"Why Medieval Logic Matters"

The three greatest centuries for logic were the 4th BC, the 14th AD, and the 19th AD. The philosopher interviewed here suggests that this order is not merely temporal but is also the order of importance, such that if we were to speak of the "two greatest centuries for logic" the 19th century would drop out.

Want to know why? Enjoy wrestling with a thorny paradox or two?
What truly deserves the title ‘paradox’ is the Knower paradox. Consider the proposition, ‘You don’t know this proposition’—call it U, say. Suppose you know U. Then U is true (one can only know truths), so you don’t know U. Contradiction, so (by reductio ad absurdum) you don’t know U. But that is what U says. So U is true, and moreover, you’ve just proved it’s true, so you know U. That really is a contradiction—we can prove both that you know U and that you don’t, that is, that U is both true and false. But surely that’s impossible!
Consider the solutions. Do you like the 14th century solution better than the contemporary ones?


Eric Blair said...

The proposition is false from the start because it doesn't actually propose anything. It's akin to 'how many angels can dance on the head of a pin"? sort of musing.

Rumsfeld actually said it best, I think.

There are the things we know.
There are the things we know we don't know.
Then there are the things we don't know that we don't know.

Ymar Sakar said...

Heard that before already.

Grim said...

Well, that's very roughly the medieval solution, Eric: the proposition is false, not because it isn't true, but because a statement of that sort can't be true. Thus, the paradox doesn't arise because we can declare a statement of that kind to be false from the get-go.

Ymar Sakar said...

Quantum mechanics and the eastern yin/yang deals with that paradox differently.