XPost: sci.logic

On 7/21/24 9:20 AM, olcott wrote:

On 7/21/2024 4:27 AM, Mikko wrote:

On 2024-07-20 13:22:31 +0000, olcott said:

On 7/20/2024 3:42 AM, Mikko wrote:

On 2024-07-19 13:48:49 +0000, olcott said:

Some undecidable expressions are only undecidable because
they are self contradictory. In other words they are undecidable
because there is something wrong with them.

Being self-contradictory is a semantic property. Being uncdecidable is >>>> independent of any semantics.

Not it is not. When an expression is neither true nor false
that makes it neither provable nor refutable.

There is no aithmetic sentence that is neither true or false. If the
sentnece
contains both existentia and universal quantifiers it may be hard to
find out
whether it is true or false but there is no sentence that is neither.

 As Richard
Montague so aptly showed Semantics can be specified syntactically.

An arithmetic sentence is always about
numbers, not about sentences.

So when Gödel tried to show it could be about provability
he was wrong before he even started?

Gödel did not try to show that an arithmetic sentence is about
provability.
He constructed a sentence about numbers that is either true and provable
or false and unprovable in the theory that is an extension of Peano
arithmetics.

You just directly contradicted yourself.

No, Godel didnt show that arithmetic is about provablity, but that
provability can be reduced to arithmetic.

As with many things, you get your direction of implication reversed.

A proof is about sentences, not about
numbers.

The Liar Paradox: "This sentence is not true"

cannot be said in the language of Peano arithmetic.

Since Tarski anchored his whole undefinability theorem in a
self-contradictory sentence he only really showed that sentences that
are neither true nor false cannot be proven true.

By Gödel's completeness theorem every consistent incomplete first order
theory has a model where at least one unprovable sentence is true.

https://liarparadox.org/Tarski_247_248.pdf // Tarski Liar Paradox basis
https://liarparadox.org/Tarski_275_276.pdf // Tarski proof

It is very simple to redefine the foundation of logic to eliminate incompleteness. Any expression x of language L that cannot be shown
to be true by some (possibly infinite) sequence of truth preserving operations in L is simply untrue in L: True(L, x).

And if you try that you find that your logic system can't handle very
complex topics without becoming inconsistent. And that level turns out
to be well below what we normally want out of logic.

Tarski showed that True(Tarski_Theory, Liar_Paradox) cannot be defined
never understanding that Liar_Paradox is not a truth bearer.

But he didn't do that, that is just your misunderstanding of what he
did. Your stupidity doesn't negate the work he did that was above your head.

If you think he made an error, show the exact step where he did
something that violates the rules of logic that he was using.

Special note, that doesn't mean coming up with a result you find wrong,
show the operation that he did that is incorrect.

Your problem is the point you like to point to isn't a point where he
makes an assumption, but a point were he calls forward something he
previously proved, so if you don't like that, you need to find the error
with that proof.

But, since you don't seem to understand how formal logic and
meta-theories work, I don't think you can understand that.

I think Formal Logic and Meta-Theories are just to abstract of a concept
for you to understand.


Note, if you ACTUALLY want to "redefine" the Foundations of Logic, go
ahead, just remember when you tear down a foundation, you also tear down everything built on it, so you need to rebuild them, especially since
you GOAL seems to be to change some of the things above the foundation.

Go ahead and try that, but remember, you need to start AT THAT
FOUNDATION, and to be honest, I don't think you understand how that sort
of logic actually works well enough to make a foundation that would
actual\ly hold anything. I don't think you have the time to do it eather
since you wasted the last 20 years on your lies.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

XPost: sci.logic

On 7/22/24 10:40 AM, olcott wrote:

On 7/22/2024 3:14 AM, Mikko wrote:

On 2024-07-21 13:20:04 +0000, olcott said:

On 7/21/2024 4:27 AM, Mikko wrote:

On 2024-07-20 13:22:31 +0000, olcott said:

On 7/20/2024 3:42 AM, Mikko wrote:

On 2024-07-19 13:48:49 +0000, olcott said:

Some undecidable expressions are only undecidable because
they are self contradictory. In other words they are undecidable >>>>>>> because there is something wrong with them.

Being self-contradictory is a semantic property. Being
uncdecidable is
independent of any semantics.

Not it is not. When an expression is neither true nor false
that makes it neither provable nor refutable.

There is no aithmetic sentence that is neither true or false. If the
sentnece
contains both existentia and universal quantifiers it may be hard to
find out
whether it is true or false but there is no sentence that is neither.

