Re: Tarski Undefinability and the correctly formalized Liar Paradox

On 5/25/2024 2:23 PM, Richard Damon wrote:

On 5/25/24 2:32 PM, olcott wrote:

On 5/25/2024 1:16 PM, Richard Damon wrote:

On 5/25/24 1:51 PM, olcott wrote:

On 5/25/2024 10:56 AM, Richard Damon wrote:

On 5/25/24 11:27 AM, olcott wrote:

x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
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First we convert the clumsy indirect approximation of
self-reference by getting rid of the extraneous x we
also swap the LHS with the RHS.
p if and only if p ∉ True

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But, your final sentence no longer DEFINES what p is, it just references an undefined term, whch is an error.
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You didn't finish reading the rest of my correction
to Tarski's formalization of the Liar Paradox.
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p if and only if p ∉ True
The above sentence says that p is logically equivalent
to itself not being a member of true sentences.
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No that ststement says that p is true only if p is not an element of the set True.
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So you said it was meaningless (undefined) and now you provide
its meaning. Can you at least be consistent with yourself?
(Probably not when rebuttal mode has higher priority for you).
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  The statement has a meaning, but about a statement that has no meaning.
 

This sentence is not true.
What is it not true about?
It is not true about being not true.
What is it not true about being not true about.
It is not true about being not true about being not true.
OK, so it NEVER gets to the point
thus NEVER derives any truth value,
thus is not a truth-bearer,
thus must be rejected by any formal system
of bivalent logic as a type mismatch error.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer