XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   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.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)