Re: Mathematical incompleteness has always been a misconception --- Ultimate Foundation of Truth

On 2025-02-25 21:10:10 +0000, olcott said:

On 2/25/2025 9:35 AM, Mikko wrote:

On 2025-02-24 21:44:10 +0000, olcott said:
 

On 2/24/2025 2:58 AM, Mikko wrote:

On 2025-02-22 18:42:44 +0000, olcott said:
 

On 2/22/2025 3:25 AM, Mikko wrote:

On 2025-02-22 04:44:35 +0000, olcott said:
 

On 2/21/2025 7:05 PM, Richard Damon wrote:

On 2/21/25 6:19 PM, olcott wrote:

On 2/20/2025 2:54 AM, Mikko wrote:

On 2025-02-18 03:59:08 +0000, olcott said:

 

Tarski anchored his whole proof in the Liar Paradox.
 

 By showing that given the necessary prerequisites, The equivalent of the Liar Paradox was a statement that the Truth Predicate had to be able to handle, which it can't.
 

 It can be easily handled as ~True(LP) & ~True(~LP), Tarski just
didn't think it through.

 No, it can't. Tarski requires that True be a predicate, i.e, a truth
valued function of one term.

 It does not matter a whit what the Hell his misconceptions
required.

 It is not required by any misconception. It is required by the
meanings of the words and symbols, in particular "predicare"
and "~".

 That none of modern logic can handle expressions
that are not truth bearers is their error and
short-coming.

 Why should any logic permit formulas that are not truth-bearers?
(Of course, term expressions are not truth-bearers.)

 Undecidable expressions are only undecidable because they
are not truth bearers. Logic ignores this and faults the
system and not the expression

An undecidable expression is a thruth bearer. It may be false in some
applications and true in another but it alsways has some truth value.
Often its truth value is irrelevant to practical application. For
example, the arithmetic of natural number is useful for many purposes
although some formulas about natural numbers are undecidable and
there is no method to determine which ones.
--
Mikko