From Newsgroup: comp.ai.philosophy
<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
If simulating halt decider H correctly simulates its
input D until H correctly determines that its simulated D
would never stop running unless aborted then
H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
On 10/14/2022 7:44 PM, Ben Bacarisse wrote:
I don't think that is the shell game.
PO really /has/ an H (it's trivial to do for
this one case) that correctly determines that P(P)
*would* never stop running *unless* aborted.
He knows and accepts that P(P) actually does stop.
The wrong answer is justified by what would
happen if H (and hence a different P) where not
what they actually are.
Principle 1: Turing machine deciders compute functions
from finite strings to {accept, reject} according to
whether the input has a syntactic property or specifies
a semantic property.
Principle 2: We measure the semantic property that
the finite string specifies by a UTM-based halt
decider that simulates its input finite string
step-by-step and watches the execution trace of
this behavior.
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.
This required establishing a new foundation
for correct reasoning.
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