XPost: comp.theory, sci.logic   
   From: richard@damon-family.org   
      
   On 3/14/24 3:54 PM, olcott wrote:   
   > 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   
      
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