XPost: comp.theory, sci.math, comp.ai.philosophy   
   XPost: comp.lang.prolog   
   From: mikko.levanto@iki.fi   
      
   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.   
   >>>>>   
   >>>>> 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   
      
   [continued in next message]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)