To understand the misconception of mathematical incompleteness...

[olcott]

In order to see exactly where arithmetic truth correctly plugs into
analytic truth we must first understand that this is true:

An analytic expression is: Any expression of language verified as
completely true entirely on the basis of its relation to other
expressions of language that derive their meaning from truth
conditional semantics. (AKA stipulated truth).

*Truth-conditional semantics* is an approach to semantics of natural
language that sees meaning (or at least the meaning of assertions) as
being the same as, or reducible to, their truth conditions.
https://en.wikipedia.org/wiki/Truth-conditional_semantics

*Analytic truth is*
(a) Expressions stipulated to be true thus giving semantic meaning to
terms. *similar to axioms*

(b) Expressions derived by applying truth preserving finite string
transformations to elements of (a) *similar to proofs from axioms*

'True in Russell's system' means, as was said:
proved in Russell's system; and
'false in Russell's system' means:
the opposite has been proved in Russell's system
https://www.liarparadox.org/Wittgenstein.pdf

AKA True(RS, G) ≡ (RS ⊢ C)
AKA False(RS, G) ≡ (RS ⊢ ¬G)





--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

[Richard Damon]

On 2/3/24 7:03 PM, olcott wrote:
> In order to see exactly where arithmetic truth correctly plugs into
> analytic truth we must first understand that this is true:
>
> An analytic expression is: Any expression of language verified as
> completely true entirely on the basis of its relation to other
> expressions of language that derive their meaning from truth
> conditional semantics. (AKA stipulated truth).
>
> *Truth-conditional semantics* is an approach to semantics of natural
> language that sees meaning (or at least the meaning of assertions) as
> being the same as, or reducible to, their truth conditions.
> https://en.wikipedia.org/wiki/Truth-conditional_semantics
>
> *Analytic truth is*
> (a) Expressions stipulated to be true thus giving semantic meaning to
> terms. *similar to axioms*
>
> (b) Expressions derived by applying truth preserving finite string
> transformations to elements of (a) *similar to proofs from axioms*

Note, the ABOVE is NOT from your refernce, and the definition normally
used does not include your end note of "similar to proof from axioms",
but allows for the application of an INFINITE sequence to establish
truth, while proofs require a finite sequences.

Note also, your reference is almost exclusively about why
"Truth-Condition Semantics" are not used/valid, so trying to use it to
support your position is counter-productive.

This has been pointed out to you many times, and your refusal to learn
it just shows your total ignorance and stupidity with regard to logic.

>
> 'True in Russell's system' means, as was said:
> proved in Russell's system; and
> 'false in Russell's system' means:
> the opposite has been proved in Russell's system
> https://www.liarparadox.org/Wittgenstein.pdf
>
> AKA  True(RS, G) ≡ (RS ⊢ C)
> AKA False(RS, G) ≡ (RS ⊢ ¬G)
>
>

Which isn't actually a true statement, and others have show that to be true.

Thus, your fallacious appeal to authority is just invalid logic, proving
that you just don't un

[olcott]

On 2/3/2024 6:03 PM, olcott wrote:

Math tries to override and supersede the generic way that analytical
truth really works.

*An analytic expression* is any expression of language verified as

completely true entirely on the basis of its relation to other

expressions of language that are stipulated to be true thus providing
the semantic meaning of terms.

*Analytic truth is*
(a) Expressions stipulated to be true thus giving semantic meaning to

terms. (similar to axioms)

(b) Expressions derived by applying truth preserving finite string

transformations to elements of (a) (similar to proofs from axioms)

[olcott]

>> AKA  True(RS, P) ≡ (RS ⊢ P)
>> AKA False(RS, P) ≡ (RS ⊢ ¬P)

>>
>>
>
> Which isn't actually a true statement, and others have show that to be
> true.

*This <is> what Wittgenstein is saying*
True(RS, P) ≡ (RS ⊢ P)
False(RS, P) ≡ (RS ⊢ ¬P)

I know that Wittgenstein is correct because I came up with
his same reasoning before I ever herd of him.

*This <is> the generic way that ALL analytical truth really works*
*thus when math and logic diverge from this THEY ARE WRONG*

[Richard Damon]

WHICH ISN'T THE DEFINITION OF TRUE in Russel's system.

So, an ERROR.

>
> I know that Wittgenstein is correct because I came up with
> his same reasoning before I ever herd of him.

And you are BOTH WRONG.

>
> *This <is> the generic way that ALL analytical truth really works*
> *thus when math and logic diverge from this THEY ARE WRONG*
>

Nope, just shows you are a stupid ignroant pathological lying idiot.

[olcott]

*It is really stupid to rely on ad hominem so much*
An actual rebuttal requires a valid counter-example.

That you and others simply don't believe me is not any
sort of valid counter-example.

Try and find any expression of language that must be true or false
that has no sequence of steps infinite or otherwise that derive
its truth or falsity.

*If this can't possibly be done then that proves that I am correct*

[Richard Damon]

I don't use ad hominem, and your claim just shows you don't know what it
means.

ad-hominem would be to say you are wrong because you are "stupid" (or
some other attribute).

I say you are stupid because you are constistantly WRONG, and point out
why you are wrong.

> An actual rebuttal requires a valid counter-example.

Which you fail to do.

YOU are the one claiming that the Halting Proof is wrong, and claim to
do so by claiming to show a counter example.

I point out the errors in your definitions, That dosn't need a
counter-example.

I show that your counter-example fails to meet the definitions,

The DEFINITION of Halting is based the behavior of the actual machine,
not some unsound logic based on a partial simulation.] That behavior is
to reach a final state.

In EVERY case where you propose an H that actually gives an answer, I
show that the answer it gives is wrong.

>
> That you and others simply don't believe me is not any
> sort of valid counter-example.

It isn't "beleive" we PROVE you are using the WRONG definitions, by
looking at your own words.

>
> Try and find any expression of language that must be true or false
> that has no sequence of steps infinite or otherwise that derive
> its truth or falsity.

So, more Strawmen and lies of altering statements.

I NEVER said that something could be true with NO sequence of steps, not
even infinite.

I have ALWAYS said that Truth is establisheb by a chain, either finite
or infinite, from the truth makers of the system.

YOU have tried to claim that it must be a finite chain (and thus usable
as a proof).

If you accept that Truth can be established by an infinite chain of
steps, then you admit that some truth might not be Provable, as the
definition of proof (at least in normal logic system) requires a finite
chain to the statement, not infinite.

>
> *If this can't possibly be done then that proves that I am correct*
>

NO, it prove yourself to be a lying idiot.

It really looks like you are having mental problems, I do suggest you
seek professional help. It may well be that you are too far gone, but
your logic has visible deteriated over the last couple of years.

You have stopped coming up with new ways to phrase your errors, and have
just gotten repetitive,

[olcott]

*That aspect of your reasoning seems superior to most*

What you don't seem to understand is that some expressions
are unprovable and irrefutable because there is something
wrong with them such as:

...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof... (Gödel 1931:43)

[Richard Damon]

Yes, there are statements which are unprovable or irrefutable because
the statement has not truth value. The Liar is one of them.

But, you do not understand what Godel did, so your argument there is
just invalid.

He did not "start" with a reasoning form the epistemological antinomy,
but used a transformation that takes the FORM of one, and makes it intp
a statement that actually has semantic meaning and a truth value.

The methods seem to be beyond your reasoning, so I won't try to explain
it, but TRY to find where in his proof he actually does what you say he
does.

Where is the Liar's Paradox actually used in part of the proof. (Not
just his statement about being able to "use" something else that is
similar).

Note, the statement "G is defined as G is not provable in F if and only
if G is True if F" is NOT "the Liars Paradox" as that has the assertion
that the Liar is FALSE if and only if it is True. Not being provable is
definitionally different than not being true.

You have even admitted it, as you just recently admited that Truth can
have an infinite chain connection, while proof must have a finite chain,
so any statement with only an infinite chain would be True but not Provable.

[olcott]

He does not matter what Gödel did nearly as much that he did not
understand that epistemological antinomies are erroneous. You
seem to understand this thus putting you above him.

> He did not "start" with a reasoning form the epistemological antinomy,
> but used a transformation that takes the FORM of one, and makes it intp
> a statement that actually has semantic meaning and a truth value.
>

Tarski proved that the Liar Paradox (when applied to itself) is true.
This sentence is not true: "This sentence is not true" is true.

He and Gödel never understood that epistemological antinomies are
erroneous. You do understand this placing you above both of them.

