XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: polcott333@gmail.com   
      
   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.   
      
   --   
   Copyright 2026 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)