Monday, March 27, 2006

Edinburgh: Gödel, Raphael, ...

In a world of such ready e-communication, where people put work-in-progress online, where there are terrific discussion forums like FOM, not to mention blogs and the like, I do wonder about the value of so many conferences. I'm just back from one in Edinburgh on Truth and Proof: Gödel and the Foundations of Mathematics. The first conference I'd travelled to for some time, and to be honest I wasn't really very encouraged to repeat the experience soon, good though it was to put some faces to some familiar names. In the event, only two papers were directly on Gödel, one by Richard Zach (based on the draft paper which you can read here), the other by Panu Raatikainen (based on his paper which you can read here): both interesting pieces, particularly Richard's, but I had read them long since. Oh well, ...

But Edinburgh of course was quite wonderful, not least because I got to the National Gallery of Scotland more than once. (And a happy discovery since: you can get some impression of most of their major pictures on-line, as e.g. here or here.)

Saturday, March 18, 2006

A spell broken?

Out last night to hear Dan Dennett lecture, talking about his new book Breaking the Spell. A pretty terrific lecture. But the book is, in a word, disappointing. Which is not to deny that it's full of intriguing insights and illuminating suggestions about e.g. the possible evolutionary sources of dispositions to religious belief. But the structure of the book is surely a little too meandering (I found the first 100 pages dragged), the writing too allusive, to get through to the wide audience he is aiming for. I can see why Dennett often pulls his punches. Full frontal assaults on the frankly dotty aspects of mainstream religious belief-systems would just produce an unthinkingly hostile response, while the cumulative effect of jokes, analogies, biological speculation, just-so stories, reminders of what we all know (e.g. about the variability of religious beliefs), etc., might just get under the defences of some of those he wants to reach, and give them serious pause for thought. I hope so. But the pace isn't zestful enough, the points not pressed hard enough and clearly enough to really have the impact Dennett wants. In fact, I suspect he should have written two books: a punchier, shorter, less complex book for his desired wider audience and a more fact-strewn, more analytically complex book for those who want the whole story as Dennett currently sees it.

But we'll see. And certainly, I'm all for his spell-breaking project (the spell he wants to release us from is the idea that we shouldn't treat religion as a natural human phenomenon with its own biological rationale). Dennett is dead right that we can hardly overestimate the importance of understanding more about religion as a natural phenomenon.

Friday, March 10, 2006

To begin ... a Gödel talk at CUSPOMMS

To blog or not to blog? I'm in two minds. But why not just dive in and see how it goes?

Today was my second outing this academic year to talk to non-philosophers in Cambridge about Gödel, incompleteness and the like. The first time was at a meeting of the Trinity Math. Society. Rather staggeringly, there were more than eighty people there. Perhaps not a brilliantly judged talk, but I did have good fun e.g. telling them about Goodstein's Theorem. (Having a lot of bright mathmos getting the point and smiling at the cheek of the Goodstein proof made a nice change.)

Today's outing was to give a talk at CMS to the slightly unfortunately named CUSPOMMS. A very mixed audience, we meet there approximately fortnightly for talks on the philosophy of mathematics, broadly construed. Rather perversely, I suppose, there was less philosophy than in the Trinity talk. In the event, I was explaining one pretty way of proving (a version of) Gödel's First Theorem without explicitly constructing a Gödel sentence that codes up 'I am unprovable'. The point of doing this is to counteract that familiar tendency to think that the Gödelian result must be fishy because it depends on something too close to the Liar paradox for comfort.

Paul Erdös had the fantasy of a Book in which God records the smartest and most elegant proofs of mathematical results (have a look at the terrific Proofs from the Book by Aigner, Hofmann and Ziegler). So I was aiming to outline one Book proof: a version of the talk can be downloaded here