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

On 2025-02-28 23:47:11 +0000, olcott said:

On 2/28/2025 4:59 AM, Mikko wrote:

On 2025-02-26 05:02:13 +0000, olcott said:
 

On 2/25/2025 10:21 PM, Richard Damon wrote:

On 2/25/25 4:10 PM, olcott wrote:

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
 

 Nope. And "expressions" are not "undecidable", but "Problems" are.
 

 A specific problem instance is a single finite string expression input
to a specific decider.

 No, it is not. The decider is no way a part of a specific problem
instance unless it is a part of that finite string expression.

 Is the term decider/input pair over your head?

No, only an idiot could think so.

A unique finite string of integers combined
with a specific decider is a SPECIFIC PROBLEM INSTANCE.

No, it is not. It is a computation.

A decider is itself a unique finite string of integer
values for any 100% specific system of Turing Machine
descriptions.

No, it is not. A decider is a Turing (or similar) machine that for
every valid input either accepts or rejects. It can be encoded as
a unique finite string of integer values but usually other ways of
presentation are better.

That a specific problem instance is a single finite string expression
is true about formal problems but usually not about practical problems.

 Like how to get your wife to quit yelling at you?

Yes, for example.
--
Mikko