XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   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.   
   >   
   >> 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.   
   >   
   > Yes it certainly does. Requiring the impossible is always an error.   
      
   It is a perfectly valid question to ask whther a particular reuqirement   
   is satisfiable.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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