XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/16/2026 3:32 AM, Mikko wrote:   
   > On 15/01/2026 22:30, olcott wrote:   
   >> 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.   
   >   
   > ZF or ZFC is to some extent useful for addressing Russell's paradox.   
   > It is an example of a set theory where Russell's paradox is avoided.   
   > If your "Proof Theretic Semantics" cannot handle the existence of   
   > a counter example for every Turing decider then it is not usefule   
   > for those who work on practical problems of program correctness.   
   >   
      
   Proof theoretic semantics addresses Gödel Incompleteness   
   for PA in a way similar to the way that ZFC addresses   
   Russell's Paradox in set theory.   
      
   ZFC resolves Russell’s paradox by restricting the formation   
   of sets to those justified by proof‑theoretic rules.   
      
   Proof‑theoretic semantics resolves the meaning‑theoretic   
   issues behind Gödel incompleteness by restricting the   
   formation of truth‑bearing statements to those justified   
   by inference rules.   
      
   In both cases, paradox arises only when the semantics   
   is too permissive, and disappears when meaning is grounded   
   proof‑theoretically.   
      
   Proof Theoretic Semantics Blocks Pathological Self-Reference   
   https://philpapers.org/rec/OLCPTS   
      
   --   
   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)