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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 --HOL--
Date: Thu, 14 Mar 2024 18:09:15 -0500
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On 3/14/2024 11:58 AM, Ross Finlayson wrote:
> On 03/13/2024 10:20 PM, olcott wrote:
>> 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".
>>>>>>
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