XPost: comp.theory, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   The message body is Copyright (C) 2025 Tristan Wibberley except   
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   the sig.   
      
   On 14/12/2025 16:16, polcott wrote:   
   > On 12/14/2025 6:51 AM, Tristan Wibberley wrote:   
   >> On 13/12/2025 19:50, olcott wrote:   
   >>> On 12/13/2025 1:33 PM, Tristan Wibberley wrote:   
   >>>> On 13/12/2025 16:44, olcott wrote:   
   >>   
   >>>>> Turing machine Deciders are a subset of this   
   >>>>> where the value indicates accept or reject a   
   >>>>> finite string by some criterion measure.   
   >>>>   
   >>>> I continue to reject the use of "accept" and "reject" here. And I also   
   >>>> reject the use of "indicates" wrt to them.   
   >>>>   
   >>>   
   >>> My goal is to have accepted definitions as my only basis.   
   >>   
   >> Oh! I just noticed it's a new statement with "by some criterion measure"   
   >> which makes it excellent. I retract my rejection.   
   >>   
   >   
   > Good.   
   >   
   > This is my first post on the halting Problem   
   > https://groups.google.com/g/sci.logic/c/V7wzVvx8IMw/m/ggPE6a-60cUJ   
   >   
   > I worked for 15 years mostly on the basis of intuition.   
   > Then 2 more years creating fully operational code. Then   
   > 3 years of discussing this code.   
   >   
   > Now I am finally getting around to anchoring these   
   > intuitions and my working code in standard definitions.   
   >   
   > My current working code.   
   > https://github.com/plolcott/x86utm/blob/master/Halt7.c   
   >   
   > I had to refrain from learning the standard definitions   
   > before now or they would have boxed me into the standard   
   > views.   
   >   
   > My insights are entirely from slight nuances of meaning   
   > that are abstracted away in the standard definitions.   
   >   
   > I had to carefully reverse-engineer the exact details   
   > of what was actually happening before I could see what   
   > nuances of meaning were being left out. Initially I   
   > had to use my own non-standard terminology to do this.   
   >   
   > This is my first principle   
   > All Turing machines only compute the mapping   
   > from input finite strings to some value.   
      
   My second correction of three that are needed (I will return to the   
   third later once I've thought more):   
      
   "value" is not defined, a first principle must be elementary (introduces   
   terms of art but does not depend on them).   
      
   Here are two alternatives to illuminate the matter, but I think they're   
   not good enough:   
      
   1st alternative: You need a prior principle defining "value". That's not   
   entirely intuitive though we pretend it is, like so much that you   
   correctly find to be a problem.   
      
   2nd alternative: All Automatic Turing Machines compute only an output   
   finite string from an input finite string.   
      
   They're wrong because a turing machine has a state (m-configuration),   
   whose change--and given a constant initial state then also itself--is,   
   in effect, computed.   
      
   The 3rd alternative is contingent as noted, a contingency whose premise   
   I think you suppose:   
      
   3rd alternative, admissible when considering an ATM to be a physical   
   machine rather than a mere formal system: An Automatic Turing Machine is   
   one of those things restricted--at least in part--such that it computes   
   nothing more than an output finite string along with its own halting   
   state from an input finite string along with its own pre-nominated   
   initial state.   
      
      
   --   
   Tristan Wibberley   
      
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