XPost: comp.theory, sci.logic   
   From: polcott2@gmail.com   
      
   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.   
   >>>>>>>   
      
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