XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 1/14/2026 1:40 AM, Mikko wrote:   
   > On 13/01/2026 16:27, olcott wrote:   
   >> 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.   
   >   
   > That no Turing machine is a halt decider is a proven theorem and a   
   > truth about Turing machines. If your "Proof Thoeretic Semnatics"   
   > does not regard it as true then your "Proof Theoretic Semantics"   
   > is incomplete.   
   >   
      
   My long‑term goal is to make ‘true on the basis of meaning’ computable.   
   That requires handling undecidability structurally. Proof‑theoretic   
   semantics gives meaning via inferential roles, and only well‑founded   
   ones are admissible. Combined with Curry’s idea that truth is grounded   
      
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