What Are Numbers? | Michael Harris

What Is X?

What does it mean for a number to exist? In the philosophy of mathematics, there are two general camps when it comes to numbers: there are the Platonists—or the “realists”—who think numbers somehow really exist, and there are the constructivists, who think they’re the products of mathematical activity. In this episode of “What Is X?” Justin invites on the Columbia University mathematician Michael Harris to try to figure out what the ontological status of numbers is. Are they the ultimate abstractions, or is there something "more real" to numbers than even our physical world? If we ran into them in outer space, would aliens understand numbers as we've conceived of them here on earth? Over the course of the hour, you'll get to listen in on: a discussion of the relationship between numbers and culture, a true story that sounds like a joke about three mathematicians who walk into a bar, and a back-and-forth about why certain philosophers are obsessed with mathematics (hint: its unmediated access to truth).