XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/15/2025 10:13 AM, olcott wrote:   
   > On 12/15/2025 2:09 AM, Tristan Wibberley wrote:   
   >> The message body is Copyright (C) 2025 Tristan Wibberley except   
   >> citations and quotations noted. All Rights Reserved except as noted in   
   >> 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.   
   >>   
   >>   
   >   
   > A TM halt decider computes the halt status specified   
   > by an input finite string on its tape. It begins in its   
   > own start state and ends in one of its own final   
   > halt states.   
   >   
   > To say that a TM halt decider determines whether or   
   > not machine M halts on input w is less than precisely   
   > accurate.   
   >   
      
   This need not be a physical machine yet it must be   
   a coherent abstraction.   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)