Re: Refuting the {Linz, Sipser, Kozen} HP Proofs [---Pathological self-reference(Olcott 2004)---]

[olcott]

On 1/1/2021 5:01 AM, André G. Isaak wrote:
> On 2020-12-31 22:26, olcott wrote:
>> On 12/31/2020 9:43 PM, Richard Damon wrote:
>>> On 12/31/20 10:14 PM, olcott wrote:
>>>> On 12/31/2020 8:23 PM, Richard Damon wrote:
>>>>>
>>>>>
>>>>> Self Reference is NOT pathological, but is an important property to
>>>>> express the fullness of mathematics and logic.
>>>>>
>>>>> Yes, once your logic system allows this sort of self reference, you
>>>>> get
>>>>> properties like incompleteness which seems to be something you do not
>>>>> like. But it is important to fully be able to describe the infinity of
>>>>> mathematics.
>>>>>
>>>>>
>>>>> You really need to make up your mind. Either you are dealing with the
>>>>> classical Halting Problem, in which case you need to work within the
>>>>> rules of that problem, or you admit that you are working on a
>>>>> different
>>>>> problem, at which point you need to stop presuming your answers
>>>>> have any
>>>>> bearing on those classical problems.
>>>>>
>>>>
>>>> You must be far too dumb to realize that refuting the conclusion of a
>>>> proof refutes the proof.
>>>
>>> What about MY refuting YOUR proof. You conclusion has been shown to be
>>> wrong many times.
>>>
>>>>
>>>> A universal halt decider only needs to divide all of its inputs into
>>>> those having the property of infinite execution and those that do not
>>>> have this property.
>>>
>>> Yes, and if Halts is a decider, which means it returns its answer to its
>>> caller. (and that is the ONLY way a Turing Machine can give an answer,
>>
>> Sure and like infinite loops that only loop ten times infinite
>> recursion only recurs ten times, so whenever any function is invoked
>> in infinite recursion it always returns the result to its caller after
>> its tenth invocation.
>
> You keep raising this point about loops and recursion as if it somehow
> obviates the need to return a value. All this does is illustrate the
> fact that you don't grasp what a 'decider' is.
>
> To constitute a decider, a program *must* be constructed in such a way
> that it always returns a value. That means that it must be constructed
> in such a way that it is not possible for it to get stuck in an infinite
> loop or in infinite recursion.

Bullshit. Your dogma is logically incoherent.

void H_Hat(u32 P)
{
u32 Input_Halts = Halts(P, P);
if (Input_Halts)
HERE: goto HERE;
return;
}

int main()
{
HERE goto HERE;
u32 Input_Halts = Halts((int)H_Hat, (int)H_Hat);
Output("Input_Halts = ", Input_Halts);
}

(1) If it is not possible for it to get stuck in an infinite loop that
rules out local halt deciding.

(2) If we rule out local halt deciding then when the global halt decider
aborts main() because of the infinite loop it has no where to return a
value to.

Your dogma is logically incoherent, therefore provably incorrect.

>
> No one here disputes the fact that a routine that is infinitely
> recursive cannot return a value to its caller. The point which you keep
> failing to get, though, is that any such routine cannot be described as
> a decider, because a decider, by definition, is guaranteed to return a
> value for every possible input.
>
> André
>
>


--
Copyright 2020 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein