On 11/19/2025 5:36 PM, Ben Bacarisse wrote:
dart200 <user7160@newsgrouper.org.invalid> writes:
On 11/17/25 9:29 AM, Alan Mackenzie wrote:
The Halting Theorem is wholly a theorem of mathematics,
and only secondarily about computer science.
the original proof as written by turing uses notions justified in turing
machines to then support godel's result, not the other way around
No. Turing was working on the Entscheidungsproblem. A different
problem altogether.
it is fundamentally based in computer science using turing machines as
"axioms", which are in turn justified by our ability to mechanically
undertake the operations, not set theory
No. Turing machines are not "axioms" in any sense of the word; they are entirely mathematical entities built from the axioms of set theory.
Turing was writing for an audience that would know that a "tape" was
just a convenient term for a function from Z to Gamma (the tape
alphabet), that the "head" is just an integer and "writing to the tape"
just results in a new function from Z to Gamma. The "machine
configuration" is just a tuple as is the TM itself. I.e. a TM is just a
set (though you need to know how tuples and function are just sets in
order to believe this).
The Entscheidungsproblem is an entirely mathematical question about
formal systems. Cranks focus on Turing's work because the metaphors of
tapes and so on are easy to get one's head around (no pun intended!).
This is also why Turing gets so much credit, but Church, technically,
got there first with his proof using the lambda calculus. No crank ever disputes this proof because they can't waffle about it (or, in most
cases, even understand it).
None-the-less Turing machines became the foundation of computer science
<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 words10/13/2022>
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.
D() executed from main
does stop running without needing to be aborted
this proves itself to be a different D()
D() executed from main
does stop running without needing to be aborted
this proves itself to be a different D()
D() executed from main
does stop running without needing to be aborted
this proves itself to be a different D()
D() executed from main
does stop running without needing to be aborted
this proves itself to be a different D()
D() executed from main
does stop running without needing to be aborted
this proves itself to be a different D()
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning" computable.
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* Origin: Dragon's Lair, PyGate NNTP<>Fido Gate (3:633/10)