> The methods seem to be beyond your reasoning, so I won't try to explain
> it, but TRY to find where in his proof he actually does what you say he
> does.
>

I have done that many times with Tarski and you simply don't believe me

But the diagonal lemma yields a counterexample to this equivalence, by
giving a "liar" formula S such that S ⟺ ¬True(g(A)) holds in N. This
is a contradiction QED.

https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem#General_form

> Where is the Liar's Paradox actually used in part of the proof. (Not
> just his statement about being able to "use" something else that is
> similar).
>
> Note, the statement "G is defined as G is not provable in F if and only
> if G is True if F"  is NOT "the Liars Paradox" as that has the assertion
> that the Liar is FALSE if and only if it is True. Not being provable is
> definitionally different than not being true.
>
> You have even admitted it, as you just recently admited that Truth can
> have an infinite chain connection, while proof must have a finite chain,
> so any statement with only an infinite chain would be True but not
> Provable.

[Richard Damon]

Then it doesn't matter what you claim, it is just enough to know that
Truth is Truth and some Truth is unprovbable, so your claim otherwise is
just noise.

You err when you claim someone is wrong for doing something they did not to.

THAT is Libel.

>
>> He did not "start" with a reasoning form the epistemological antinomy,
>> but used a transformation that takes the FORM of one, and makes it
>> intp a statement that actually has semantic meaning and a truth value.
>>
>
> Tarski proved that the Liar Paradox (when applied to itself) is true.
> This sentence is not true: "This sentence is not true" is true.

Right, CONDITIONED on the assumption that a computable procedure to
determine the Truth of a sentence existed, thus, that assumption must be
wrong.

>
> He and Gödel never understood that epistemological antinomies are
> erroneous. You do understand this placing you above both of them.

No, they both understood it, better than you, as they understood the
implications of that.

>
>> The methods seem to be beyond your reasoning, so I won't try to
>> explain it, but TRY to find where in his proof he actually does what
>> you say he does.
>>
>
> I have done that many times with Tarski and you simply don't believe me

Because you don't do what you claim.

The statement you point to is either where he PROVES the Liar, based on
an assumption, which shows the assumption can not be true, or he uses it
as a base to transform into a sentence that DOES have a truth value via
a syntatic transformation that doesn't preserve sematics (and thus
doesn't carry the antinomy with it).

>
> But the diagonal lemma yields a counterexample to this equivalence, by
> giving a "liar" formula S such that S ⟺ ¬True(g(A)) holds in N. This
> is a contradiction QED.
>
> https://en.wikipedia.org/wiki/Tarski%27s_undefinability_theorem#General_form

And where is the contradiction in that?

You are just showing your ignorance.

[olcott]

That Gödel did not understand that epistemological antinomies must
be rejected as erroneous is factual. This by itself proves that he
did not correctly understand undecidability, the key element of
his proof.

>>
>>> He did not "start" with a reasoning form the epistemological
>>> antinomy, but used a transformation that takes the FORM of one, and
>>> makes it intp a statement that actually has semantic meaning and a
>>> truth value.
>>>
>>
>> Tarski proved that the Liar Paradox (when applied to itself) is true.
>> This sentence is not true: "This sentence is not true" is true.
>
> Right, CONDITIONED on the assumption that a computable procedure to
> determine the Truth of a sentence existed, thus, that assumption must be
> wrong.
>

Not at all. As soon as it is understood that epistemological
antinomies must be rejected as erroneous his proof loses its basis.

>>
>> He and Gödel never understood that epistemological antinomies are
>> erroneous. You do understand this placing you above both of them.
>
> No, they both understood it, better than you, as they understood the
> implications of that.
>

*That is counter-factual*
If they understood that epistemological antinomies are erroneous
they would have understood that they must be rejected instead
of using them as any basis in any proof.

Your reasoning is incoherent. I think that you know that.
Trollish head games seems to be your thing.

[Richard Damon]

But he didn't do what you claim, showing that YOU are the stupid and
ignorant one.

>>>
>>>> He did not "start" with a reasoning form the epistemological
>>>> antinomy, but used a transformation that takes the FORM of one, and
>>>> makes it intp a statement that actually has semantic meaning and a
>>>> truth value.
>>>>
>>>
>>> Tarski proved that the Liar Paradox (when applied to itself) is true.
>>> This sentence is not true: "This sentence is not true" is true.
>>
>> Right, CONDITIONED on the assumption that a computable procedure to
>> determine the Truth of a sentence existed, thus, that assumption must
>> be wrong.
>>
>
> Not at all. As soon as it is understood that epistemological
> antinomies must be rejected as erroneous his proof loses its basis.

