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

On 7/22/2024 3:46 PM, Mild Shock wrote:

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?
 

You have it backwards.
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
The above is a very clumsy way of saying
that x is only true if x is not true.
We can know this because Tarski said the was using the
Liar Paradox as his model:
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.

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.
>
>
>

>

>

 

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