AgustinRayo

Interesting question... I think they're linked for (at least!) three different reasons:

1. There is a certain kind of beauty that philosophy and math both share.

2. Mathematics gives rise to interesting philosophical questions. (How should we develop set theory after Russell's Paradox? How can we know about numbers if they are abstract?)

3. Philosophers -- like economists -- sometimes use mathematical tools to develop their ideas. (Much of my own work on the philosophy of mathematics, for example, is about thinking of how best to respond to a theorem that shows that there is a certain sense in which it is impossible to reduce mathematics to logic.)

I was always torn about whether to become a philosopher or a mathematician, and now that I'm a philosopher I often miss mathematics...

Hi holiday_bandit!

I fell in love with philosophy reading two classics: Plato's Apology and Descartes' Meditations.

Those aren't really about the sorts of things that Susanna and I teach, though. A wonderful book that is about the sorts of things I cover in Paradox and Infinity is Hofstadter's Gödel, Escher, Bach.

I also think that Logicomix is pretty cool...

Dear completely-ineffable,

I have much sympathy for what you're saying. Ideas that are motivated because of their "pleasant feeling of paradox" are usually obscure, and trading with obscurity is no way to do philosophy.

(Oxford philosopher Timothy Williamson has a memorable quote about this sort of thing. I can't remember exactly how it goes, but it's to do with philosophers who think the muddy river is deeper than the open pond because they're unable to see the bottom...)

The nice thing about Infinity and Gödel's Theorem is that they involve both beautiful mathematics and fertile philosophical terrain. And both the mathematics and the philosophy stand on their own: they don't have to be motivated by pleasant obscurity.

The mathematics is so beautiful that it doesn't have to be buttressed by philosophy. And the philosophy is interesting not because it gives rise to a "pleasant feeling of paradox", but because it sheds light on the foundations of our thinking about mathematics.

Gödel's Theorem, for example, is philosophically important because it teaches us that we cannot aspire to absolute certainty in mathematics. And that's important because it changes our conception of what mathematical knowledge is all about, not because it's pleasantly obscure.

Dear scmbradley,

Your question is also close to my heart. It's an issue I've thought about a lot, and that has sometimes made me uncomfortable.

I think it's a mistake to think that ideas are only valuable insofar as they have practical applications. Finding a cure for a deadly disease is valuable, but so is creating a wonderful piece of music or proving a beautiful theorem.

We live in a world which is filled with horrible problems, and it makes sense to work hard to find solutions. But that doesn't mean that the only thing we should do with our lives is work hard to find solutions to our problems. That would be a bit like spending one's entire life making money -- for one's self and for one's children -- without ever finding time for other kinds of fulfillment.

Imagine a world in which most of our practical problems have disappeared. What would you want to spend your life doing in that world? If you're like me, you'd like to have meaningful relationships, and you'd like to surround yourself by art, and mathematics and philosophy. So there is a certain sense in which those things are what matters most of all. If they don't seem urgent to us now it's because we have so many problems. But, then again, someone who is worried about money might easily forget that making money is not the only thing there is to life.

Dear tsarnicky,

You're not going to believe this, but as I started reading your post I was thinking "I'll respond by recommending Scott Aaronson's "Why philosophers should care about computational complexity"." But you know it already, and the sad truth is that I don't know of many other texts that do what you want.

My guess -- but it's only a guess -- is that we will continue to discover deep connections between math (including computer science) and philosophy. But I think it's hard to predict where they will come from.

A recent example of discipline jumping involves philosophy and linguistics. Ideas in pragmatics which were largely the work of philosophers suddenly hit the point in which they could be developed systematically, and have led to incredibly interesting work in linguistics.