An astronomer, a physicist, and a mathematician...

...are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, "how odd. Scottish sheep are black."

"No, no, no!" says the physicist. "Only some Scottish sheep are black."

The mathematician rolls his eyes at his companions' muddled thinking and says, "in Scotland, there is at least one sheep, at least one side of which appears to be black from here."

There is danger in inductive thinking, as even Hume acknowledged.

I've been reading up on epistemology for my MLA class's initial foray into the philosophy of mathematics: Bacon, Hume, Descartes, Kant, and Popper...and of course Lakatos! We're going to get in pretty deep. For good measure we'll prove Euler's formula for polyhedra and try to understand what's so unsettling about the Law of Excluded Middle, the Axiom of Choice, and the proof of the Four Color Theorem.

You know you want to join us!