Nope. Because he DOES reject the epistmemological antinomies as soon as
it comes up as something that would appear to have a truth value.

>
>>>
>>> He and Gödel never understood that epistemological antinomies are
>>> erroneous. You do understand this placing you above both of them.
>>
>> No, they both understood it, better than you, as they understood the
>> implications of that.
>>
>
> *That is counter-factual*
> If they understood that epistemological antinomies are erroneous
> they would have understood that they must be rejected instead
> of using them as any basis in any proof.

SO, I guess you admit that YOUR "proof" must be rejected, as it is
"based" on epistemological antinomies.

Your problem is that you crude parsing can't handle the nuances of their
logic. You are admitting that by not answering the question of showing
exact where they do this. Every point you have tried, it wasn't an
assumption that it was true, but a RESULT of prior logic that it was
true, showing the tentative assumption prior must have been wrong.

>
> Your reasoning is incoherent. I think that you know that.
> Trollish head games seems to be your thing.
>

YOUR reasoning is incoherent. You make so many claims that are just not
true, you

[olcott]

Whether or not he did or did not do what I claim, he did assert
that he intended to do what I claim.
...We are therefore confronted with a proposition which asserts its own
unprovability...(Gödel 1931:43-44)

and proved that he failed to understand that epistemological antinomies
must be rejected as incorrect thus not the basis for any proof.

...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43)

Gödel did not say I am going to use something in a proof that I
already know cannot correctly be used in a proof. He thought
that he could use it in a proof and HE WAS WRONG.

[Richard Damon]

Nope.

So, you ADMIT you are just making up your claims.

Good that you are honest about something

>
> and proved that he failed to understand that epistemological antinomies
> must be rejected as incorrect thus not the basis for any proof.
> ...14 Every epistemological antinomy can likewise be used for a similar
> undecidability proof...(Gödel 1931:43)
>
> Gödel did not say I am going to use something in a proof that I
> already know cannot correctly be used in a proof. He thought
> that he could use it in a proof and HE WAS WRONG.
>

Nope, YOU are wrong, because you don't understand what he did.

You have admitted that, and thus, you are just admitting that you are a
LIAR.

You have totally killed any reputation you have. Maybe you can get some
support from MAGA, as they like your type of logic.

[olcott]

WRONG !!!

...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43)

WRONG !!!

...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43)

WRONG !!!

...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43)

WRONG !!!

...14 Every epistemological antinomy can likewise be used for a
similar undecidability proof...(Gödel 1931:43)

WRONG !!!

[Richard Damon]

Which doesn't meen he built the proof of an assumption that the
epistemological antinomy was anything other than an epistemological
antinomy, and thus didn't drive any statement truth from such a statement.

You don't seem to understand the morphological operations he used.

You have admitted that what he did isn't a problem, as you can't find
the spot he actually did what you claim

Thus, you are admitting that you yourself is the liar.

[olcott]

It conclusively proves that he did not understand the key idea of his
whole proof: undecidability.

[Richard Damon]

Nope.

I don't think YOU know what that terms means (in computation theory),
and you clearly don't know what the things in the proof means, so your
"opinion" on it is just more of your POOP.

[olcott]

Gödel proved that he did not understand undecidability.

[Richard Damon]

Nope, YOUprove you don't understand the proof, and are just too stupid
to understand even the simplified explaination.

Try to prove me wrong and show the actual step in the proof where he
assumes an epistemological antinomy is a truth bearer.

If you say just talking about them is enough to invalid a proof, you
just invalidated your own, as you talked about one.

YOU FAIL.

[olcott]

*You are almost there, and still ahead of both Gödel and Tarski*

Let's start with the easier one first.

Do you understand that non-truth bearers are out-of-scope of a truth
predicate?

[Richard Damon]

Wrong, a Truth Predicate must take every statement that is an element of
the System.

The definition of a Predicate means it can take anything in its domain,
and the requried domain for Tarski Truth Predicate is any statement in
the system L.


You keep on making this sort of error, you don't actually know the
definitions of terms, so you guess, and are wrong.

[olcott]

You understand that epistemological antinomies are not truth
bearers. Truth predicates only take truth bearers anything
else is a type mismatch error.

> The definition of a Predicate means it can take anything in its domain,

Its domain is expressions of language that are truth bearers.

When a halt decider is determining whether or not a TM description
specifies a halting computation an English poem is invalid input
only TM descriptions are in its domain.

