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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,sci.logic
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Sat, 5 Jul 2025 09:14:57 -0400
Organization: i2pn2 (i2pn.org)
Message-ID: <89d2edbab76401270efa67a8fbc135d5c47fefab@i2pn2.org>
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On 7/4/25 6:11 PM, olcott wrote:
> On 7/4/2025 3:53 PM, Richard Damon wrote:
>> On 7/4/25 4:43 PM, olcott wrote:
>>> On 6/3/2025 10:02 PM, dbush wrote:
>>>> On 6/3/2025 10:58 PM, olcott wrote:
>>>>> On 6/3/2025 9:46 PM, dbush wrote:
>>>>>> On 6/3/2025 10:34 PM, olcott wrote:
>>>>>>> On 6/3/2025 9:12 PM, dbush wrote:
>>>>>>>>
>>>>>>>> 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
>>>>>>>>
>>>>>>>
>>>>>>> Yes there is no algorithm that does that 
>>>>>>
>>>>>> Excellent!
>>>>>>
>>>>>> Let The Record Show
>>>>>>
>>>>>> That Peter Olcott
>>>>>>
>>>>>> Has *EXPLICITLY* admitted
>>>>>>
>>>>>> That no algorithm H exists that meets the above requirements, 
>>>>>> which is precisely the theorem that the halting problem proofs prove.
>>>>>
>>>>> In the exact same way that there is no set of all set
>>>>> that contain themselves. ZFC did not solve Russell's
>>>>> Paradox as much as it showed that Russell's Paradox
>>>>> was anchored in an incoherent foundation, now called
>>>>> naive set theory.
>>>>
>>>> Which arose because the axioms of naive set theory created a 
>>>> contradiction.
>>>>
>>>
>>> Likewise with halt deciders that are required to report
>>> on the behavior of directly executed Turing machines.
>>
>> And what is the CONTRADICTION?
>>
>> The result is just some things are not computable.
>>
> 
> The result is that there cannot possibly be
> an *ACTUAL INPUT* that does the opposite of
> whatever its partial halt decider decides
> thus the HP proof fails before it begins.
> 

Sure there is.

Why doesn't P / D / DD actually do the opposite of what H decides?

Remember, "behavior" is DEFINED as what the machine it represents does 
when directly run, not does the partial simulation of it by the decider 
reach a final state.

Or alternativly, what a UTM would do with the input representing the 
FULL program.

Both of these REQUIRE that the code of the decider be included in "the 
input", not your lie of trying to claim to exclude it.

You are just proving your stupidity.