Archive for February, 2008

Mathematical Thought and Its Objects

Friday, February 8th, 2008

I’ve only just noticed that Charles Parsons’ long awaited book Mathematical Thought and Its Objects is due out this month here (and indeed has been out a few weeks in the US). From the CUP website:

Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a ‘nature’ than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.

Obviously going to be a must-read.

Seminar styles

Thursday, February 7th, 2008

I put some quick notes together for myself for the Hodges reading group yesterday: I’ll work away at them again in the next few days (and certainly before the next seminar), and post the resulting after-the-event handout here, for it’s worth [Later, this might take longer than I wanted]. I must say that the Hodges book is turning out to be harder going than I had imagined: he is capable elsewhere of writing about difficult stuff with verve and great clarity, but here things get a lot denser. I thought it might just be that my pure maths (group theory and the like) is rusty enough for me not to be getting enough out of some of the examples he gives: but then some mathmos have expressed similar views about his approachability.

A very noticeable difference in style is emerging between a logic reading group run for philosophers and one with a mixed group of philosophers, mathmos and compscis. Philosophers — ok, our friendly local lot — seem to be happy to share their ignorance, and take turns week-by-week to introduce a chapter or a paper, albeit fairly briefly, even if they make no pretence to really be on top of the stuff. And they will dive into the discussion, cheerfully asking for clarification, or trying out toy mini-examples, etc. Mathmos and compscis on the other hand — although personally a perfectly friendly bunch! — seem on the whole very reluctant to volunteer to have a bash at introducing a chapter, or indeed to say anything much after someone has given the intro. Which is a pity, as I learn a lot from the exchanges when they do happen.

Logical Options, 4

Sunday, February 3rd, 2008

For what they are worth, you can find my reading notes for next week’s seminar on Sections 2.5 and 2.6 of Logical Options here (they might help some students). Writing these notes has very much been displacement behaviour in the last day or two: I should really be preparing something on Ch. 4 of the Shorter Hodges for the model theory seminar this week, which I daftly promised to introduce. But heavens, that is not exactly an easy read. Gulp.

Three cheers for Andy Clark

Sunday, February 3rd, 2008

Thursday’s Routledge Lecture here was given by Andy Clark. I thought he did a terrific job for a lecture intended for an audience not just of philosophers. I don’t know if he is right or indeed if I fully understand what his position about the messiness of the mind comes to (and for once “I’m not sure I understand …” is not philosopher-speak for “I’m damned sure he is horribly confused …”). But I certainly think that he is concerned with a bunch of interesting issues, the kind of thing that is actually worth working on in the philosophy of mind — engaging hands-on with the sciences of the mind.

I always thought of my old intro book with Owen Jones, The Philosophy of Mind, as an exercise in getting out of the way the relatively uninteresting a priori arm-chair stuff, kicking into touch various bits of mystery-mongering, leaving the field clear to get on with the interesting stuff engaging with work in cognitive neuro-psychology, artificial intelligence and the like. To be sure, we no doubt didn’t get the a priori story dead right. But who really cares? We only need to get it, so to speak, right enough to enable us stop worrying that there might be mysterious obstacles in the way to a many-pronged empirically-informed assault on the interesting stuff. When I dip into the journals is a bit depressing to find in some areas epicycles of armchair reflection still being piled up by philosophers of mind. So three cheers for the likes of Andy Clark who remind us that it doesn’t have to be that way.