Re: Incorrect requirements --- Computing the mapping from the input to HHH(DD)

On 5/11/2025 12:44 PM, olcott wrote:

On 5/11/2025 6:13 AM, joes wrote:

Am Sat, 10 May 2025 15:42:13 -0500 schrieb olcott:

On 5/10/2025 3:22 PM, Alan Mackenzie wrote:

>

OK, then, give the page and line numbers from Turing's 1936 paper where
this alleged mistake was made.  I would be surprised indeed if you'd
even looked at Turing's paper, far less understood it.  Yet you're
ready to denigrate his work.
Perhaps it is time for you to withdraw these uncalled for insinuations.
>

It is the whole gist of the entire idea of the halting problem proof
that is wrongheaded.
(1) It is anchored in the false assumption that an input to a
termination analyzer can actually do this opposite of whatever value
that this analyzer returns. No one ever notices that this "do the
opposite" code is unreachable.

 

The simulated DDD doesn't matter. HHH returns to DDD, and DDD then does
the opposite.
>

 HHH is only allowed to report on the behavior that
its actual input actually specifies.

False.  It must report on the behavior of the algorithm described by the input, as per the requirements:
Given any algorithm (i.e. a fixed immutable sequence of instructions) X described as <X> with input Y:
A solution to the halting problem is an algorithm H that computes the following mapping:
(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly

 int sum(int x, int y) { return x + y; }
sum(3,2) is not allowed to report on the sum of 5 + 7
because that is not what its input specifies.
 

(2) It expects a self-contradictory (thus incorrect)
question to have a correct answer.

Whether a program halts is not contradictory.
>

 Asking sum(3,2) about the sum of 5 + 7
is the same as asking HHH(DDD) about the
direct execution of DDD().

False, as the former is not what is required to compute the sum mapping, while the latter is what's required to compute the halting mapping.

 

Can Carol correctly answer “no” to this (yes/no) question?
When the context of who is asked is understood to be an aspect of the
full meaning of the question then the question posed to Carol is
incorrect because both yes and no are the wrong answer.

Yes, HHH cannot answer correctly.
>

 Any yes/no question where both yes and no are the
wrong answer is an incorrect polar question.
Copyright PL Olcott 2025.
 

And the question of does the algorithm described by <X> with input Y halt when executed directly is not such a question.