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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: ""self contradictory"" (Was: Analytic Truth-makers)
Date: Mon, 22 Jul 2024 15:32:12 -0500
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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.
>>
>>
>>
> 

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