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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) --- Dogma
Date: Sat, 22 Jun 2024 09:03:35 -0400
Organization: i2pn2 (i2pn.org)
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On 6/22/24 12:31 AM, olcott wrote:
> On 6/21/2024 11:24 PM, joes wrote:
>> Am Fri, 21 Jun 2024 22:16:55 -0500 schrieb olcott:
>>> On 6/21/2024 6:38 PM, Richard Damon wrote:
>>>> On 6/21/24 7:27 PM, olcott wrote:
>>>>> On 6/21/2024 4:46 PM, Richard Damon wrote:
>>>>>> On 6/21/24 5:25 PM, olcott wrote:
>>>>>>> On 6/21/2024 4:10 PM, Richard Damon wrote:
>>>>>>>> On 6/21/24 4:52 PM, olcott wrote:
>>>>>>>>> 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:
>>
>>>>>>>>>>>> Nope. H(M,d) is DEFINED (if it is correct) to determine if M(d)
>>>>>>>>>>>> will Halt.
>>
>>>>>>>>>> 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.
>>
>>>>>>>> The DEFINITION of a Halt Decider gives what H is SUPPOSED to do, if
>>>>>>>> it is one.
>>>>>>>> You claim it is a correct Halt decider
>>>>>>>>
>>>>>>> When we do not simply make false assumptions about the behavior that
>>>>>>> the input to H(D,D) specifies:
>>>>>>>     That the call from D correctly simulated by H to H(D,D) returns
>>>>>>
>>>>>> What "False Assumption"?
>>>>>> You just are ignorant of the DEFINTION of the problem.
>>>>>>
>>>>> *DOGMA DOES NOT COUNT AS SUPPORTING REASONING*
>>>>
>>>> But DEFINITIONS DO.
>>
>>>>> To "define" that the call from the D correctly simulated by H to
>>>>> H(D,D) returns when the actual facts prove that this call *DOES NOT
>>>>> RETURN* is ultimately unreasonable because *THERE IS NO REASONING*
>>>>> that supports this.
>> If H really is a decider, it returns.
>>
>>>> But that isn't the definition that we are using.
>>
>>> NOTHING talks about the correct simulation of D ONLY because I am the
>>> sole inventor of simulating halt deciders that no one ever thought
>>> ALL-THE-WAY through before.
>> Unlikely.
>> Again, the simulation shouldn't change anything.
>>
>>> The semantics of the x86 language conclusively proves as a verified fact
>>> that the behavior that D specifies to H is different than the behavior
>>> that D specifies to H1.
>> But D is the same in either case?!
>>
>>> You cannot simply correctly ignore that the pathological relationship
>>> that D calls H(D,D) and does not call H1(D,D) changes the behavior of D
>>> between these two cases.
> 
>> The behaviour changes only because of the called H.
>>
> 
> void DDD()
> {
>    H0(DDD);
> }
> 
> int main()
> {
>    H0(DDD);
>    H1(DDD);
> }
> 
> DDD correctly simulated by H1 halts.
> DDD correctly simulated by H0 never halts.
> 
> 

And thus you prove that your criteria, "Correctly simulated by the 
decider" is NOT a valid property of the input, because there is not a 
mapping of (input) -> (output), but only a mapping of:

(input, decider) -> (output)

Thus, it is not a property of the input alone.

So, NOT a valid property to be a replacement for Halting.

Note, the problem is you are creating a SUBJECTIVE property when you 
need an OBJECTIVE property. The fact we need to know who is being asked 
to know what the right answer is makes the property subjective, and thus 
not the sort of thing that the logical system talks about.