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From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.theory,sci.logic
Subject: Re: ""self contradictory"" (Was: Analytic Truth-makers)
Date: Mon, 22 Jul 2024 22:46:41 +0200
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And why is there no sequence of
logical transformations that leads to:

p

and no sequence of logical
transformations that leads to:

~p

Is p self contradictory?

olcott schrieb:
> On 7/22/2024 3:18 PM, Mild Shock wrote:
>>
>> What do you mean by self contradictory.
>> Why is there no sequencce to:
>>
>> p
>>
>> or to
>>
>> ~p
>>
>> Is p self contradictory?
>>
> 
> This sentence is not true is *self* contradictory.
> When it is formalized in Tarski formal system it
> becomes the basis for his undefinability theorem.
> 
> 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
> 
> Formalized as:
> x ∉ True if and only if p
> where the symbol 'p' represents the whole sentence x
> https://liarparadox.org/Tarski_275_276.pdf
> 
> 
>> olcott schrieb:
>>> I have focused on analytic truth-makers where an expression of 
>>> language x is shown to be true in language L by a sequence of truth 
>>> preserving operations from the semantic meaning of x in L to x in L.
>>>
>>> In rare cases such as the Goldbach conjecture this may require an 
>>> infinite sequence of truth preserving operations thus making analytic 
>>> knowledge a subset of analytic truth. 
>>> https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
>>>
>>> There are cases where there is no finite or infinite sequence of
>>> truth preserving operations to x or ~x in L because x is self-
>>> contradictory in L. In this case x is not a truth-bearer in L.
>>>
>>>
>>>
>>
>