4 Quotes by Dan Cryan

I see nobody on the road,” said Alice. “I only wish I had such eyes,” the King remarked in a fretful tone. “To be able to see Nobody!

Gottlob Frege’s Begriffsschrift.

Russell’s point is that if the set is a member of itself, then by definition it can’t be a member of itself. But if it is not a member of itself, then it is a member of itself. So it is both a member of itself and not a member of itself. And that is a contradiction. This glaring mistake, allegedly, left Frege a broken man.

The great advantage of the reductio method is that it allows us to tell if a statement is true, even if we do not know how to construct a proof for it. We can tell a statement is true by showing that its negation leads to a contradiction.