XPost: comp.theory, sci.logic   
   From: richard@damon-family.org   
      
   On 3/14/24 12:01 PM, olcott wrote:   
   > 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   
      
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