XPost: sci.logic, comp.theory, sci.math   
   XPost: comp.lang.prolog   
   From: mikko.levanto@iki.fi   
      
   On 16/01/2026 17:12, olcott wrote:   
   > 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   
      
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