Suppose per hypothesis that, tomorrow, "p & ~p" becomes true. One response is to reject the hypothesis. That is, to say that such a scenario is impossible and thus cannot obtain. Another response is to change the rules of logic to accommodate the scenario. — Andrew M
Can you give an example of ostensive talk that doesn't assume non-trivialism? — Andrew M
I do believe we were created but it should be noted if you roll a million sided die one million times trying to roll a 566 you will almost definitely roll a 566. This was pointed out in the book "a brief history of time" by Stephen Hawkings. — christian2017
In turn, accepting inconsistency seems to take one out of the bounds of meaningful language. — Andrew M
No, we would just look for ways to model the world that avoided inconsistency. — Andrew M
As long as P does not change, then Q will keep necessarily following. — alcontali
Free will is impossible with or without determinism and it's not circular reasoning ... it's a basic argument. Namely:
(1) Ultimately, to control your actions you have to control your fundamental nature.
(2) But you can't control your fundamental nature.
(3) So, ultimately, you can't control your actions.
This is true with or without determinism. — luckswallowsall
So would you say that you're choosing to believe the principle of noncontradiction, for example, where you could just as easily choose to believe the opposite? — Terrapin Station
The whole notion of "free reasoning" seems rather odd. That doesn't seem to mesh with the logical notions of validity, soundness, implication, etc. We don't choose what follows logically. — Terrapin Station
Aside from the problem of reifying abstractions and positing some questionable definitions there, you don't actually present any sort of argument as to why something can't "come from nothing." — Terrapin Station
If your point is only that this sentence can't be represented within classical logic, then duh. — Srap Tasmaner
So you're thinking that since you have, in essence, "[the Liar] & P" as your conjunction, we'll be unable to construct a truth table because the first conjunct is not truth-apt. True. — Srap Tasmaner
They're not. Whether you want to say "all statements are false" is false or "all statements are false" is neither true nor false, it is still the case that "all statements are false" isn't true and "at least one statement is true" is true. — Michael
Because ∀x(Sx→Fx) and ∀x(Sx∧Fx) don't say the same thing. — Srap Tasmaner
So not having a truth value is the third option. If we have the conjunction p ∧ q and if p is false and q doesn't have a truth value then the conjunction as a whole is false. — Michael
As I mentioned in a private message, I'm not entirely sure this step holds. What is the reference of "this" above? If it is "this statement is false" (taking it to have small scope), then your proposed rule would take us from "All statements are false" to ""This statement is false" is false". But the latter one is false, not truth-valueless. So the whole conjunction is false. — Nagase
University logic says you did not prove anything. Your statements are meaningless. — Meta
So you're saying S can't be false because S', the equivalent statement, can't be false because of the "S is false" part. — TheMadFool