Wittgenstein conference
I'm attending a conference on Wittgenstein's Philosophy of Mathematics at the end of the week, and will report back on it next week. I've always been a little wary of reading much Wittgenstein for fear of being drawn too far into his world, without much assurance of intellectual profit. Mathematicians have generally not looked too kindly on his work. Saunders Mac Lane certainly didn't think too highly of it, as mentioned here on page 2 of this obituary, (see also his 'Mathematics: Form and Function'), but then Mac Lane was dismissive of much post-war philosophy of mathematics.
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I was really big on Wittgenstein in my senior year of college, before I went to grad school at MIT and started studying Heidegger, first with Rota and then with a gang of friends (the "Heidegger group - we'd meet every Friday night at Au Bon Pain).
As someone trying to wriggle out of the dead-end of Anglo-Saxon analytical philosophy, Wittgenstein inevitably talks about issues that touch on mathematical logic, like "what does it mean to follow a rule". But I don't think he was interested in "real mathematics", so I don't think his stuff is especially useful to mathematicians - unless they just happen to be grappling with the same issues he was... as I was, back then - but no longer.
I still have his Philosophical Investigations in my office. It's very strange to look at them now, when the problems that once gripped me most painfully seem completely dull and harmless.
He writes:
309. What is your aim in philosophy? - To shew the fly the way out of the fly-bottle.
But this suggests that once the fly is out, it has no need for this sort of philosophy anymore.
Yes, philosophy as a form of therapy. But did Heidegger influence your mathematics at all?
David wrote:
Yes, philosophy as a form of therapy. But did Heidegger influence your mathematics at all?
He influenced something much more basic: my life. Before reading his stuff I was stuck on a bunch of epistemological and ontological questions: "how can we know anything?", "what does it means to say something is good?", and so on. It was really quite agonizing. Somehow reading Heidegger got me unstuck.
(Not just Heidegger, but also Plato and the Presocratics. Heidegger kept telling everyone to go back and read the Greeks, and he came up with interesting ways to interpret the Greeks, which made them seem much less stuffy and idiotic than before. So, my whole gang of friends wound up reading Plato.)
This influenced my mathematics indirectly: once I calmed down about issues of philosophy, I became happier and made a lot more progress on mathematics.
I should emphasize that I no longer care much about Heidegger's philosophy. I don't even remember it in precise detail! But, reading it helped nudge me in good directions.
Rota was also very helpful. When I told him I wanted to go into a career in philosophy, he forcefully told me that this was a terrible idea. He said I should become a mathematician and do philosophy on the side. This was great advice - for me, that is.
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