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 21:10, olcott wrote: > On 6/30/2026 10:02 PM, dbush wrote: >> What is was is a way to show more easily how you're wrong. That you >> claim that "no number is equal to its successor" is semantically >> invalid shows everyone that your ideas are worthless. >> > > This is more accurate: > The truth value of (∀ x, S(x) ≠ x) does not exist in Q. But as soon as you bring up truth values you're no longer talking about PTS which semantically divides expressions into 'provable' and 'not provable'. In truth-functional semantics, the law of the excluded middle dictates that ∀x, S(x) ≠ x must be either true or false. It's truth value might be unknown to us but there is a big difference between unknown and nonexistent. Within PTS there is absolutely no contradiction about claiming that ∀x, S(x) ≠ x is unprovable while at the same time claiming that its negation is unprovable, but that both are perfectly legitimate and meaningful expressions of Q. If you think otherwise, provide a reference to some author working in PTS who actually asserts something of this sort. I suspect you can't because this simply isn't what PTS claims. It's you imposing your own views on a system developed by others which you do not fully understand. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.