Re: William T. Parry gets rid of Disjunction introduction
André G. Isaak <[email protected]>
| Newsgroups | sci.logic,comp.theory,comp.ai.philosophy,sci.math |
|---|---|
| Organization | Christians and Atheists United Against Creeping Agnosticism |
| Message-ID | <[email protected]> |
On 2026-07-07 15:30, olcott wrote: > On 7/7/2026 4:24 PM, André G. Isaak wrote: >> On 2026-07-07 15:13, olcott wrote: >>> On 7/7/2026 3:08 PM, André G. Isaak wrote: >>>> On 2026-07-07 13:53, olcott wrote: >>>>> On 7/7/2026 2:29 PM, André G. Isaak wrote: >>>>>> On 2026-07-07 13:19, olcott wrote: >>>> >>>>>>> To do with with minimal simplicity the axioms of >>>>>>> PA are construed as semantic entailment thus when >>>>>>> there is no sequence of inference steps between G >>>>>>> and PA then G is Kripke undefined in PA. >>>>>> >>>>>> So why don't you illustrate this with an actual proof? >>>>>> >>>>>> André >>>>>> >>>>> >>>>> The principle is simply whenever X cannot be proven >>>>> in F then X is ungrounded in the atomic base F. Even >>>>> diagonalization makes to attempt at actual proof. >>>> >>>> I can't make heads or tails of that. >>>> >>> >>> The actual proof in meta-math that G cannot be >>> proved in PA is itself not any sequence of inference >>> steps. It simply uses a version of the proof that >>> Cantor use to show that reals are not countable. >> >> ??? >> >> Cantor's proof absolutely contained inference steps, as did Gödels. I >> don't think you actually know what you're talking about. >> >>>> If you can't illustrate your alleged system with a simple proof, >>>> then I have no choice but to conclude that it is as ill-defined to >>>> you as it is to me. >>>> >>>> André >>>> >>> >>> 2 + 3 = 4 in PA cannot be proven because >>> s(s(0)) + s(s(s(0))) != s(s(s(s(0)))) >> >> I asked you to provide an example of a proof which illustrates what >> you mean by "semantic entailments encoded syntactically in the >> language". I didn't ask for an example of something which cannot be >> proven. >> >> André >> > > PTS simply declares by fiat that syntactic inference steps > are semantic steps. I actually mean natural language semantic > inference in the CycL programming language. This is the place > where nothing follows form a contradiction is most easily seen. So basically you're saying that you are incapable of constructing even a simple mathematical proof. Gödel is about theories of arithmetic. CycL is not. If you can't construct proofs in an arithmetic framework you really have no business talking about Gödel. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.