> and the requried domain for Tarski Truth Predicate is any statement in
> the system L.
>

Thus an English poem is valid input to a halt decider.

>
> You keep on making this sort of error, you don't actually know the
> definitions of terms, so you guess, and are wrong.

Not at all. I was able to understand these definitions at a
much deeper level by having first-hand understanding instead
of just memorizing what textbooks say.

I see ALL of the reasoning behind these definitions thus can
correctly adapt them to new situations. Others reject these
new situations because they never read about them in any textbook.

Epistemological antinomies are not truth bearers thus cannot
be included in any formal system. You have a better understanding
of this that Tarski or Gödel, at least you understand that they
are not truth bearers. Neither Tarski nor Gödel understood this.

[immibis]

On 5/02/24 15:45, olcott wrote:
> Thus an English poem is valid input to a halt decider.

Only if it is an encoding of a Turing machine.

Every encoding of Turing machines are valid input to a halt decider.
THERE IS NO ENCODING OF A TURING MACHINE WHICH IS NOT A VALID INPUT.

[immibis]

On 4/02/24 01:03, olcott wrote:
> In order to see exactly where arithmetic truth correctly plugs into
> analytic truth we must first understand that this is true:
>
> An analytic expression is: Any expression of language verified as
> completely true entirely on the basis of its relation to other
> expressions of language that derive their meaning from truth
> conditional semantics. (AKA stipulated truth).
>
> *Truth-conditional semantics* is an approach to semantics of natural
> language that sees meaning (or at least the meaning of assertions) as
> being the same as, or reducible to, their truth conditions.
> https://en.wikipedia.org/wiki/Truth-conditional_semantics
>
> *Analytic truth is*
> (a) Expressions stipulated to be true thus giving semantic meaning to
> terms. *similar to axioms*
>
> (b) Expressions derived by applying truth preserving finite string
> transformations to elements of (a) *similar to proofs from axioms*
>
> 'True in Russell's system' means, as was said:
> proved in Russell's system; and
> 'false in Russell's system' means:
> the opposite has been proved in Russell's system
> https://www.liarparadox.org/Wittgenstein.pdf
>
> AKA  True(RS, G) ≡ (RS ⊢ C)
> AKA False(RS, G) ≡ (RS ⊢ ¬G)
>

So you refute that a fact is true in one system by inventing a
completely different system.

You reject truth by contradiction, leading to "constructivist logic"
where the fact that something is proven not to be false does not mean it
is true.

[Richard Damon]

Nope, predicates take any expression of the language they are in.

>
>> The definition of a Predicate means it can take anything in its domain,
>
> Its domain is expressions of language that are truth bearers.

Nope, statement of the language.

>
> When a halt decider is determining whether or not a TM description
> specifies a halting computation an English poem is invalid input
> only TM descriptions are in its domain.

It depends if that poem looks like the representation of a Halting
Computation or not.

>
>> and the requried domain for Tarski Truth Predicate is any statement in
>> the system L.
>>
>
> Thus an English poem is valid input to a halt decider.
>

Not if the input symbol set allows the poem to be encoded on the tape.

The question is does the input represent a Halting Computation.

>>
>> You keep on making this sort of error, you don't actually know the
>> definitions of terms, so you guess, and are wrong.
>
> Not at all. I was able to understand these definitions at a
> much deeper level by having first-hand understanding instead
> of just memorizing what textbooks say.

So, why do you keep having inputs that are not representaiton of
Computations?

>
> I see ALL of the reasoning behind these definitions thus can
> correctly adapt them to new situations. Others reject these
> new situations because they never read about them in any textbook.

Nope, you MISUNDERSTAND the meanings and perform illlogical operations
on the wrong definition.

>
> Epistemological antinomies are not truth bearers thus cannot
> be included in any formal system. You have a better understanding
> of this that Tarski or Gödel, at least you understand that they
> are not truth bearers. Neither Tarski nor Gödel understood this.
>
>

Yes, a non-contradictory system that support the property of the
excluded middle can not express an Epistemoogical Antinomy in its language.

If adding a "rule" that ends up allowing one to be expressed, then the
system must no longer be a non-contradictory system that supports the
property of the excluded middle.

YOU don't understand what Trski or Godel did in their proof, so you are
not in a position to put them down. You have effectively admitted this
by refusiong to even try to point out the step where they actually USED
an Epistemological Antinomy in a what that assumes it has a truth value.

Thus, you are just admitting to being a pathological liar.