XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   On 13/01/2026 16:17, olcott wrote:   
   > On 1/13/2026 2:46 AM, Mikko wrote:   
   >> 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.   
   >   
   > It is not irrelevant at all. Most all of undecidability   
   > cease to exist in this system:   
      
   It does not help if the system is not sound. Or if the particuar   
   undecidability that one happens to care about does not cease to   
   exist.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)