XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   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.   
   Of course, it one can prove that the required result is not computable   
   then that helps to avoid wasting effort to try the impossible. The   
   situation is worse if it is not known that the required result is not   
   computable.   
      
   That something is not computable does not mean that there is anyting   
   "incorrect" in the requirement. In order to claim that a requirement   
   is incorrect one must at least prove that the requirement does not   
   serve its intended purpose. Even then it is possible that the   
   requirement serves some other purpose. Even if a requirement serves   
   no purpose that need not mean that it be "incorrect", only that it   
   is useless.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)