XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/13/2026 3:11 AM, Mikko wrote:   
   > On 12/01/2026 16:29, olcott wrote:   
   >> On 1/12/2026 4:44 AM, Mikko wrote:   
   >>> On 11/01/2026 16:18, olcott wrote:   
   >>>> On 1/11/2026 4:13 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.   
   >>>>>   
   >>>>> You can't determine whether the required result is computable before   
   >>>>> you have the requirement.   
   >>>>   
   >>>> *Computation and Undecidability*   
   >>>> https://philpapers.org/go.pl?aid=OLCCAU   
   >>>>   
   >>>> We know that there does not exist any finite   
   >>>> string transformations that H can apply to its   
   >>>> input P to derive the halt status of any P   
   >>>> that does the opposite of whatever H returns.   
   >>>   
   >>> Which only nmakes sense when the requirement that H must determine   
   >>> whether the computation presented by its input halts has already   
   >>> been presented.   
   >>>   
   >>>> *ChatGPT explains how and why I am correct*   
   >>>>   
   >>>>    *Reinterpretation of undecidability*   
   >>>>    The example of P and H demonstrates that what is   
   >>>>    often called “undecidable” is better understood as   
   >>>>    ill-posed with respect to computable semantics.   
   >>>>    When the specification is constrained to properties   
   >>>>    detectable via finite simulation and finite pattern   
   >>>>    recognition, computation proceeds normally and   
   >>>>    correctly. Undecidability only appears when the   
   >>>>    specification overreaches that boundary.   
   >>>   
   >>> It tries to explain but it does not prove.   
   >>   
   >> Its the same thing that I have been saying for years.   
   >> It is not that a universal halt decider cannot exist.   
   >   
   > It is proven that an universal halt decider does not exist.   
      
   “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.”   
      
   Under a system like the above rough draft all inputs   
   having pathological self reference such as the halting   
   problem counter-example input are simply rejected as   
   non-well-founded. Tarski Undefinability, Gödel's   
   incompleteness and the halting problem cease to exist.   
      
   > A Turing   
   > machine cannot determine the halting of all Turing machines and is   
   > therefore not an universla halt decider.   
      
   This is not true in Proof Theoretic Semantics. I   
   still have to refine my words. I may not have said   
   that exactly correctly. The result is that in Proof   
   Theoretic Semantics the counter-example is rejected   
   as non-well-founded.   
      
   > An oracle machine may be   
   > able to determine the haltinf of all Turing machines but not of all   
   > oracle machines with the same oracle (or oracles) so it is not   
   > universal.   
   >   
   >> It is that an input that does the opposite of whatever   
   >> value the halt decider returns is non-well-founded   
   >> within proof-theoretic semantics.   
   >   
   > Yes, it is. What the "halt decider" returns is determinable: just run   
   > it and see what it returns. From that the rest can be proven with a   
   > well founded proof. In particular, there is a well-founded proof that   
   > the "halt decider" is not a halt decider.   
   >   
      
      
   --   
   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)