XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   On 1/12/2026 4:51 AM, Mikko wrote:   
   > On 11/01/2026 16:23, olcott wrote:   
   >> On 1/11/2026 4:22 AM, Mikko wrote:   
   >>> On 10/01/2026 17:47, olcott wrote:   
   >>>> On 1/10/2026 2:23 AM, Mikko wrote:   
   >>>>> On 09/01/2026 17:52, olcott wrote:   
   >>>>>> On 1/9/2026 3:59 AM, Mikko wrote:   
   >>>>>>> On 08/01/2026 16:22, olcott wrote:   
   >>>>>>>> On 1/8/2026 4:22 AM, Mikko wrote:   
   >>>>>>>>> On 07/01/2026 13:54, olcott wrote:   
   >>>>>>>>>> On 1/7/2026 5:49 AM, Mikko wrote:   
   >>>>>>>>>>> On 07/01/2026 06:44, olcott wrote:   
   >>>>>>>>>>>> All deciders essentially: Transform finite string   
   >>>>>>>>>>>> inputs by finite string transformation rules into   
   >>>>>>>>>>>> {Accept, Reject} values.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> The counter-example input to requires more than   
   >>>>>>>>>>>> can be derived from finite string transformation   
   >>>>>>>>>>>> rules applied to this specific input thus the   
   >>>>>>>>>>>> Halting Problem requires too much.   
   >>>>>>>>>>   
   >>>>>>>>>>> In a sense the halting problem asks too much: the problem is   
   >>>>>>>>>>> proven to   
   >>>>>>>>>>> be unsolvable. In another sense it asks too little: usually   
   >>>>>>>>>>> we want to   
   >>>>>>>>>>> know whether a method halts on every input, not just one.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Although the halting problem is unsolvable, there are partial   
   >>>>>>>>>>> solutions   
   >>>>>>>>>>> to the halting problem. In particular, every counter-example   
   >>>>>>>>>>> to the   
   >>>>>>>>>>> full solution is correctly solved by some partial deciders.   
   >>>>>>>>>>   
   >>>>>>>>>> *if undecidability is correct then truth itself is broken*   
   >>>>>>>>>   
   >>>>>>>>> Depends on whether the word "truth" is interpeted in the standard   
   >>>>>>>>> sense or in Olcott's sense.   
   >>>>>>>>   
   >>>>>>>> Undecidability is misconception. Self-contradictory   
   >>>>>>>> expressions are correctly rejected as semantically   
   >>>>>>>> incoherent thus form no undecidability or incompleteness.   
   >>>>>>>   
   >>>>>>> The misconception is yours. No expression in the language of the   
   >>>>>>> first   
   >>>>>>> order group theory is self-contradictory. But the first order goupr   
   >>>>>>> theory is incomplete: it is impossible to prove that AB = BA is true   
   >>>>>>> for every A and every B but it is also impossible to prove that   
   >>>>>>> AB = BA   
   >>>>>>> is false for some A and some B.   
   >>>>>>>   
   >>>>>>   
   >>>>>> All deciders essentially: Transform finite string   
   >>>>>> inputs by finite string transformation rules into   
   >>>>>> {Accept, Reject} values.   
   >>>>>>   
   >>>>>> When a required result cannot be derived by applying   
   >>>>>> finite string transformation rules to actual finite   
   >>>>>> string inputs, then the required result exceeds the   
   >>>>>> scope of computation and must be rejected as an   
   >>>>>> incorrect requirement.   
   >>>>>   
   >>>>> 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.   
   >>>>   
   >>>>> Of course, it one can prove that the required result is not computable   
   >>>>> then that helps to avoid wasting effort to try the impossible. The   
   >>>>> situation is worse if it is not known that the required result is not   
   >>>>> computable.   
   >>>>>   
   >>>>> That something is not computable does not mean that there is anyting   
   >>>>> "incorrect" in the requirement.   
   >>>>   
   >>>> Yes it certainly does. Requiring the impossible is always an error.   
   >>>   
   >>> It is a perfectly valid question to ask whther a particular reuqirement   
   >>> is satisfiable.   
   >>   
   >> Any yes/no question lacking a correct yes/no answer   
   >> is an incorrect question that must be rejected on   
   >> that basis.   
   >   
   > Irrelevant. The question whether a particular requirement is satisfiable   
   > does have an answer that is either "yes" or "no". In some ases it is   
   > not known whether it is "yes" or "no" and there may be no known way to   
   > find out be even then either "yes" or "no" is the correct answer.   
   >   
      
   Now that I finally have the standard terminology:   
   Proof-theoretic semantics has always been the correct   
   formal system to handle decision problems.   
      
   When it is asked a yes/no question lacking a correct   
   yes/no answer it correctly determines non-well-founded.   
   I have been correct all along and merely lacked the   
   standard terminology.   
      
   --   
   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)