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Friday, March 10, 2006

Mathematicians reading philosophy

In the comments to this post, John Baez talks about reading Wittgenstein and then later Heidegger. I'd be very interested to know which philosophers other mathematicians/mathematical physicists are glad they have read, even if not recently.


Peter Woit said...

I've enjoyed reading lots of philosophers over the years, but the one that has had a bit of influence on how I think about science and its relation to philosophy is Quine. Haven't really found a canonical philosopher whose views on mathematics are especially congenial.

March 10, 2006 4:53 PM  
Kea said...

For physics, I like Hegel best, though I confess to having often resorted to later analyses of his writing.

March 11, 2006 1:18 AM  
Tom Leinster said...

I went to an excellent course on Buddhist philosophy. At the time a lot of it seemed to resonate with my mathematical experience (although I wondered whether that just meant I was filtering *everything* through my mathematical experience).

I was interested in what John wrote - "once I calmed down about issues of philosophy, I became happier and made a lot more progress on mathematics" - and something in Joyal's interview about how some mathematicians are driven by anger, or (perhaps more commonly) by the competitive urge.

For sheer pleasure, the philosopher I've most enjoyed reading is Russell, though I wouldn't say he's had any effect on the maths I do.

March 11, 2006 12:18 PM  
Sid said...

As a math student (just finishing my undergrad degree and going on to grad school) I can say with confidence that it was reading Kant that set me down this road. Though I don't buy much of his metaphysics, when I first came across his central (metaphysical) question "How is a priori knowledge possible?", it really lit me up, and I started trying to understand the canonical example of a priori knowledge to get some insight. Of course, once I started to get into the math, there was no hope for me anymore...

March 13, 2006 4:55 AM  
John Baez said...

I might as well list, in chronological order, some of the philosophers who had the biggest impact on me.

In early high school I was a logical positivist of the worst sort, into Ayer and Russell.

As a junior in high school (that's age 16, in case you're not from the US and don't know this system) I went to a Telluride Association Summer Program on social philosophy - I remember being scared that I didn't know anything about "social philosophy", but none of the other kids did, either. We read Mill, Marx, Freud and Nietzsche. Nietzsche made the biggest impression on me - my logical positivism evolved into a kind of nihilism. I was fairly miserable.

In college I got into Quine and Wittgenstein, who didn't make me feel better.

In grad school I got into Heidegger, thanks to Gian-Carlo Rota, and thereby into Plato and the Presocratics.

In parallel to all this I've always been interested in Taoism and Buddhism, thanks in part to my mother. So, I always kept reading the Tao Te Ching, the "Inner Chapters" of Chuang-Tse, and miscellaneous Buddhist writings, especially Suzuki and a bunch of Zen stuff.

I also read a bunch of psychologists, especially crazy ones like Jung and R. D. Lang.

Somehow around the end of grad school I became sufficiently at home in the world that I stopped feeling the need to think much about philosophy. Falling in love probably had a lot to do with it, but it's not clear that I could have done that without getting my act together a little beforehand. Whatever the cause, the Taoism, the Plato, the Zen Buddhism and the Heidegger blended into something very clear and simple, which I would be hard pressed to explain.

This is, of course, an oversimplified and parodistic sketch of a process that seemed very serious at the time.

Whatever philosophical urges I have these days, I usually express via math and physics.

March 13, 2006 7:23 AM  
Fabien Besnard said...

JB said
>I became sufficiently at home in the world that I stopped feeling the need to think much about philosophy

Perhaps it's time to read Spinoza ?

March 14, 2006 9:17 PM  
John Baez said...

Fabien Besnard wrote:

Perhaps it's time to read Spinoza?

Funny, that's what Carlo Rovelli recently suggested too. I'd glanced at Spinoza's Ethics once, but the superficially precise but actually fuzzy nature of his "deductive" approach to philosophy instantly repelled me. What are we supposed to make of "axioms" like

Everything which exists, exists either in itself or in something else.


That which cannot be conceived through anything else must be conceived through itself.

I'm not such an inborn mathematician as to forbid vagueness in philosophical discourse - in fact I think it's essential! So, I don't mind it when philosophers say things like the above sentences. But at the time, the combination of ordinary-language vagueness and the attempt to "prove" philosophical points by deducing them from "axioms" a la Euclid struck me as painfully wrongheaded.

Rovelli, however, told me that Spinoza has given a nice explanation of how free will is possible in a deterministic universe - almost the same explanation that I favor, in fact.

So, maybe now I could loosen up, laugh off Spinoza's "deductive method", and focus on whatever interesting things he has to say.

March 19, 2006 8:15 PM  
Fabien Besnard said...

I understand your reaction John. But you should also remember the vagueness of Euclid's definition of a point, straight line etc... The level of mathematical rigor was different at the time. Spinoza also builded on theological concepts which were mainstream at the time but are now completely forgotten, and make him difficult to understand at times. But that's worth the effort. The system he builds has a real coherence and beauty.
>So, maybe now I could loosen up, >laugh off Spinoza's "deductive >method", and focus on whatever >interesting things he has to say.
I think so. There is also the philosophico-political treatise and the correspondence which are not written in this style you don't like.

March 20, 2006 9:07 AM  
JJL said...

I've always been a fan of C.S. Peirce. However, most of the philosophy I read is second-hand--surveys of an area rather than the contributions of an individual. The Mathematical Experience by Davis and Hersch cemented my decision to go to grad. school, and was my first introduction to the philosophy (and history) of math. Since then I've read a number of books on the phil. of math., sci., and lang., but haven't found myself overly attracted to any one person's writings. Quine and Russell can both be fun to read but don't speak to me more than others.

April 12, 2006 8:28 PM  

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