XPost: comp.theory, comp.ai.philosophy   
   From: 563-365-8930@kylheku.com   
      
   ["Followup-To:" header set to comp.theory.]   
   On 2020-12-17, olcott  wrote:   
   > On 12/16/2020 10:50 PM, Kaz Kylheku wrote:   
   >> On 2020-12-17, olcott  wrote:   
   >>> On 12/16/2020 10:24 PM, Kaz Kylheku wrote:   
   >>>> On 2020-12-17, olcott  wrote:   
   >>>>> On 12/16/2020 7:51 PM, Kaz Kylheku wrote:   
   >>>>>> If the progression is caused by an infinite recursion of a function   
   >>>>>> with the same paraemters, then all of the simulation levels are   
   >>>>>> indistinguishable. No UTM knows how many levels are above,   
   >>>>>> and each one has the same number of identical levels below.   
   >>>>>>   
   >>>>>> That's it.   
   >>>>>>   
   >>>>>   
   >>>>> If we allowed the infinite recursion to infinitely recur this would be   
   >>>>> true. We cut off the otherwise infinite recursion at three.   
   >>>>>   
   >>>>>> While it is possible to break that, by doing so you break the   
   >>>>>> premise that we have a pure function.   
   >>>>>>   
   >>>>>   
   >>>>> Halts() is a function of its inputs.   
   >>>>   
   >>>> Unfortunately "inputs" no longer refers to "those argument things   
   >>>> between the parentheses that we are painstakingly keeping the same".   
   >>>>   
   >>>   
   >>> I think that may be simply because you have a narrow minded view of   
   >>> inputs as some fixed sized set of objects.   
   >>   
   >> Oh, I specifically do not. Above, I'm demonstrating flexibility and   
   >> insight; I'm recognizing the new situation that there are more inputs   
   >> than just the arguments to those function parameters, and I'm   
   >> acknowleding that those are bona fide inputs.   
   >>   
   >   
   > Great !   
   >   
   >> However, the proofs that are used to demonstrate the nonexistence of a   
   >> universal halting aglorithms specify certain functions which have   
   >> certain inputs, and only those inputs, and are generally pure.   
   >   
   > The dynamically generated execution trace of the simulation of H_Hat and   
   > its input are what Halts bases its halting decision on. That the   
   > conventiopal proof may have incorectly assumed static analysis is merely   
   > a false assumption on its part.   
      
   The conventional proofs have no such problem. They place absolutely no   
   restrictions on Halts other than that it have two arguments, return a   
   Boolean indication and be a function. Within these constraints, no   
   technique, be it "static" or "dynamic" is off the table.   
      
   The proofs show that no definition of Halts, under their constraints,   
   can be a universal halting decider. Because Halts is constrained in such   
   a way that it can be comprised of any Turing machine (there is an   
   equivalence between pure funcions and Turing machines), the proofs show   
   that no Turing machine can be a universal halting decider.   
      
   Your apparatus contains contains functions which meet a different,   
   informal definition of the word "function" denoting an imperative   
   procedure that returns a value, that may access (and even mutate) state   
   information not contained in its arguments.   
      
   Your claim is that your apparatus is an embodiment of the entities   
   described in the proof, and therefore properties of the apparatus speak   
   to the proof. This claim is false, and is to a large extent based   
   on equivocation over word semantics: changing between the definition of   
   "function" in mathematics jargon, and the definition of "function" in   
   the jargon of certain programming languages.   
      
   Equivocation is one of the most embarrassing errors of inference that   
   man can make: not pinning down the meanings of words.   
      
   The assumptions which a proof makes are its privilege, and they   
   contribute to its definition. If you have to change them in order to   
   challenge the proof, you're attacking a strawman caricature of the proof,   
   not the real one.   
      
   > The halting proofs merely falsely assume static rather than dynamic   
   > analysis. That is their mistake not mine.   
      
   No such words appear in any proof you can cite from any credible   
   textbook or paper. All proper presentations of the proof allow the   
   decider simply be an arbitrary recursive funtion, which allows it to be   
   any Turing machine.   
      
   (Quite literally, the decider function can encode the arguments P and I   
   onto a tape of symbols, and feed it to an actual Universal Turing Machine.)   
      
   The techniques you are using do not allow this; you could not translate   
   your simulation approach such that Halts encodes P and I onto a tape and   
   just launches a UTM, and then (if the UTM halts) collects the return   
   value from the tape.   
      
   Your approach would require the multiple invocations of that UTM to be   
   diddled by an interfering process into incorrectly producing different   
   results.   
      
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