XPost: comp.theory, sci.math, comp.ai.philosophy   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 1/15/2026 3:48 AM, Mikko wrote:   
   > On 14/01/2026 19:28, olcott wrote:   
   >> 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"   
      
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