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From: olcott <polcott2@gmail.com>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Thu, 14 Mar 2024 00:20:26 -0500
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On 3/13/2024 1:16 PM, Ross Finlayson wrote:
> On 03/12/2024 09:00 PM, olcott wrote:
>> On 3/12/2024 10:49 PM, Ross Finlayson wrote:
>>> On 03/12/2024 08:23 PM, Ross Finlayson wrote:
>>>> On 03/12/2024 07:52 PM, olcott wrote:
>>>>> On 3/12/2024 9:28 PM, Richard Damon wrote:
>>>>>> On 3/12/24 4:31 PM, olcott wrote:
>>>>>>> On 3/12/2024 6:11 PM, Richard Damon wrote:
>>>>>>>> On 3/12/24 3:53 PM, olcott wrote:
>>>>>>>>> On 3/12/2024 5:30 PM, Richard Damon wrote:
>>>>>>>>>> On 3/12/24 2:34 PM, olcott wrote:
>>>>>>>>>>> On 3/12/2024 4:23 PM, Richard Damon wrote:
>>>>>>>>>>>> On 3/12/24 1:11 PM, olcott wrote:
>>>>>>>>>>>>> On 3/12/2024 2:40 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 3/12/24 12:02 PM, olcott wrote:
>>>>>>>>>>>>>>> On 3/12/2024 1:31 PM, immibis wrote:
>>>>>>>>>>>>>>>> On 12/03/24 19:12, olcott wrote:
>>>>>>>>>>>>>>>>> ∀ H ∈ Turing_Machine_Deciders
>>>>>>>>>>>>>>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>>>>>>>>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> There is some input TMD to every H such that
>>>>>>>>>>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> And it can be a different TMD to each H.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> When we disallow decider/input pairs that are incorrect
>>>>>>>>>>>>>>>>> questions where both YES and NO are the wrong answer
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Once we understand that either YES or NO is the right
>>>>>>>>>>>>>>>> answer, the whole rebuttal is tossed out as invalid and
>>>>>>>>>>>>>>>> incorrect.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>> halts
>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ 
>>>>>>>>>>>>>>> does
>>>>>>>>>>>>>>> not halt
>>>>>>>>>>>>>>> BOTH YES AND NO ARE THE WRONG ANSWER FOR EVERY Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> No, because a given H will only go to one of the answers. 
>>>>>>>>>>>>>> THAT
>>>>>>>>>>>>>> will be wrong, and the other one right.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> ∀ H ∈ Turing_Machine_Deciders
>>>>>>>>>>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>>>>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>>>>>>
>>>>>>>>>>>>> Not exactly. A pair of otherwise identical machines that
>>>>>>>>>>>>> (that are contained within the above specified set)
>>>>>>>>>>>>> only differ by return value will both be wrong on the
>>>>>>>>>>>>> same pathological input.
>>>>>>>>>>>>
>>>>>>>>>>>> You mean a pair of DIFFERENT machines. Any difference is
>>>>>>>>>>>> different.
>>>>>>>>>>>
>>>>>>>>>>> Every decider/input pair (referenced in the above set) has a
>>>>>>>>>>> corresponding decider/input pair that only differs by the return
>>>>>>>>>>> value of its decider.
>>>>>>>>>>
>>>>>>>>>> Nope.
>>>>>>>>>>
>>>>>>>>> ∀ H ∈ Turing_Machines_Returning_Boolean
>>>>>>>>> ∃ TMD ∈ Turing_Machine_Descriptions  |
>>>>>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>>>>>
>>>>>>>>> Every H/TMD pair (referenced in the above set) has a
>>>>>>>>> corresponding H/TMD pair that only differs by the return
>>>>>>>>> value of its Boolean_TM.
>>>>>>>>
>>>>>>>> That isn't in the set above.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> That both of these H/TMD pairs get the wrong answer proves that
>>>>>>>>> their question was incorrect because the opposite answer to the
>>>>>>>>> same question is also proven to be incorrect.
