sci.logic Daryl McCullough Jun 25, 2004, 6:30:39 PM
You ask someone (we'll call him "Jack") to give a truthful
yes/no answer to the following question:

Will Jack's answer to this question be no?
Jack can't possibly give a correct yes/no answer to the question.

When the halting problem is construed as requiring a correct yes/no
answer to a self-contradictory question it cannot be solved.

My semantic linguist friends understand that the context of the question
must include who the question is posed to otherwise the same
word-for-word question acquires different semantics.

The input D to H is the same as Jack's question posed to Jack, has no
correct answer because within this context the question is
self-contradictory.

When we ask someone else what Jack's answer will be or we present a
different TM with input D the same word-for-word question (or bytes of
machine description) acquires entirely different semantics and is no
longer self-contradictory.

When we construe the halting problem as determining whether or not an
(a) Input D will halt on its input <or>
(b) Either D will not halt or D has a pathological relationship with H

Then this halting problem cannot be showed to be unsolvable by any of
the conventional halting problem proofs.

The x86utm operating system
(includes several termination analyzers)
https://github.com/plolcott/x86utm

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Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer