XPost: sci.logic, comp.theory, sci.math   
   XPost: comp.lang.prolog   
   From: polcott333@gmail.com   
      
   On 1/16/2026 3:17 AM, Mikko wrote:   
   > On 16/01/2026 01:38, olcott wrote:   
   >> 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.   
   >>>>>>   
      
   [continued in next message]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)