XPost: comp.theory, sci.logic   
   From: polcott2@gmail.com   
      
   On 3/14/2024 5:01 PM, Richard Damon wrote:   
   > 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   
      
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