainly isn't how the terms are defined in modal logic.
That was their official definition in Wikipedia for many years.
You might want to learn some modal logic before you attempt to use it.
I am only referring to the formalized semantic meaning of the English
word: Necessarily.
What I mean by Necessarily is that expression x is true in BOAK
iff and only if there is a complete sequence of deductions from
the formalized natural language axioms of BOAK to x.
Also note that 'modal logic' refers to a large class of different
logics, and you have never clarified which one you are referring to.
I am only referring to the formalized semantic meaning of the English
word: Necessarily.
The conventional a notion of deductive validity derive this nonsense:
The Moon is made from green cheese therefore 2 + 3 = 5.
Very obviously not relevant at natural language the semantic level.
My system starts with a model of the current world specified
as Richard Montague meaning postulates as its axioms.
The above statement is meaningless.
Anything I say will necessarily remain meaningless to someone
that does not bother to find out what my terms mean.
{Model of the current world} has a very well defined meaning
from the body of knowledge known as {possible worlds}. https://plato.stanford.edu/entries/possible-worlds/
{Richard Montague meaning postulates} has a very well defined meaning
from the body of knowledge known formalized natural language. https://plato.stanford.edu/entries/montague-semantics/
On 12/23/2023 3:12 PM, André G. Isaak wrote:
On 2023-12-23 13:01, olcott wrote:
Anything I say will necessarily remain meaningless to someone
that does not bother to find out what my terms mean.
I am well aware of what these terms mean. I am stating that you are
throwing them together in a way which is nonsensical, largely because
*you* do not understand these terms.
{Model of the current world} has a very well defined meaning
from the body of knowledge known as {possible worlds}. https://plato.stanford.edu/entries/possible-worlds/
{Richard Montague meaning postulates} has a very well defined meaning
from the body of knowledge known formalized natural language. https://plato.stanford.edu/entries/montague-semantics/
The axioms of the body of analytic knowledge BOAK are the
basic facts of the model of the current world translated from
natural language into Montague meaning postulates.
On 12/23/2023 5:28 PM, André G. Isaak wrote:
On 2023-12-23 15:12, olcott wrote:
On 12/23/2023 3:12 PM, André G. Isaak wrote:
On 2023-12-23 13:01, olcott wrote:
Anything I say will necessarily remain meaningless to someone
that does not bother to find out what my terms mean.
I am well aware of what these terms mean. I am stating that you are
throwing them together in a way which is nonsensical, largely
because *you* do not understand these terms.
{Model of the current world} has a very well defined meaning
from the body of knowledge known as {possible worlds}.
https://plato.stanford.edu/entries/possible-worlds/
{Richard Montague meaning postulates} has a very well defined meaning
from the body of knowledge known formalized natural language.
https://plato.stanford.edu/entries/montague-semantics/
Repeating these definitions isn't adding anything to the conversation.
I already indicated that I am familiar with these terms.
The axioms of the body of analytic knowledge BOAK are the
basic facts of the model of the current world translated from
natural language into Montague meaning postulates.
And again, you're not saying anything meaningful here.
The problem is that you are relying on encyclopaedias for your
information. The purpose of an encyclopaedia is to provide a rather
superficial overview of a topic aimed at non-specialists. You're
picking up some terms without really understanding them and then
assigning your own private meanings to these terms.
I am relying on the Cyc system that applies a human degree of
reasoning on the basis of its inheritance hierarchy tree of knowledge.
I have spoken with Doug Lenat directly about his system and how
my ideas apply to it.
I can directly see how such a tree of knowledge directly provides
a human degree of reasoning. Can you see this?
If you want to base some theory on Montague Grammar and modal logic,
you need to actually read Montague and a good textbook on modal logic.
And
It is not about the specific details that you keep pointing
to. It is that the gist of the ideas involved in the mathematical formalization of natural language do entail the architecture
of a the formal system of all analytical knowledge.
On the basis of the architecture of such a formal system
we can easily reverse-engineer any details that Montague
may have never fully addressed.
then you then need to actually *work* within these frameworks -- do the
Not the least little bit. A learned-by-rote person may
think this way. Thinking this way makes sure to box you
in to rejecting any new ideas as incorrect entirely on
the basis that these new ideas do not correspond to what
you learned by rote.
textbook exercises on modal logic and try to analyze fragments of
natural language in terms of PTQ to see what these things actually can
and cannot do.
André
On 12/23/2023 5:28 PM, André G. Isaak wrote:
On 2023-12-23 15:12, olcott wrote:
On 12/23/2023 3:12 PM, André G. Isaak wrote:
On 2023-12-23 13:01, olcott wrote:
Anything I say will necessarily remain meaningless to someone
that does not bother to find out what my terms mean.
I am well aware of what these terms mean. I am stating that you are
throwing them together in a way which is nonsensical, largely
because *you* do not understand these terms.
{Model of the current world} has a very well defined meaning
from the body of knowledge known as {possible worlds}.
https://plato.stanford.edu/entries/possible-worlds/
{Richard Montague meaning postulates} has a very well defined meaning
from the body of knowledge known formalized natural language.
https://plato.stanford.edu/entries/montague-semantics/
Repeating these definitions isn't adding anything to the conversation.
I already indicated that I am familiar with these terms.
The axioms of the body of analytic knowledge BOAK are the
basic facts of the model of the current world translated from
natural language into Montague meaning postulates.
And again, you're not saying anything meaningful here.
The problem is that you are relying on encyclopaedias for your
information. The purpose of an encyclopaedia is to provide a rather
superficial overview of a topic aimed at non-specialists. You're
picking up some terms without really understanding them and then
assigning your own private meanings to these terms.
If you want to base some theory on Montague Grammar and modal logic,
you need to actually read Montague and a good textbook on modal logic.
And then you then need to actually *work* within these frameworks
*Reverse-engineering the solution from the problem definition*
*is most efficient and effective for solving complex problems*
I simply reverse engineer the nature of the solution on the basis
of the problem definition. This takes whatever it needs from existing
ideas and creates new ideas as needed.
In this case we need to reverse-engineer whatever the heck architecture
is required to encode the body of all analytical knowledge.
This system requires an algorithm that applies semantic deduction to the axioms of this system.
These axioms are formalized natural language facts comprising the model
of the actual world.
It also must be able to perform any mathematical and logical operation.
| Sysop: | Keyop |
|---|---|
| Location: | Huddersfield, West Yorkshire, UK |
| Users: | 715 |
| Nodes: | 16 (4 / 12) |
| Uptime: | 29:35:36 |
| Calls: | 12,108 |
| Calls today: | 8 |
| Files: | 15,006 |
| Messages: | 6,518,245 |
