It might be that by deducing “B” from “A” and “if A then B” we thereby deduce something false. But then either “A” or “if A then B” must have been false
This is key. I like to say that we play logic with a stacked deck. We’ve dealt all the aces to a few logical rules. This doesn’t mean that logic isn’t in some sense absolute, but it removes any whiff of theology that might be suspected to be attached.
Users of a language have to agree on the meanings of primitive words like ‘and’, ‘if’, ‘then’, or else they’re just ‘playing a different game’.
True, but there is more to being logical than just following linguistic convention. The philosophers’ classic “tonk” operator works like this: From A, one is licensed to infer “A tonk B”. From “A tonk B” one is licensed to infer B. Luckily for language users everywhere, there is no actual language with these conventions.
I agree but with some spin control.
This is key. I like to say that we play logic with a stacked deck. We’ve dealt all the aces to a few logical rules. This doesn’t mean that logic isn’t in some sense absolute, but it removes any whiff of theology that might be suspected to be attached.
True, but there is more to being logical than just following linguistic convention. The philosophers’ classic “tonk” operator works like this: From A, one is licensed to infer “A tonk B”. From “A tonk B” one is licensed to infer B. Luckily for language users everywhere, there is no actual language with these conventions.