XPost: sci.logic, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 1/24/2026 11:10 AM, Richard Damon wrote:   
   > On 1/24/26 10:44 AM, olcott wrote:   
   >> On 1/24/2026 8:51 AM, Richard Damon wrote:   
   >>> On 1/20/26 1:35 PM, 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.   
   >>>>>   
      
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