Re: ""self contradictory"" (Was: Analytic Truth-makers)

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:

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What do you mean by self contradictory.
Why is there no sequencce to:
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p
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or to
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~p
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Is p self contradictory?
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 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.
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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
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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.
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