XPost: comp.theory, sci.math, comp.lang.prolog   
   XPost: comp.software-eng   
   From: mikko.levanto@iki.fi   
      
   On 14/01/2026 21:35, olcott wrote:   
   > On 1/14/2026 3:04 AM, Mikko wrote:   
   >> 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.   
   >   
   > Soundness is exactly why proof‑theoretic semantics matters here.   
   > When meaning is grounded in inferential structure and truth is anchored   
   > in an axiomatic base, only well‑founded expressions are admissible.   
      
   A system is useful only if admissibility is computable with a known   
   algorithm.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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