XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   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.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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