The most popular resolution to Zeno's paradoxes is to say, "Calculus solves it!" But, as I've written and spoken about before, the logic of calculus might be dubious. Can we really complete an infinite series?

My guest this week is Dr. Michael Huemer, who has recently written a book called Approaching Infinity, where he claims that the modern theory of infinities do need to be revised - that calculus does not solve Zeno's paradoxes - and that we have to distinguish between completable and non-completable infinities.

Though Dr. Huemer and I disagree on the metaphysics of mathematics, and I have an even more radical position on infinities, we agree that more work needs to be done to place modern mathematics onto sounder footing.