Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Flibble=E2=80=99s_Leap=3A_Why_Behavioral_Divergence?=
 =?UTF-8?Q?_Implies_a_Type_Distinction_in_the_Halting_Problem?=
Date: Sun, 11 May 2025 18:03:30 +0100
Organization: Fix this later
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In-Reply-To: <vvqja4$gldn$10@dont-email.me>

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
Sig line 4 vacant - apply within