Re: Nature of undecidable halting --- Connecting truth-bearers to their truthmaker

On 5/16/2024 8:20 AM, joes wrote:

Am Thu, 16 May 2024 13:42:41 +0300 schrieb Mikko:

On 2024-05-15 15:06:26 +0000, olcott said:

I refer to transitioning through a specific state to indicate a
specific halt status value, for Turing Machines.

>
That does not satisfy the usual definition of "halt decider". However,
we could accept that as a solution to the halting problem if one could
prove that there is a Turing machine that can indicate halting or
non-halting that way for all computations.
>
However, it is possible to prove that every Turing machine that
indicates halting that way fails to indicate correctly at least some
computations.

 Are these all of the liar paradox kind, such that one could easily
exclude them? Or do they form a more interesting class?
 

Good question!
"a sentence may fail to make a statement if it is paradoxical or ungrounded."
*Outline of a Theory of Truth --- Saul Kripke*
https://www.impan.pl/~kz/truthseminar/Kripke_Outline.pdf
How to define a True(L, x) predicate that refutes Tarski Undefinability:
*The grounding of a truth-bearer to its truthmaker*
True(L,x) returns true when x is derived from a set of truth preserving
operations from finite string expressions of language that have been stipulated to have the semantic value of Boolean true. False(L,x) is defined as True(L,~x).  Copyright 2022 PL Olcott
The above architecture detects and rejects every epistemology
antinomy such as the Liar Paradox. This proves that Gödel is
wrong about this:
...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...(Gödel 1931:43-44)
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer