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 2026-07-01 12:01, olcott wrote: > On 7/1/2026 12:33 PM, dbush wrote: >> On 7/1/2026 10:40 AM, olcott wrote: >>> The truth value of (∀ x, S(x) ≠ x) does not exist in Q. >> >> In your own words, what does it mean for the truth value of statement >> to not exist in a formal system? >> > > The same thing as: "cats are animals" expressed in > English has no English meaning in Chinese. > > Until "cats are animals" is translated into Chinese > it is just random gibberish that has no meaning or > truth value in Chinese. But ∀ x, S(x) ≠ x *isn't* random gibberish in Q. It is a well-formed expression of Q that has a well-defined meaning. It just happens to be unprovable. If it were random gibberish no one would have entertained the question of whether it could or could not be proven in Q. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.