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From: joes <noreply@example.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: H(D,D) cannot even be asked about the behavior of D(D) ---
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Date: Sat, 22 Jun 2024 04:09:21 -0000 (UTC)
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Am Fri, 21 Jun 2024 15:52:21 -0500 schrieb olcott:
> On 6/21/2024 3:00 PM, Richard Damon wrote:
>> On 6/21/24 3:45 PM, olcott wrote:
>>> On 6/21/2024 2:33 PM, Richard Damon wrote:
>>>> On 6/21/24 3:19 PM, olcott wrote:

>>>>> When H is asked H(D,D) this maps to D correctly simulated by H.
Like every other input, it should map to the behaviour of D(D).
You are talking about H(H, D(D)), which is H simulating itself.
>>>>> When H is asked H(D,D) this DOES NOT map to behavior that halts.
Only if H returns.

>>>> Nope. H(M,d) is DEFINED (if it is correct) to determine if M(d) will
>>>> Halt.
>>> If one "defines" that the input to H(D,D) maps to the behavior of D(D)
>>> yet cannot show this because it does not actually map to that behavior
>>> *THEN THE DEFINITION IS SIMPLY WRONG*
Ridiculous. H is wrong. Your modification is not useful.
>> But we CAN show that it maps to the behavior of D(D) (at least when the
>> representation of D includes the H that is giving the 0 answer) by just
>> runnig it and seeing what it does.
> No you cannot show that the mapping for the input to H(D,D) maps to the
> behavior of D(D).
If it doesn't, H is not a simulator.
The input D(D) absolutely describes the behaviour of that machine.
H just can't map it.

> You assume that the call to H(D,D) from D correctly simulated by H *must
> return* against the verified facts that it does not return.
Either H is not a decider or it returns.

> The directly executed D(D) is essentially the first call in a recursive
> chain where the second call is always aborted.
> *these two calls are not identical*
They most definitely are. The input is the same.

> H(D,D) is not free to simply assume that the call from D(D) to H(D,D)
> will return.
Yes it is, because it is a decider. It (incorrectly) aborts nonterminating
inputs.

-- 
Man kann mit dunklen Zahlen nicht rechnen. Für die eigentliche Mathematik 
sind sie vollkommen nutzlos. --Wolfgang Mückenheim