Philosophy of mathematics, also disappearing over the horizon?

Long ago, I posted a piece here under the mournful title “Logic disappearing over the horizon ….”.

I’ve just had an invitation to give a talk at the University of X, a distinguished place, with a philosophy graduate community of about fifty (according to their website). So I checked out how much logic/phil maths is going on, what I could reasonably take as given. Zilch. Apart from a first year course perhaps approaching the level of my intro logic book, nothing at all, as far as I can tell. Which leaves me a bit bereft of anything to go to talk about. But more to the point, it means that for students at X a central swathe of the work of lasting value from the last hundred years has disappeared over the horizon. Which is, shall we say, a pity.

My sense is that this is happening more and more in UK universities. I’d be delighted to learn that I’m wrong.

There was some discussion on the blog at the time, not very cheering. And my current sense is that the situation is getting worse and worse. How many logic-orientated posts in philosophy departments have been advertised and filled in the UK in the last dozen years? Very few, as far as I know.

And things are just as grim, if not more so, with the philosophy of mathematics. Here is Jeremy Avigad, in a recent essay which I’ve just noticed:

A recent analysis of tenure-track positions advertised in Jobs for Philosophers in the 2021–2022 academic year doesn’t even mention philosophy of mathematics in its categorization. Digging into the data shows that the phrase “philosophy of mathematics” occurs in only three of the 201 advertisements, in each case listed among multiple areas of potential interest. Surely this is an indication that the field is no longer viewed as important. It is sad that a discipline that was so central to the philosophical tradition from ancient times to the middle of the twentieth century now barely registers a pulse.

An Avigad now would, it seems, have a pretty hard time getting an academic post in philosophy. Sad indeed.

Is it always the fate of those in their declining years to think important bits of their world are falling apart? Probably so. But we’re not always wrong to thing so ….

5 thoughts on “Philosophy of mathematics, also disappearing over the horizon?”

      1. I see. I was particularly taken aback by Ananyo’s claim (apparently backed by von Plato) that Gödel stole the idea of arithmetization from von Neumann (of course, things seem to be more complicated: from what I gathered, Gödel’s original proof, remarkably, did not make use of arithmetization, and von Neumann suggested that it could be done, but did not give an implementation—that was supplied by Gödel). In fact, given that this is such an integral part of the theorem now, this seems to me more significant than the alleged fact that he blocked von Neumann’s publication of the second theorem…

  1. Unfortunately, that recent essay from Jeremy Avigad is the one written in the style of the Raymond Carver short story “What We Talk About When We Talk About Love”, and so (in addition to being rather annoying to read) it doesn’t explain some things as much as an academic essay normally would.

    (It is a great relief to reach the appendix where he stops imitating Carver and finally names the “guy I know who writes about mathematics”: it’s Jeremy Gray, author of Plato’s Ghost: The Modernist Transformation of Mathematics and of books such as The Real and the Complex: A History of Analysis in the 19th Century.)

    I am wondering especially about this:

    But let me temper this doom and gloom with some more positive notes. First, colleagues assure me that the outlook for philosophy of mathematics is more optimistic in Europe, and I would not be surprised to learn that other communities have also managed to escape the gravity of the Anglo-American analytic tradition.

    What is that about? Would Alain Badiou’s Being and Event and its use of set-theoretic forcing be an example? Talk of European philosophy that “managed to escape the gravity of the Anglo-American analytic tradition” brings to mind the sorts of things that feature in Sokal and Bricmont’s Fashionable Nonsense, a.k.a. Intellectual Impostures. This is not to disparage Badiou (who’s understanding of set theory seems pretty good) or to endorse Sokol’s tactics (which are often questionable). The combination of “Europe” and a dig at analytic philosophy does make me wonder, though, whether ‘fashionable nonsense’ might be involved.

    Still, and setting the ‘Carver’ style aside, there are some things about the essay I like, such as its dismissal of Benacerraf’s problem. It does seem that (some) philosophers “can’t get over it”, and some mathematicians too, when they see how it can be turned against certain parts of mathematics (chiefly set theory).

    And even if Avigad would have a pretty hard time getting an academic post in philosophy, I don’t think he’d have much trouble getting one in computer science or, probably, mathematics. How much does philosophy of maths have to be in philosophy departments anyway?

    I thought that even more about “Logic disappearing over the horizon”. In my experience (which may be atypical), there wasn’t much focus on logic in philosophy departments, but there was plenty of interest in logic in maths, computing, AI, and Cognitive Science.

    1. I should have said, perhaps, that I wasn’t recommending Avigad’s essay for any its content, other than the report of depressing statistics. Though I imagine that when Avigad was a bit optimistic about phil maths in Europe he might have had in mind e.g. the Munich Center for Mathematical Philosophy and the Institute for Logic, Language and Computation at Amsterdam. Though I’m baffled by what he means by “escaping the gravity of the Anglo-American analytic tradition” if it isn’t a nod to fashionable nonsense.

      “How much does philosophy of maths have to be in philosophy departments anyway?” Well, I do think the answer is more-than-none! Those non-philosophers who have a go, left to themselves, tend to fall into all sorts of arm-waving exaggerations (to be friendly), as you yourself have in the past noted about some category theorists!

      And of course I agree that “there wasn’t much focus on logic in [UK] philosophy departments” in many cases,“but there was plenty of interest in logic in maths, computing, AI, and Cognitive Science.” But again, my thought was that even some philosophy departments which really cared about logic in the past apparently don’t any more: and in too many places philosophy students just don’t get a chance to pick up much logic at all. A whole area, which was supposedly one of the lasting legacies of twentieth century analytic philosophy, becomes a closed book.

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top