Back in August, I did a bit of reading on category theory. I’m now taking that up again with a group of graduate students. We’ve started working through Robert Goldblatt’s Topoi: The Categorical Analysis of Logic (an amazing bargain reprint from Dover). And this time I’m getting more of a feel for what is going on. Or at least, I have the comforting illusion of understanding — but it could all be shattered soon, when it is my turn to talk at the reading group next week, supposedly helping us through chapters 5 and 6.

Up to about half-way through chapter 3, Goldblatt proceeds at a pretty gentle pace; he then accelerates a bit alarmingly. Reading his first three chapters in parallel with the first six chapters of Steve Awodey’s Category Theory works well, however, if you have the time.

And is the effort worth it? Well, we’ll see (though my sense so far is that the answer should be very positive). But in the meantime, we’re certainly having fun …

It’s a familiar fact of academic life that you can go to hear a talk with great expectations of something arresting from someone who you have read with admiration, and then be bored or even irritated by a banal recycling of half-baked ideas. Equally, you can dutifully turn out to a unpromising-seeming seminar, apparently remote from your interests, feeling for some reason that you really ought to be there — and you find yourself riveted and enthused.

So three cheers for Piers Bursill-Hall, who was talking at the clumsily named CUSPOMMS last Friday. “Descartes’s Earlier Epistemology in Natural Philosophy” wasn’t exactly a title to set me alight. In the event, his talk was wonderfully entertaining but also a highly illuminating lightening tour through ancient and Renaissance takes on the problem of the unreasonable effectiveness of mathematics in its application to the material world, and Descartes’s attempt to resolve the problem without committing himself to the theologically dangerous idea of mathematics as a direct route to reading the mind of God. Enthusiasm is always engaging, and Piers has it in spades. (You can get a glimpse of his style here.)

The photographer Steven Pyke has produced another set of photos of great and not-so-great living philosophers. The style is, as with his earlier set published as a book, dramatically black-and-white, distinctly pretentious — and so, of course, in some cases the portraits are hardly recognizable.

Pyke asks his sitters to describe ‘in fifty words of so their own idea of what philosophy means’. So what’s it all about then? Ruth Millikan gives a favourite quotation of mine from Sellars: ”The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term.” (I wonder how many students, at least this side of the Atlantic, read Sellars any more?)

Here are two other answers that chimed with me. David Papineau: “Some hold that the aim of philosophy is to construct theories that confirm everyday intuitions. What a dispiriting ambition. In my book, the best philosophy overturns common sense. Often, the impetus for change comes from outside philosophy, in the form of scientific or cultural innovation. The task of the philosopher is then to show how the new ideas reshape everyday thinking. Does this reduce philosophy to the status of a hand-maiden? Well, far better a hand-maiden of change than a lackey of the intellectual status quo.”

And Steve Stich: “The idea that philosophy could be kept apart from the sciences would have been dismissed out of hand by most of the great philosophers of the 17th and 18th centuries. But many contemporary philosophers believe they can practice their craft without knowing what is going on in the natural and social sciences. If facts are needed, they rely on their “intuition”, or they simply invent them. The results of philosophy done in this way are typically sterile and often silly. There are no proprietary philosophical questions that are worth answering, nor is there any productive philosophical method that does not engage the sciences. But there are lots of deeply important (and fascinating and frustrating) questions about minds, morals, language, culture and more. To make progress on them we need to use anything that science can tell us, and any method that works.”

I went this week to the Moral Sciences Club for the first time in a while. I don’t entirely know why, but I don’t find the format or atmosphere of MSC meetings at all congenial. But the speaker this week was one of our own grad students, Ben Colburn, who put up a terrific performance talking about the value of autonomy and the role of the state in promoting the autonomy of its citizens. And that’s a theme that mattered rather a lot to one of my heroes, Alexander Herzen. As it happens, at the moment my late-night (re)reading is his great My Life and Thoughts. (I have the four-volume translation of the whole thing, all 1800 pages of it. It is indeed a loose and baggy monster, but a wonderful read. I see there is a more sensible sized abridged version available these days, which looks a bargain.)

Then today Thierry Libert gave an informal talk at CUSPOMMS on positive set theory. I confess this was all news to me. I’m not sure I have a real grasp on what the resulting ‘filled out’ universe of sets is like, but I got intriguing glimpses. Something else, then, to add to list of things to chase up, given world enough and time …

By popular request, I’m continuing an informal lunchtime Mathematical Logic Reading Group with a number of grad students. This term, the plan is to do a ‘slow read’ of Gentzen’s two great papers on the consistency of arithmetic. But we started today with the lecture he wrote between the two papers, ‘The concept of infinity in mathematics’. This is short, very accessible, and gives a great sense of the conceptual problems that Gentzen sees as shaping his work. It is also very clearly sets out the headline news about the structure of his (first) consistency proof and about its supposed finitist/constructivist credentials.

The lecture has its shortcomings — there’s a general murkiness about the notion of a ‘constructivist’ view of infinity (why should a constructivist view of sets in the sense of the paradox-busting idea of a hiearchy in which sets at higher levels are formed from sets already constructed at lower levels go along with a constructivist rejection of excluded middle at the level of classical analysis?). But still it is wonderful, thought-provoking stuff.

I was moved to try editing the piece on Gentzen on Wikipedia in very modest ways (e.g. adding that he was Hilbert’s assistant, which you might have thought was a rather central fact about his intellectual trajectory). But twice my efforts were removed. And I wonder if that was because I’d over-written the claim that he was imprisoned after the war “due to his Nazi loyalties” (I’d put something less specific, but more detailed, i.e. the story as told by Szabo in his introduction to the Collected Papers). Is it true about Gentzen having Nazi sympathies? Regrettably it seems so. Discovering this was really rather depressing, as I’ve belatedly become a great admirer of Gentzen.

One of my Christmas presents was Renée Fleming’s Homage: The Age of the Diva. It is luxurious, wonderful, singing, with some of the arias quite unknown to me (and I’d have thought to many opera fans). A few of Fleming’s interpretations are perhaps a bit over the top — there is a stunningly sustained note near the end of “Vissi d’arte” which is awesome but … Though it certainly does make the hairs stand up on the back of your neck, so let’s not get too purist!

The CD insert booklet has a little about Fleming’s great predecessors in this repertoire. One name stood out for me. For my mother has a copy of Kobbé’s Complete Opera Book, given her as a girl: the evocative black and white photographs include a publicity photo of the Moravian soprano Maria Jeritza in her costume as Turandot. That picture made a deep impression on me when I was small! Jeritza was one of Puccini’s favourite singers; but I’ve only ever heard short clips of her voice. I feel an internet search coming on …