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From: Richard Damon <richard@damon-family.org>
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: Fri, 21 Jun 2024 13:06:27 -0400
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On 6/21/24 12:56 PM, olcott wrote:
> On 6/21/2024 9:36 AM, Richard Damon wrote:
>> On 6/21/24 12:01 AM, olcott wrote:
> 
> 
> _DDD()
> [00002093] 55               push ebp
> [00002094] 8bec             mov ebp,esp
> [00002096] 6893200000       push 00002093 ; push DDD
> [0000209b] e853f4ffff       call 000014f3 ; call HH0
> [000020a0] 83c404           add esp,+04
> [000020a3] 5d               pop ebp
> [000020a4] c3               ret
> Size in bytes:(0018) [000020a4]
> 
>>>
>>> That is the only definitive way to determine the
>>> actual behavior that the finite string specifies.
>>>
>>
>> It is the only was to COMPUTE the actual behavior, but to DETERMINE it 
>> doesn't need that.
>>
> 
> Ah so you expect that HH0 must use its intuition to
> determine that behavior that it is supposed to report on.
> 


Nope, if it exists, it needs to compute the answer. But, it doesn't need 
to exist as a correct decider for halting.

That is part of your problem, you think that all problems need to be 
computable, but it is proven that they can not be by simple counting.

Thus, we KNOW that some problems that can be properly thought of as 
mappings are not computable, so, the fact that Halting is one of them is 
not a problem.

Remember, problems in Computation Theory are about CAN we build a 
machine to compute a given mapping, so forming a question about an 
uncomputable mapping isn't an "invalid" question, but just a question 
for which the computablity question is NO.

So, all your arguments about the Halting Question not being answerable 
by a computation are just proving the Halting Theorem, that the Halting 
Function is uncomputable, and not that the Halting Question is "Invalid" 
for some reason.

Every proper input (the representation of an actual Machine) has a 
correct answer, as defined by the behavior of the machine the input 
represents, but there just doesn't exist a machine that can compute the 
answer, and trying to redefine the criteria to be a computable one just 
shows that you don't understand that basic concept of the field.

Perhaps because it just breaks your fundamental (and wrong) idea that 
all Truth must be knowable/provable.