In this episode, we’re joined by Daniel Sutherland, Associate Professor of Philosophy at the University of Illinois at Chicago. Click here to listen to our conversation with him.
In this technological age, most of our day-to-day tasks involve numbers and arithmetic. And yet, it can be difficult to say what a number is. Consider the number 3. In the room where I’m sitting, there are three bottles of detergent. But what about the number three itself? Where is that? On the shelf, where the bottles themselves are? Is the number three itself sitting here in the room, next to me? That seems like kind of a strange thing to say. So maybe it isn’t anywhere. But how could there be something that isn’t anywhere? Isn’t everything in our lives located somewhere? Sheesh. Ok, I give up. I guess there isn’t any such thing as the number three. But wait a minute–if numbers aren’t real, then what exactly was I doing all those years in math class?! It certainly seemed like I was hard at work, solving problems that ought to be taken seriously.
And that’s just the tip of the iceberg. We might also wonder how it’s possible to learn arithmetic. It’s clear enough how we learn about observable, physical facts: I can learn that fire is hot by trying to touch it. But how do I learn that 2 + 2 = 4? If the number 2 isn’t located anywhere, then I couldn’t have observed it. No one could have. But isn’t everything I learn based on observation? Isn’t it either something I observed myself, or something that someone else observed?
Daniel Sutherland takes us through a wide variety of answers you might give to these questions, and talks about the trade-off between telling a plausible story about what numbers are and telling a plausible story about how we learn arithmetic.