XPost: comp.theory, sci.logic, sci.math   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 1/15/2026 3:34 AM, Mikko wrote:   
   > On 14/01/2026 21:32, olcott wrote:   
   >> On 1/14/2026 3:01 AM, Mikko wrote:   
   >>> On 13/01/2026 16:31, olcott wrote:   
   >>>> On 1/13/2026 3:13 AM, Mikko wrote:   
   >>>>> On 12/01/2026 16:32, olcott wrote:   
   >>>>>> On 1/12/2026 4:47 AM, Mikko wrote:   
   >>>>>>> On 11/01/2026 16:24, Tristan Wibberley wrote:   
   >>>>>>>> On 11/01/2026 10:13, Mikko wrote:   
   >>>>>>>>> On 10/01/2026 17:47, olcott wrote:   
   >>>>>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:   
   >>>>>>>>   
   >>>>>>>>>>> No, that does not follow. If a required result cannot be   
   >>>>>>>>>>> derived by   
   >>>>>>>>>>> appying a finite string transformation then the it it is   
   >>>>>>>>>>> uncomputable.   
   >>>>>>>>>>   
   >>>>>>>>>> Right. Outside the scope of computation. Requiring anything   
   >>>>>>>>>> outside the scope of computation is an incorrect requirement.   
   >>>>>>>>>   
   >>>>>>>>> You can't determine whether the required result is computable   
   >>>>>>>>> before   
   >>>>>>>>> you have the requirement.   
   >>>>>>>>   
   >>>>>>>>   
   >>>>>>>> Right, it is /in/ scope for computer science... for the /ology/.   
   >>>>>>>> Olcott   
   >>>>>>>> here uses "computation" to refer to the practice. You give the   
   >>>>>>>> requirement to the /ologist/ who correctly decides that it is   
   >>>>>>>> not for   
   >>>>>>>> computation because it is not computable.   
   >>>>>>>>   
   >>>>>>>> You two so often violently agree; I find it warming to the heart.   
   >>>>>>>   
   >>>>>>> For pracitcal programming it is useful to know what is known to be   
   >>>>>>> uncomputable in order to avoid wasting time in attemlpts to do the   
   >>>>>>> impossible.   
   >>>>>>   
   >>>>>> It f-cking nuts that after more than 2000 years   
   >>>>>> people still don't understand that self-contradictory   
   >>>>>> expressions: "This sentence is not true" have no   
   >>>>>> truth value. A smart high school student should have   
   >>>>>> figured this out 2000 years ago.   
   >>>>>   
   >>>>> Irrelevant. For practical programming that question needn't be   
   >>>>> answered.   
   >>>>   
   >>>> The halting problem counter-example input is anchored   
   >>>> in the Liar Paradox. Proof Theoretic Semantics rejects   
   >>>> those two and Gödel's incompleteness and a bunch more   
   >>>> as merely non-well-founded inputs.   
   >>>   
   >>> For every Turing machine the halting problem counter-example provably   
   >>> exists.   
   >>   
   >> Not when using Proof Theoretic Semantics grounded   
   >> in the specification language. In this case the   
   >> pathological input is simply rejected as ungrounded.   
   >   
   > Then your "Proof Theoretic Semantics" is not useful for discussion of   
   > Turing machines. For every Turing machine a counter example exists.   
   > And so exists a Turing machine that writes the counter example when   
   > given a Turing machine as input.   
   >   
      
   It is "not useful" in the same way that ZFC was   
   "not useful" for addressing Russell's Paradox.   
      
   The halting problem is not undecidable because computation   
   is weak, but because the classical formulation uses a   
   denotational semantics that is too permissive.   
      
   In operational/proof‑theoretic semantics, where meaning   
   is grounded in finite derivations, the halting predicate   
   is not a well‑formed judgment — just as unrestricted   
   comprehension was not a well‑formed judgment in naïve   
   set theory.   
      
      
   --   
   Copyright 2026 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)