Logic Matters

The word has got around quickly of tough times ahead for philosophy at KCL. Quoting the letter of vigorous protest from the UCL philosophy department, which you can read in full in the comments here,  ”Prof Shalom Lappin and Dr Wilfried Meyer-Viol are to face compulsory redundancy as of autumn 2010, and … Prof Charles Travis is to be forced into retirement contrary to the contract on which he was hired in 2005.” (See also Shalom Lappin’s statement here.)

Rumour also has it that the other members of the department have been told to reapply for their jobs, under threat of redundancy (whatever that exactly means).

These are pretty grim developments.

Not too surprising, though. In a long series of steps over the time during which I have been an academic, the accommodations between universities and their staff, and the myths we live by, have changed almost out of recognition. Once upon a time, it would have been more or less unthinkable for a university adminstration to act as precipitately as KCL seem to have done. These days, it happens more and more.

True, we used to be much less well paid. You almost never got promoted before trundling through all eighteen steps on the lecturer scale (there was indeed an “age/wage” scale). Very few got personal chairs. Research leave was a rarity in many universities. But, on the other hand, you were left alone to get on with your work as best you could. And in my experience, relatively few abused the great privilege (to be sure, people tended to publish much less, and care about their students more, but that looks a rather good thing, as we drown in the sea of not-good-not-bad articles and books). Tenure meant tenure (more or less). Short of “gross moral turpitude” it was exceedingly difficult to get sacked: and even when departments closed — say  by taking advantage of a spate of retirements —  the expectation was that remaining established staff would be redeployed somehow (maybe not ideally, but at least not thrown onto the scrap heap).

Since those more comfortable days a quarter of a century ago, we’ve taken the bribe of significantly better pay (for a start because of vastly better promotion prospects), at the cost of a different kind of university with different conceptions of what is proper and improper. And of course, the ambitious and successful tended not to resist the changes. They tended to like the bargain, took the money and thought that the downside — the insecurity, the vulnerability to managerial agendas — wouldn’t affect them.

But as we see in the developments in KCL, the world doesn’t actually work like that. Once the devil’s bargain has been made, the good can get shafted just as much as anyone.

You can follow developments on the Leiter blog, no doubt, and on Facebook. Also, do read Mary Beard’s piece, and the first comment below.

I’ve been distracted by various things (including preparing talks/lectures for my upcoming NZ trip): but at last it’s time to get back to thinking about Francesco Berto’s book.

The last chapter is called “Gödel versus Wittgenstein and the Paraconsistent Interpretation”. Which gives you an idea of how much Berto is taking on in this chapter. There’s the question of the interpretation of Wittgenstein’s prima facie point-missing remarks about the incompleteness theorem. Then what are we to make of Routley and Priest’s take on the message of the first theorem? And, ambitiously, there’s the claim that the “paraconsistent interpretation” throws light on, or can be seen as bring out strands in, Wittgenstein’s take on Gödel. Which is a lot to try to deal with in a bit over twenty pages.

And in fact I think I’ll pass over the discussion of Wittgenstein here. Berto himself acknowledges that his reading at best reflects some “intuitions at the core of Wittgenstein’s philosophy of mathematics”, and that it leads him to advocate “a strong revisionism with respect to classical logic and classical mathematics” — and such revisionism doesn’t sound too Wittgensteinian.

One quick remark though, which connects up with another line of discussion in this blog. Berto quotes some remarks of Wittgenstein’s on Hilbert, and endorses Wittgenstein’s supposed critique of Hilbert’s “metamathematics”. Berto summarizes Wittgenstein as emphasizing that “Hilbert’s metamathematics is, in fact, nothing but mathematics”. But that’s no critique of Hilbert — for it just reiterates what was surely Hilbert’s view too. The Hilbertian project is use finitarily “safe” mathematics to prove consistency results about theories considered as finite objects, and thereby remove the temptation to look for foundations for those theories outside mathematics (in logic, in intuition, or whatever): see here and here. Which rather suggests that Wittgenstein was as insensitive — shall we say? — in his readings (if any?) of Hilbert as he seems to have been in his readings of Gödel. And it suggests too that Berto, while leaning over backwards to try to find why he thinks is a charitable reading of Wittgenstein, is not extending the same courtesy to Hilbert.

But be that as it may: I’ll now set aside what else Berto says about Gödel,  and concentrate on the remarks about his “paraconsistent interpretation”. To be continued

There are slightly revised versions of the episodes on the First Incompleteness Theorem and the Diagonalization Lemma now online.

And there is a cheeringly short episode on The Second Theorem, newly added.

(As before, you can download the latest versions of earlier episodes here, as well as a composite PDF of all the episodes to date.)

Not my photo, I should add: but I couldn’t resist posting it here.

There’s a slightly extended version of the treatment of the First Incompleteness Theorem now online, with a short section added about the historically first First Theorem.

And newly added is an episode on The Diagonalization Lemma, also covering Rosser’s and Tarski’s Theorems.

(You can download the latest versions of earlier episodes here, as well as a composite PDF of all the episodes to date.)

I’ve one more chapter of Berto’s Gödel book to comment on here, which I’ll do very shortly, and I mean to get back to the rest of Franks’s The Autonomy of Mathematical Knowledge (I got rather stuck on Franks’s tussle with Herbrand: I think I’ll just have to skip over that — but watch this space).

Meanwhile I’ve started dipping into Conceptions of Philosophy, a newly published collection of lectures given to the Royal Institute of Philosophy on the nature of philosophy.

Most of the contributors are my generation or older. Is that because reflecting on what we’ve been idling our time away with, hopefully finding something positive to be said for it, is a game for us old lags? Maybe. But I have to report that, so far, I don’t recognize very many of my own concerns in these contributors’ descriptions of what they think philosophers are/should be up to. Perhaps that’s because — though I’ve comfortably enough spent my time tucked away in philosophy departments — I’m not really philosophically minded. Well, I’m not if philosophy involves e.g. arm-waving blether about the True and the Good (David Cooper) or ignorant balderdash about the nature of mathematics (Peter Hacker).

Actually, it seems here that age  tends to bring not wisdom but bollocks.