>>>>>>>>>
>>>>>>>>>
>>>>>>>> Nope, since both aren't in the set selected.
>>>>>>>>
>>>>>>>
>>>>>>> When they are deciders that must get the correct answer both
>>>>>>> of them are not in the set.
>>>>>>
>>>>>> *IF* they are correct decider.
>>>>>>
>>>>>> WHen we select from all Turing Machine Deciders, there is no
>>>>>> requirement that any of them get any particular answer right.
>>>>>>
>>>>>> So, ALL deciders are in the set that we cycle through and apply the
>>>>>> following logic to ALL of them.
>>>>>>
>>>>>> Each is them paired with an input that it will get wrong, and the
>>>>>> existance of the input was what as just proven, the ^ template
>>>>>>
>>>>>>>
>>>>>>> When they are Turing_Machines_Returning_Boolean the this
>>>>>>> set inherently includes identical pairs that only differ
>>>>>>> by return value.
>>>>>>
>>>>>> But in the step of select and input that they will get wrong, they
>>>>>> will be givne DIFFERENT inputs.
>>>>>>
>>>>>>>
>>>>>>>> You just don't understand what that statement is saying.
>>>>>>>>
>>>>>>>> I've expalined it, but it seems over you head.
>>>>>>>>
>>>>>>> No the problem is that you are not paying attention.
>>>>>>
>>>>>> No, you keep on making STUPID mistakes, like thinking that select a
>>>>>> input that the machine will get wrong needs to be the same for two
>>>>>> differnt machines.
>>>>>>
>>>>>>
>>>>>>
>>>>>>>
>>>>>>>> For Every H, we show we can find at least one input (chosen just 
>>>>>>>> for
>>>>>>>> that machine) that it will get wrong.
>>>>>>>>
>>>>>>> When we use machine templates then we can see instances of
>>>>>>> the same machine that only differs by return value where both
>>>>>>> get the wrong answer on the same input. By same input I mean
>>>>>>> the same finite string of numerical values.
>>>>>>>
>>>>>>
>>>>>> But if they returned differnt values, they will have different
>>>>>> descriptions.
>>>>>>
>>>>>> Otherwise, how could a UTM get the right answer, since it only gets
>>>>>> the description.
>>>>>
>>>>> We can get around all of this stuff by simply using this criteria:
>>>>> Date 10/13/2022 11:29:23 AM
>>>>> *MIT Professor Michael Sipser agreed this verbatim paragraph is
>>>>> correct*
>>>>> (He has neither reviewed nor agreed to anything else in this paper)
>>>>> (a) If simulating halt decider H correctly simulates its input D
>>>>> until H
>>>>> correctly determines that its simulated D would never stop running
>>>>> unless aborted then
>>>>> (b) H can abort its simulation of D and correctly report that D
>>>>> specifies a non-halting sequence of configurations.
>>>>>
>>>>> *When we apply this criteria* (elaborated above)
>>>>> Will you halt if you never abort your simulation?
>>>>> *Then the halting problem is conquered*
>>>>>
>>>>> When two different machines implementing this criteria
>>>>> get different results from identical inputs then we
>>>>> know that Pathological Self-Reference has been detected.
>>>>>
>>>>> We don't even need to know that for:
>>>>> *denial-of-service-attack detection*
>>>>> *NO always means reject as unsafe*
>>>>>
>>>>
>>>> But, Halting theorem never said "there's an input that halts
>>>> all machines", it just says "for any machine, there's an input
>>>> that halts it".
>>>>
>>>> Where "halt the machine" means "put it in an infinite loop".
>>>>
>>>> So, rather, Halting theorem never said "there's an input that
>>>> exhausts all machines", it just says, "for any machine, there's
>>>> an input that exhausts it".
>>>>
>>>> I still don't see how that would be with infinite tapes though,
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