Re: Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction in the Halting Problem

On 11/05/2025 17:29, olcott wrote:

On 5/11/2025 10:34 AM, Mr Flibble wrote:

On Sun, 11 May 2025 16:25:14 +0100, Richard Heathfield wrote:
>

For a question to be semantically incorrect, it takes more than just you
and your allies to be unhappy with it.

>
For a question to be semantically correct, it takes more than just you and
your allies to be happy with it.
>
Your turn, mate.
>
/Flibble

 For a polar yes/no question to be proven incorrect
only requires that both yes and no are the wrong answer.

Fair enough.
Definition: YNA - a type of answer that has exactly one of exactly two possible values, either 'yes' xor 'no' - not both, not neither, and not banana or half-past four.
The two questions I presented upthread, which I'll now label QA and QB, are both of type YNA. They are as follows:
QA: "P is a syntactically correct program in some well-defined Turing-complete language. Does P stop when it is applied to this data X?"
QB: ``Is it possible to write a program that answers QA for arbitrary P and arbitrary X?"
For any P and any X, QA has a correct YNA answer. What that answer is depends on P and X, but QA(P,X) can correctly answer with one valid YNA response or the other.
QB, similarly, asks a YNA question. Either it's possible or it isn't. Alan Turing's work on decidability proved that the answer is 'no'. Mr Olcott believes that the proof is erroneous, so he might prefer to answer 'yes'. But one and only one of those answers is correct.
The question, then, is semantically correct in accordance with Mr Olcott's criterion.
I find it hard to credit that a grown man needs this stuff spelled out, but there it is.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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