XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   On 12/01/2026 16:43, olcott wrote:   
   > On 1/12/2026 4:51 AM, Mikko wrote:   
   >> On 11/01/2026 16:23, olcott wrote:   
   >>> On 1/11/2026 4:22 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.   
   >>>>>   
   >>>>>> 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.   
   >>>   
   >>> Any yes/no question lacking a correct yes/no answer   
   >>> is an incorrect question that must be rejected on   
   >>> that basis.   
   >>   
   >> Irrelevant. The question whether a particular requirement is satisfiable   
   >> does have an answer that is either "yes" or "no". In some ases it is   
   >> not known whether it is "yes" or "no" and there may be no known way to   
   >> find out be even then either "yes" or "no" is the correct answer.   
   >   
   > Now that I finally have the standard terminology:   
   > Proof-theoretic semantics has always been the correct   
   > formal system to handle decision problems.   
   >   
   > When it is asked a yes/no question lacking a correct   
   > yes/no answer it correctly determines non-well-founded.   
   > I have been correct all along and merely lacked the   
   > standard terminology.   
      
   Irrelevant, as already noted above.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)