XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   On 13/01/2026 16:31, olcott wrote:   
   > On 1/13/2026 3:13 AM, Mikko wrote:   
   >> On 12/01/2026 16:32, olcott wrote:   
   >>> On 1/12/2026 4:47 AM, Mikko wrote:   
   >>>> On 11/01/2026 16:24, Tristan Wibberley wrote:   
   >>>>> On 11/01/2026 10:13, Mikko wrote:   
   >>>>>> On 10/01/2026 17:47, olcott wrote:   
   >>>>>>> On 1/10/2026 2:23 AM, Mikko wrote:   
   >>>>>   
   >>>>>>>> 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.   
   >>>>>>   
   >>>>>> You can't determine whether the required result is computable before   
   >>>>>> you have the requirement.   
   >>>>>   
   >>>>>   
   >>>>> Right, it is /in/ scope for computer science... for the /ology/.   
   >>>>> Olcott   
   >>>>> here uses "computation" to refer to the practice. You give the   
   >>>>> requirement to the /ologist/ who correctly decides that it is not for   
   >>>>> computation because it is not computable.   
   >>>>>   
   >>>>> You two so often violently agree; I find it warming to the heart.   
   >>>>   
   >>>> For pracitcal programming it is useful to know what is known to be   
   >>>> uncomputable in order to avoid wasting time in attemlpts to do the   
   >>>> impossible.   
   >>>   
   >>> It f-cking nuts that after more than 2000 years   
   >>> people still don't understand that self-contradictory   
   >>> expressions: "This sentence is not true" have no   
   >>> truth value. A smart high school student should have   
   >>> figured this out 2000 years ago.   
   >>   
   >> Irrelevant. For practical programming that question needn't be answered.   
   >   
   > The halting problem counter-example input is anchored   
   > in the Liar Paradox. Proof Theoretic Semantics rejects   
   > those two and Gödel's incompleteness and a bunch more   
   > as merely non-well-founded inputs.   
      
   For every Turing machine the halting problem counter-example provably   
   exists. From the existence of the counter-example it is provable that   
   the first Turing machine is not a halting decider. With universal   
   quationfication follows that no Turing machine is a halting decider.   
      
   Besides, there are other ways to prove that halting is not Turing   
   decidable.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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