Re: Categorically exhaustive reasoning applied to the decision to abort

On 3/23/2024 5:58 PM, immibis wrote:

On 23/03/24 16:02, olcott wrote:

(b) H(D,D) that DOES abort its simulation is correct
     (ABOUT THIS ABORT DECISION)
     because it would halt and all deciders must always halt.

 To be a decider it has to give an answer.
 To be a halt decider it has to give an answer that is the same as whether the direct execution of its input would halt.
 

That would entail that H must report on different behavior
than the behavior that H actually sees thus violate the
definition of a decider that must compute the mapping from
its inputs...
On 3/22/2024 9:17 PM, Richard Damon wrote:
 >
 > The problem is that even if the "C function" D is
 > the same machine code, the fact that it calls an
 > external H means *the code of H affects its*
 > *behavior, and that must be taken into account*
Nicholas J. Macias. *Context-Dependent Functions*
Narrowing the Realm of Turing’s Halting Problem
13 Nov 2014
https://arxiv.org/abs/1501.03018
arXiv:1501.03018 [cs.LO]
    The concept of a "Context-Dependent Function" (CDF),
    whose behavior varies based on seemingly irrelevant
    changes to a program calling that function, is introduced,
    and the proof of HP's undecidability is re-examined in
    light of CDFs. (quoted from the above paper)
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer