XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   On 1/13/2026 2:46 AM, Mikko wrote:   
   > On 12/01/2026 16:43, olcott wrote:   
   >> 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.   
   >   
   > Irrelevant, as already noted above.   
   >   
      
   It is not irrelevant at all. Most all of undecidability   
   cease to exist in this system:   
      
   “The system adopts Proof-Theoretic Semantics:   
   meaning is determined by inferential role,   
   and truth is internal to the theory. A theory   
   T is defined by a finite set of stipulated atomic   
   statements together with all expressions derivable   
   from them under the inference rules. The statements   
   belonging to T constitute its theorems, and these   
   are exactly the statements that are true-in-T.”   
      
   Is the foundation of the system that I have been   
   talking about all of these years making   
   ∀x ∈ T ((True(T, x) ≡ (T ⊢ x))   
   and Gödel Incompleteness impossible.   
      
   The above system fulfills:   
   My 28 year goal has been to make   
   "true on the basis of meaning expressed in language"   
   reliably computable.   
      
   Formal systems with undecidability and incompleteness   
   merely had the wrong foundation.   
      
      
   --   
   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)