Re: The simple essence of Proof Theoretic Semantics
André G. Isaak <[email protected]>
| Newsgroups | sci.logic,comp.theory,sci.math,comp.ai.philosophy |
|---|---|
| Organization | Christians and Atheists United Against Creeping Agnosticism |
| Message-ID | <[email protected]> |
On 2026-06-30 16:42, olcott wrote: > On 6/30/2026 5:06 PM, André G. Isaak wrote: >> On 2026-06-30 15:56, olcott wrote: >>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>> On 2026-06-29 21:06, olcott wrote: >>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>> On 2026-06-29 20:42, olcott wrote: >>>> >>>>>>> Those are specific concrete examples of how >>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>> as Proof Theoretic Semantically incoherent. >>>>>> >>>>>> No, they are not. No author writing in the framework of proof- >>>>>> theoretic semantics has ever offered those examples or comparable >>>>>> examples or made any claims about 'rejecting expressions as proof >>>>>> theoretic semantically incoherent'. And there's nothing incoherent >>>>>> about the statement 'no number is equal to its successor' which is >>>>>> the example under discussion. >>>>>> >>>>>> André >>>>>> >>>>> >>>>> None-the-less what I have said remains completely true. >>>>> What I have spent 28 years reverse-engineering from first >>>>> principles is exactly that. That no one applied PTS >>>>> exactly that way before does not mean that it is not >>>>> exactly correct PTS. >>>> >>>> Unfortunately, your say so carries very little weight. >>>> >>>> Would you agree that there is a difference between a statement being >>>> false and a statement being meaningless? >>>> >>> >>> Of course and that is such a dumb question that I >>> ignored it. >> >> But your interpretation of PTS claims that there is no difference. You >> claim that unprovable statements are meaningless; but any false >> statement will be unprovable in a consistent logic. >> >> PA can prove that 2 + 3 = 5 >> PA can't prove that 2 + 3 ≠ 5 >> >> But the latter isn't meaningless, it's simply false. >> > > If no connection exists between an expression E > (or its negation ~E) and the axioms of formal > system F then E is undefined in F. So now you are adding 'or its negation' to your position (something not present in your earlier presentations). Can you provide a reference to a single author writing in PTS who makes such a claim? And does 'undefined' differ from your earlier term 'meaningless'? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.