XPost: sci.math, comp.theory, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   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   
   only because back then proof theoretic semantics did   
   not exist.   
      
   No one ever understood how a truth predicate could be   
   directly added to PA. Now with Proof theoretic semantics   
   and the Haskell Curry notion of true in the system it   
   is easy to directly define a truth predicate  PA.   
      
   Truth in the standard model is meta‑mathematical.   
      
   [continued in next message]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)