XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   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. A Turing   
   machine cannot determine the halting of all Turing machines and is   
   therefore not an universla halt decider. 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.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)