From: mikko.levanto@iki.fi   
      
   On 19/01/2026 17:03, olcott wrote:   
   > On 1/19/2026 2:19 AM, Mikko wrote:   
   >> On 18/01/2026 15:28, olcott wrote:   
   >>> On 1/18/2026 5:27 AM, Mikko wrote:   
   >>>> On 17/01/2026 16:47, olcott wrote:   
   >>>>> On 1/17/2026 3:53 AM, Mikko wrote:   
   >>>>>> On 16/01/2026 17:38, olcott wrote:   
   >>>>>>> On 1/16/2026 3:32 AM, Mikko wrote:   
   >>>>>>>> On 15/01/2026 22:30, olcott wrote:   
   >>>>>>>>> On 1/15/2026 3:34 AM, Mikko wrote:   
   >>>>>>>>>> On 14/01/2026 21:32, olcott wrote:   
   >>>>>>>>>>> On 1/14/2026 3:01 AM, Mikko wrote:   
   >>>>>>>>>>>> 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.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Not when using Proof Theoretic Semantics grounded   
   >>>>>>>>>>> in the specification language. In this case the   
   >>>>>>>>>>> pathological input is simply rejected as ungrounded.   
   >>>>>>>>>>   
   >>>>>>>>>> Then your "Proof Theoretic Semantics" is not useful for   
   >>>>>>>>>> discussion of   
   >>>>>>>>>> Turing machines. For every Turing machine a counter example   
   >>>>>>>>>> exists.   
   >>>>>>>>>> And so exists a Turing machine that writes the counter example   
   >>>>>>>>>> when   
   >>>>>>>>>> given a Turing machine as input.   
   >>>>>>>>>   
   >>>>>>>>> It is "not useful" in the same way that ZFC was   
   >>>>>>>>> "not useful" for addressing Russell's Paradox.   
   >>>>>>>>   
   >>>>>>>> ZF or ZFC is to some extent useful for addressing Russell's   
   >>>>>>>> paradox.   
   >>>>>>>> It is an example of a set theory where Russell's paradox is   
   >>>>>>>> avoided.   
   >>>>>>>> If your "Proof Theretic Semantics" cannot handle the existence of   
   >>>>>>>> a counter example for every Turing decider then it is not usefule   
   >>>>>>>> for those who work on practical problems of program correctness.   
   >>>>>>>   
   >>>>>>> Proof theoretic semantics addresses Gödel Incompleteness   
   >>>>>>> for PA in a way similar to the way that ZFC addresses   
   >>>>>>> Russell's Paradox in set theory.   
   >>>>>>   
   >>>>>> Not really the same way. Your "Proof theoretic semantics" redefines   
   >>>>>> truth and replaces the logic. ZFC is another theory using ordinary   
   >>>>>> logic. The problem with the naive set theory is that it is not   
   >>>>>> sound for any semantics.   
   >>>>>   
   >>>>> ZFC redefines set theory such that Russell's Paradox cannot arise.   
   >>>>   
   >>>> No, it does not. It is just another exammle of the generic concept   
   >>>> of set theory. Essentially the same as ZF but has one additional   
   >>>> postulate.   
   >>>   
   >>> ZFC redefines set theory such that Russell's Paradox cannot arise   
   >>> and the original set theory is now referred to as naive set theory.   
   >>   
   >> ZF and ZFC are not redefinitions. ZF is another theory. It can be   
   >> called a "set theory" because its structure is similar to Cnator's   
   >> original informal set theory. Cantor did not specify whther a set   
   >> must be well-founded but ZF specifies that it must. A set theory   
   >> were all sets are well-founded does not have Russell's paradox.   
   >   
   > ZF is a redefinition in the only sense that matters:   
   > it changes the foundational rules so that Russell’s   
   > paradox cannot arise.   
      
   The only sense that matters is: to give a new meaning to an exsisting   
   term. That is OK when the new meaning is only used in a context where   
   the old one does not make sense.   
      
   What you are trying is to give a new meaning to "true" but preted that   
   it still means 'true'.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)