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Re: Tarski / Gödel and redefining the Foundation of Logic

From Richard Damon <richard@damon-family.org>
Newsgroups comp.theory, sci.logic
Subject Re: Tarski / Gödel and redefining the Foundation of Logic
Date 2024-07-21 13:53 -0400
Organization i2pn2 (i2pn.org)
Message-ID <d7a5ad332996d455b4107a0849a4e9ab6fe5e094@i2pn2.org> (permalink)
References (24 earlier) <v7dqs3$30pvh$1@dont-email.me> <v7ft98$3fbg8$1@dont-email.me> <v7gdmn$3hlc2$3@dont-email.me> <v7ikah$1hri$1@dont-email.me> <v7j1u4$3o7r$2@dont-email.me>

Cross-posted to 2 groups.

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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.

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Thread

Re: DDD correctly emulated by HHH is correctly rejected as non-halting. Mikko <mikko.levanto@iki.fi> - 2024-07-14 11:49 +0300
  Re: DDD correctly emulated by HHH is correctly rejected as non-halting. olcott <polcott333@gmail.com> - 2024-07-14 09:48 -0500
    Re: DDD correctly emulated by HHH is INcorrectly rejected as non-halting. Richard Damon <richard@damon-family.org> - 2024-07-14 14:22 -0400
    Re: DDD correctly emulated by HHH is correctly rejected as non-halting. Mikko <mikko.levanto@iki.fi> - 2024-07-15 10:57 +0300
      Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-15 08:32 -0500
        Re: DDD incorrectly emulated by HHH is incorrectly rejected as non-halting. --- You are not paying attention Richard Damon <richard@damon-family.org> - 2024-07-15 22:19 -0400
        Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-16 10:18 +0300
          Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-16 09:46 -0500
            Re: DDD INcorrectly emulated by HHH is INcorrectly rejected as non-halting. --- You are not paying attention Richard Damon <richard@damon-family.org> - 2024-07-16 21:12 -0400
            Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-17 10:08 +0300
              Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-17 08:14 -0500
                Re: DDD emulated by HHH is incorrectly rejected as non-halting. joes <noreply@example.org> - 2024-07-17 17:08 +0000
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-18 10:55 +0300
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-18 08:36 -0500
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-19 10:30 +0300
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-19 08:48 -0500
                Re: DDD incorrectly emulated by HHH is incorrectly rejected as non-halting. --- You are not paying attention Richard Damon <richard@damon-family.org> - 2024-07-19 11:28 -0400
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-20 11:42 +0300
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention olcott <polcott333@gmail.com> - 2024-07-20 08:22 -0500
                Re: DDD correctly emulated by HHH is correctly rejected as non-halting. --- You are not paying attention Mikko <mikko.levanto@iki.fi> - 2024-07-21 12:27 +0300
                Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-21 08:20 -0500
                Re: Tarski / Gödel and redefining the Foundation of Logic Richard Damon <richard@damon-family.org> - 2024-07-21 13:53 -0400
                Re: Tarski / Gödel and redefining the Foundation of Logic Mikko <mikko.levanto@iki.fi> - 2024-07-22 11:14 +0300
                Re: Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-22 09:40 -0500
                Re: Tarski / Gödel and redefining the Foundation of Logic Richard Damon <richard@damon-family.org> - 2024-07-22 20:12 -0400
                Re: Tarski / Gödel and redefining the Foundation of Logic Mikko <mikko.levanto@iki.fi> - 2024-07-23 11:07 +0300
                Re: Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-23 09:53 -0500
                Re: Tarski / Gödel and redefining the Foundation of Logic Richard Damon <richard@damon-family.org> - 2024-07-23 22:16 -0400
                Re: Tarski / Gödel and redefining the Foundation of Logic Mikko <mikko.levanto@iki.fi> - 2024-07-25 11:55 +0300
                Re: Tarski / Gödel and redefining the Foundation of Logic olcott <polcott333@gmail.com> - 2024-07-25 10:51 -0500

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