 As Richard
Montague so aptly showed Semantics can be specified syntactically.

An arithmetic sentence is always about
numbers, not about sentences.

So when Gödel tried to show it could be about provability
he was wrong before he even started?

Gödel did not try to show that an arithmetic sentence is about
provability.
He constructed a sentence about numbers that is either true and
provable
or false and unprovable in the theory that is an extension of Peano
arithmetics.

You just directly contradicted yourself.

I don't, and you cant show any contradiction.

Gödel's proof had nothing what-so-ever to do with provability
except that he proved that g is unprovable in PA.

Right, which since G was TRUE in PA, makes PA incomplete.

So, you argee that Godel was correct, but then argue he isn;t

YOU are just showing your logic is inconsistent, and thus unusable.

A proof is about sentences, not about
numbers.

The Liar Paradox: "This sentence is not true"

cannot be said in the language of Peano arithmetic.

Since Tarski anchored his whole undefinability theorem in a
self-contradictory sentence he only really showed that sentences that >>>>> are neither true nor false cannot be proven true.

By Gödel's completeness theorem every consistent incomplete first order >>>> theory has a model where at least one unprovable sentence is true.

https://liarparadox.org/Tarski_247_248.pdf // Tarski Liar Paradox
basis
https://liarparadox.org/Tarski_275_276.pdf // Tarski proof

It is very simple to redefine the foundation of logic to eliminate
incompleteness.

Yes, as long as you don't care whether the resulting system is useful.
Classical logic has passed practical tests for thousands of years, so
it is hard to find a sysem with better empirical support.

When we show how incompleteness is eliminated then this also shows
how undefinability is eliminated and this would have resulted in a
chatbot that eviscerated Fascist lies about election fraud long
before they could have taken hold in the minds of 45% of the electorate.

HOW did you "eliminate" incompleteness. YOo ADMITTED that statements
could be true by just an infinte chain of steps, which is not a proof.

You just are proving you don't unstand what you are talking about, it
seems, because you just don't understand what "Formal Systems" are,
perhaps because they are just too abstract for you.

Because people have been arguing against my correct system of reasoning
we will probably see the rise of the fourth Reich.

No, you have proved that your system of reasoning can't be correct,
because it denies things you admit are true.,

Any expression x of language L that cannot be shown
to be true by some (possibly infinite) sequence of truth preserving
operations in L is simply untrue in L: True(L, x).

That does not help much if you cannot determine whether a particular
string can be shown to be true.

Every element of the set of human knowledge can be proven true
by a finite sequence of truth preserving operations. Also every
line can be proved to be false by this same basis.

So?

You confuse KNOWLEDGE wth TRUTH.

The Heritage Foundation is the author of Project
2025 and a staunch Trump ally could only find 1546
cases of voter fraud in the last ten years.

And you ar just validating theeir method of logic by using t your self.

You ignore the truth presented to you, bacause you "know" it can't be true.

YOU USE THE METHOD OF THE BIG LIE.

#ElectionFraudLies
Even the Heritage Foundation agrees
Never any evidence of election fraud
that could possibly change the results:

Only 1,546 total cases of voter fraud
https://www.heritage.org/voterfraud
Trump is just copying Hitler's "big lie"

Tarski showed that True(Tarski_Theory, Liar_Paradox) cannot be defined
never understanding that Liar_Paradox is not a truth bearer.

However, every arithmetic sentence is either true or false.

The same diagonalization proof that Gödel used works on
the arithmetization of the Tarski proof. Diagonalization
never shows why g is unprovable in PA, it only shows that
g is unprovable in PA.

So? The fact that it IS unprovable is enough.

The Tarski proof shows why x is unprovable in the Tarski Theory
(because x is self-contradictory in the Tarski Theory)

No, he shows that the assumption of a universal truth primative leads to contradictions, and thus can not exist.

Tarski's Liar Paradox from page 248
   It would then be possible to reconstruct the antinomy of the liar
   in the metalanguage, by forming in the language itself a sentence
   x such that the sentence of the metalanguage which is correlated
   with x asserts that x is not a true sentence.
   https://liarparadox.org/Tarski_247_248.pdf

Right, he PROVES that, given the existance of the truth primative, you
can build as a sentence in the logic, a sentence of that form.

Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x

Which you don't understand where that comes from. You seem to think it
is jus something he made uo, he PROVES that you can form that statement
given that a Truth Primative exists.

https://www.researchgate.net/publication/315367846_Minimal_Type_Theory_MTT

In my own Minimal Type Theory the self contradiction
is much easier to see: LP := ~True(LP)

Because you don't actually understand what Tarski is doing.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On 7/23/24 10:53 AM, olcott wrote:

On 7/23/2024 3:07 AM, Mikko wrote:

On 2024-07-22 14:40:41 +0000, olcott said:

On 7/22/2024 3:14 AM, Mikko wrote:

On 2024-07-21 13:20:04 +0000, olcott said:

On 7/21/2024 4:27 AM, Mikko wrote:

On 2024-07-20 13:22:31 +0000, olcott said:

On 7/20/2024 3:42 AM, Mikko wrote:

On 2024-07-19 13:48:49 +0000, olcott said:

Some undecidable expressions are only undecidable because
they are self contradictory. In other words they are undecidable >>>>>>>>> because there is something wrong with them.

Being self-contradictory is a semantic property. Being
uncdecidable is
independent of any semantics.

Not it is not. When an expression is neither true nor false
that makes it neither provable nor refutable.

There is no aithmetic sentence that is neither true or false. If
the sentnece
contains both existentia and universal quantifiers it may be hard
to find out
whether it is true or false but there is no sentence that is neither. >>>>>>

 As Richard
Montague so aptly showed Semantics can be specified syntactically. >>>>>>>

An arithmetic sentence is always about
numbers, not about sentences.

So when Gödel tried to show it could be about provability
he was wrong before he even started?

Gödel did not try to show that an arithmetic sentence is about
provability.
He constructed a sentence about numbers that is either true and
provable
or false and unprovable in the theory that is an extension of
Peano arithmetics.

You just directly contradicted yourself.

I don't, and you cant show any contradiction.

Gödel's proof had nothing what-so-ever to do with provability
except that he proved that g is unprovable in PA.

He also proved that its negation is unprovable in PA. He also proved
that every consistent extension of PA has a an sentence (different
from g) such that both it and its negation are unprovable.

L is the language of a formal mathematical system.
x is an expression of that language.

When we understand that True(L,x) means that there is a finite
sequence of truth preserving operations in L from the semantic
meaning of x to x in L, then mathematical incompleteness is abolished.

~True(L,x) ∧ ~True(L,~x)
means that x is not a truth-bearer in L.
 It does not mean that L is incomplete

And thus you prove your system inconsistant, as you just admitted that
the Goldbach's conjecture COULD be an Analytic Truth, and thus a
Truth-Bearer, even without an finite sequence, but just an infinite
sequence.

You are just showing you logic is based on the need to lie at times.

You validate the election and climate change deniers, whether you mean
to or not, because you show that you agree with their basic method of logic.

A proof is about sentences, not about
numbers.

The Liar Paradox: "This sentence is not true"

cannot be said in the language of Peano arithmetic.

Since Tarski anchored his whole undefinability theorem in a
self-contradictory sentence he only really showed that sentences >>>>>>> that
are neither true nor false cannot be proven true.

By Gödel's completeness theorem every consistent incomplete first >>>>>> order
theory has a model where at least one unprovable sentence is true. >>>>>>

https://liarparadox.org/Tarski_247_248.pdf // Tarski Liar Paradox >>>>>>> basis
https://liarparadox.org/Tarski_275_276.pdf // Tarski proof

It is very simple to redefine the foundation of logic to eliminate
incompleteness.

Yes, as long as you don't care whether the resulting system is useful. >>>> Classical logic has passed practical tests for thousands of years, so
it is hard to find a sysem with better empirical support.

When we show how incompleteness is eliminated then this also shows
how undefinability is eliminated and this would have resulted in a
chatbot that eviscerated Fascist lies about election fraud long
before they could have taken hold in the minds of 45% of the electorate.

The simplest way to elimita incompleteness is to construct a theory
where everytihing is provable. Of course such theory is not useful.

The next simplest way is to construct a theory for a finite universe.
As the theory is complete it specifies the number of objects in the
universe. Then it is possible to evaluate every quantifier with a
simple finite loop or recursion, so the truth of every sentence is
computable.

This kind of theory may have some use but its applicability is very
limited. In particular, a complete theory cannot be used in situations
where somthing is not known.

Because people have been arguing against my correct system of reasoning
we will probably see the rise of the fourth Reich.

Trying something impossible does not prevent anything.

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)