From: polcott333@gmail.com   
      
   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.   
      
   Naive set theory allowed unrestricted comprehension;   
   ZF restricts it and adds Foundation. That’s exactly   
   the same structural move I’m making.   
      
   Classical semantics treats every formula as a   
   truth‑bearer and gets Gödel’s paradox. Proof‑theoretic   
   semantics restricts truth‑bearers to what PA can classify   
   and the paradox disappears.   
      
   Calling ZF “another theory” instead of a “redefinition”   
   doesn’t change the fact that it avoids the paradox by   
   changing the foundations.   
      
   >>>> Proof theoretic semantics redefines formal systems such that   
   >>>> Incompleteness cannot arise. Gödel did not do this himself because   
   >>>> Proof theoretic semantics did not exist at the time.   
   >>>   
   >>> Gödel did not do that because his topic was Peano arithmetic and its   
   >>> extensions, and more generally ordinary logic.   
   >>>   
   >>> Can you can you prove anyting analogous to Gödel's completeness   
   >>> theorem for your "Proof theoretic semantics"?   
   >   
   > Note that the question is not answered (or otherwise addressed) below.   
   >   
      
   No, there is no model‑theoretic completeness theorem here,   
   because there is no model‑theoretic semantics.   
      
      
   [continued in next message]   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)