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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: The error of the halting problem
Date: Mon, 3 Jun 2024 22:26:15 -0400
Organization: i2pn2 (i2pn.org)
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On 6/3/24 10:14 PM, olcott wrote:
> On 6/3/2024 8:58 PM, Richard Damon wrote:
>> On 6/3/24 9:51 PM, olcott wrote:
>>> On 6/3/2024 8:44 PM, Richard Damon wrote:
>>>> On 6/3/24 8:59 PM, olcott wrote:
>>>>> On 6/3/2024 7:55 PM, Richard Damon wrote:
>>>>>> On 6/3/24 4:53 PM, olcott wrote:
>>>>>>> For any program H that might determine whether programs halt, a
>>>>>>> "pathological" program D, called with some input, can pass its own
>>>>>>> source and its input to H and then specifically do the opposite 
>>>>>>> of what
>>>>>>> H predicts D will do. No H can exist that handles this case. 
>>>>>>> https://en.wikipedia.org/wiki/Halting_problem
>>>>>>>
>>>>>>> The way that the halting problem is conventionally understood is 
>>>>>>> that H
>>>>>>> must correctly answer yes or no to an input that contradicts both
>>>>>>> answers, thus H is being asked a question isomorphic to the Liar
>>>>>>> Paradox: Is this sentence true or false: "This sentence is not 
>>>>>>> true." ?
>>>>>>
>>>>>> But it doesn't reduce to that, as the decider was fixed in code 
>>>>>> first, and then, by using that code, a question is constructed 
>>>>>> WITH A RIGHT ANSWER, that just isn't the answer that this decider 
>>>>>> happens to give.
>>>>>>
>>>>>> You just don't seem to understand logic well enough to understand 
>>>>>> that not that subtitle difference.
>>>>>>
>>>>>
>>>>> In other words you are trying to get away with saying
>>>>> that it is only random chance that H gets the wrong
>>>>> answer not that the game is rigged against H.
>>>>>
>>>>>
>>>>
>>>> There is nothing "random" about it, if there was there would be a 
>>>> chance it could get it right.
>>>>
>>>
>>> Then why did you say it was random?
>>> "just isn't the answer that this decider happens to give."
>>
>> But the answer the decider gives isn't random, because algorithms are 
>> not random.
>>
> 
> Then explain exactly how this is not deception:
> "just isn't the answer that this decider happens to give."

Because the decider WILL give some answer, as it was programmed for any 
particular answer.

A priori, we don't know that that answer will be, but we know that it 
will be wrong when we run the computation on the question.

Why don't you understand that.

H(x, x) will give some difinitive answer for EVERY x (and it may be 
different for different xs).

THe fact that Turing Machine are POWERFUL enough to be able to build an 
input x, that can use the use the algorithm of the decider to get the 
answer it WILL GIVE, and then act the opposite, makes it powerful enough 
to not be able to decide on every input.

> 
>>>
>>> When H is asked a yes/no question where both answers are
>>> contradicted by its input *IT IS A FREAKING RIGGED GAME*
>>
>> But both answers aren't wrong. Remember, the question is built to make 
>> a SPECIFIC decider wrong, and by its algorithm, it will give a 
>> SPECIFIC answer to each SPECIFIC question.
>>
> 
> You can't get away with that head game by pretending
> to not understand what infinite an set of H/D pairs is.

But it doesn't matter.

The key is that EVERY element of that infinite set gives the wrong 
answer for its particular input, or it doesn't answer (which is also a 
"wrong answer").

NOTHING allows one HH to look at a DIFFERENT input then it was given, to 
argue about its answer.

And, each machine gets a different input, as for HH to be able have 
something to decide on, the "template" DD has to be converted to an 
actual instance DD[HH] that is unique for each HH.

> 
> I really hope you don't condemn yourself to Hell over this.
> But I was just having fun being a Troll... Is Hell worth that?
> I myself would not take the chance.
>