XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/14/2026 9:51 PM, Richard Damon wrote:   
   > On 1/14/26 8:25 PM, olcott wrote:   
   >> On 1/12/2026 9:19 PM, Richard Damon wrote:   
   >>> On 1/12/26 9:29 AM, 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 that an input that does the opposite of whatever   
   >>>> value the halt decider returns is non-well-founded   
   >>>> within proof-theoretic semantics.   
   >>>>   
   >>>   
   >>> But the problem is that Computation is not a proof-theoretic semantic   
   >>> system, and thus those rules don't apply.   
   >>>   
   >>   
   >> The dumbed down version is that the halting problem asks   
   >> a question outside of the scope of finite string transformations.   
   >   
   > But it doesn't, not unless you think that programs can't be represented   
   > as finite strings.   
   >   
   >>   
   >> The halting problem proof does not fail because finite computation   
   >> is too weak. It fails because it asks finite computation to   
   >> decide a judgment that is not finitely grounded under operational   
   >> semantics.   
   >   
   > But that is the issue, Operational Semantics for Programs are not   
   > actually finitely based, since programs can be non-halting.   
   >   
   > Just shows you don't know what your words actually mean.   
   >   
   >>   
   >> By operational semantics I mean the standard proof‑theoretic   
   >> account of program meaning, where execution judgments are   
   >> given by inference rules and termination corresponds to the   
   >> existence of a finite derivation.   
   >   
   > Which is just incorrect. Since infinite derivation has meaning in the   
   > field.   
   >   
      
   The halting problem is not undecidable because computation is weak, but   
   because the classical formulation uses a denotational semantics that is   
   too permissive.   
      
   In operational/proof‑theoretic semantics, where meaning is grounded in   
   finite derivations, the halting predicate is not a well‑formed judgment   
   — just as unrestricted comprehension was not a well‑formed judgment in   
   naïve set theory.   
      
      
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