From Newsgroup: sci.logic

On 10/13/2025 12:36 PM, dbush wrote:

On 10/13/2025 1:22 PM, olcott wrote:

On 10/13/2025 11:43 AM, dbush wrote:

On 10/13/2025 12:30 PM, olcott wrote:

On 10/13/2025 11:18 AM, dbush wrote:

On 10/13/2025 12:14 PM, olcott wrote:

On 10/13/2025 9:24 AM, dbush wrote:

On 10/13/2025 10:15 AM, olcott wrote:

The directly executed DD() is outside of the
domain of the function computed by HHH(DD)
because it is not a finite string thus does
not contradict that HHH(DD) correctly rejects
its input as non-halting.

Actual numbers are outside the domain of Turing machines because >>>>>>> they are not finite strings, therefore Turning machines cannot do >>>>>>> arithmetic.

Agreed?

Should I start simply ignoring everything that you say again?
Prove that you want an honest dialogue or be ignored.

You stated that Turing machines can't operate on directly executed
Turing machine because they only take finite strings as input and
not actual Turing machines.

Now ChatGPT also agrees that DD() is outside of the domain
of the function computed by HHH(DD) and HHH(DD) is correct
to reject its input on the basis of the function that it
does compute.

https://chatgpt.com/share/68ec6e96-7eb8-8011-90c7-86248034d475

And if you remind it what a finite string description is:

No, no, no, this is where you and the halting problem
definition screw up. It never was a mere finite string
machine description.

It was always the behavior that its input finite string
machine description specifies. This expressly excludes
the behavior of the directly executed DD() because the
directly executed DD() is not an input in the domain of HHH.

Nope, see below.

---
But since a Turing machine description encodes all information about
a Turing machine, Turing machines are within the domain of other
Turing machines via their description. Therefore the definition of a
halt decider, a Turing machine that determines whether any arbitrary
Turing machine X with input Y will halt when executed directly, is
correct and valid.
---

Why the three levels of quotes instead of
just plain text that was cut-and-pasted
like this cut-and-pasted quoted text?

Theorem (Domain Invalidity of the Halting Predicate
in Reflective Models): In any computational model
where programs can call the universal interpreter,
the halting predicate HALT(p) is undefined for some
syntactically valid p. Hence, the classical definition
of the halting problem as a total decision problem
over all program texts is semantically incorrect in
that model.

https://chatgpt.com/share/68ec6e96-7eb8-8011-90c7-86248034d475
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
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