Re: Nature of undecidable halting

On 2024-05-16 13:20:48 +0000, joes said:

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?

The discussions hera are mainly about the liar paradox or Quine paradox
kind. They ara not always easy to exclude, and one can always modify the
code so that exclusion becomes harder but behaviour remanis the same.
There are also very different problems that are known to be uncomputable,
e.g., the problem whether a sentence in the language of the first order
goup theory is a theorem of that theory -- nothing like the liars paradox
is possible in that language.
--
Mikko