XPost: sci.math, comp.theory, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 1/21/2026 3:03 AM, Mikko wrote:   
   > On 20/01/2026 20:35, olcott wrote:   
   >> On 1/20/2026 3:58 AM, Mikko wrote:   
   >>> 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'.   
   >>   
   >> True in the standard model of arithmetic using meta-math   
   >> has always been misconstrued as true  arithmetic   
   >   
      
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