Year: 2010

Postcard from LAX

Even after two full days at the Getty, we were very tempted to spend a third there. But we were spending an arm and a leg on taxis, so we decided to try the Los Angeles County Museum of Art instead, which was within walking distance. Their collection is quite astonishing — from some terrific Dutch landscapes and three more Rembrandts, through twenty five Picassos, to some appalling kitsch by the egregious Jeff Koons. And turning a corner, there was that old philosophers’ favourite, Magritte’s La Trahison des images. Not, of course, a case where you get anything particular out of seeing the original, but a nice surprise all the same.

The galleries themselves are rather bleakly unwelcoming and unhelpful. It doesn’t seem to have occurred to the curators that you might welcome a bit more information than title, artist, country and date (or even that you might occasionally want to sit down). The comparison with the feel of the Getty couldn’t be more marked. But the collection is still very much worth a visit.

Style note #1. To get to the LACMA we walked through some back streets full of small houses. English half-timbered cottages, mini-castles (with battlements), miniature arts-and-crafts houses, mexican shacks, sea-side-bungalows, all jumbled together. The air of good-humoured individualism gone slightly mad was, however, rather spoilt by the little signs planted in the front gardens by the owners threatening armed response if you mess with them.

Style note #2. Once upon a time, as the galleries remind you, children were dressed like little adults. Nowadays, looking at our fellow visitors, most American men — at least when not at work — dress like big children (from the playshoes upwards). I wonder what that is all about?

Postcard from Los Angeles

Pissarro, Hermitage Garden
Hermitage Garden, Maison Rouge 1877, by Camille Pissarro

We’ve been in LA for two days now, stopping over en route to NZ. Or more exactly, we been visiting the Getty Museum for two days, pretty much from opening time to closing time. We’ve been bowled over.

The buildings, the setting, the views over the city to the sea, are breathtaking. For a collection put together relatively recently, there are some quite wonderful paintings on display (including Rembrandts and Titians). And there’s a simply fantastic, and very illuminating, special comparative exhibition of drawings by Rembrandt and his pupils.

But if we could smuggle just one picture home from the Getty, I think it would just have to be Pissarro’s moment of domestic peace in a summer garden.

There’s Something about Gödel, Ch. 12 (concluded)

I’d hoped to have time, before setting off for a “term” (i.e. half a semester) in New Zealand, to comment in a bit of detail on Berto’s discussion of the dialetheist riff on Gödel’s theorem. But that’s not going to happen. And since I’m not going to pack Berto’s book, I’m afraid — if I ever get round to commenting at length — it won’t be for nearly three months.

The trouble is, however, — and no doubt this is the reason I’ve not got round to doing the job before — I do find it jolly difficult to take dialetheism here seriously.

This isn’t to dismiss dialetheism out of hand, across the board. Perhaps there’s a just-so story to be told about how, when we add a minimalist truth-like predicate to a language without prior explicit semantic apparatus, the smoothest thing to do — all things considered — allows some extraordinary sentences containing this new predicate to then come out both “true” and “false”. So be it. But the dialetheist line on Gödel incompleteness, when the wraps are off, is committed to saying that there’s a number (an ordinary, common-or-garden, natural number) which both does and does not satisfy some primitive recursive condition (a complicated condition, to be sure, but still primitive recursive in an entirely straightforward way). Here’s a sketch of why, in my words.

Recall: the Routley/Priest suggestion is that our overall informal mathematics — the body of assumptions and deductive processes that mathematicians take take to lead to proofs that establish mathematical truth — should be susceptible to being regimented as a recursively axiomatized theory T (recursively, because negotiable by us limited humans). But T is consistent (because a body of truths) and includes enough arithmetic for Gödel’s theorem to apply. So, fixing on a scheme of Gödel-numbering, there is a Gödel sentence G, true if and only if unprovable-in-T, which is indeed unprovable-in-T, and hence true. In principle, we could spell out that informal reasoning for the truth of G in our all-embracing theory T which, by hypothesis, includes all informal mathematics. So there’s a T-proof of G, which will have Gödel-number g. But, as is familiar G (truly) “says” that no number numbers a T-proof of G. So g is also not the number of a T-proof of G. But numbering a T-proof of G is a primitive recursive property.

That conclusion — that there’s a number  which both does and does not satisfy some primitive recursive condition — I, for one, just find incomprehensible.

“But an incredulous stare is not an argument!” Indeed. But I’m not incredulous in the sense of understanding what is being said to hold, but then treating the suggestion as beyond belief (“Another concrete world, as real as this one,  in which there are talking donkeys? Come off it, David, pull the other one!”). My trouble, to repeat, is that I just don’t understand what it would be for a perfectly ordinary number both to satisfy a primitive recursive condition and not to satisfy it. Not so much incredulous stare as incomprehending boggle.

Now I don’t pretend that that‘s the end of the matter. But it is, so to speak, the beginning of the matter. And I guess my main complaint about Berto in this chapter is that — although he cheerfully takes the dialetheist to be committed in the way I’ve described — he doesn’t get far enough past the beginning and  explain what that commitment could mean. True, Berto says something briefly about strict finitism — but that‘s not going to help, unless we have a proof that, whatever the system of Gödel numbering in question, the relevant number g will have to beyond a sensible finitist’s ken (so can be treated as an “inconsistent number”). And I don’t see any reason to suppose that’s true. So I’m left boggling! As will, surely, be most of Berto’s readers.

Meanwhile, in another wing of the madhouse

“The Chair of Palaeography at King’s College is the only established Professorship of Palaeography in Britain” boasts the KCL website. Not for long, it seems. It plans to axe the position too (along with the three philosophers). Another brilliant contribution to learning.

Still, it is so good to find that learning thrives elsewhere in London. For example, I see that next Monday’s lecture at CRASSH (the Cambridge Centre for Research in the Arts, Social Sciences and Humanities) is by one Professor Steve Dixon, of Brunel University , who is coming to talk about “Performing Split Selves: Doubles, Cyborgs and Multi-Identities in Theatre, Dance, Performance Art and Cyberculture”. Gosh. What a pity I’ll be in New Zealand and will have to give that a miss.

I can see that thinking (if that’s the word) about cyborgs and performance art might beat paleography and even the foundations of computational linguistics when it comes to sexiness. But call me old-fashioned, but it’s not exactly serious is it? But hey, who cares about serious scholarship any more? It’s 2010, and time for cyberculture. Oh well. But sometimes, just sometimes, Cyril Connolly’s valedictory words in Horizon come to mind again:  “It is closing-time in the gardens of the West”.

I think I’m off to read Montaigne.


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.

There’s Something about Gödel, Ch. 12

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

Planet de Botton

I’m all for popularizing philosophy in the right kind of way, and admire — not to say envy — the likes of A.C. Grayling and my colleague Simon Blackburn for their prose styles, their immense energy, good sense, ability to bring ideas to life, ability to engage with wider concerns. But I could certainly do without Alain de Botton pretentiously sounding off from whatever remote planet he inhabits. Here’s an excerpt from an interview in a Cambridge student mag.

Q: So, it’s the most obvious question to ask really: what exactly is philosophy?

A: 99% of people who call themselves philosophers are employed by universities, in the UK. And they’re really employed to teach the history of philosophy or the theory of philosophy but they’re not philosophers as such, they’re commentators on philosophy that other people have done, on the whole. …

What utter ignorant bollocks. When my colleagues wrestle as it might be with the philosophical foundations of set theory, or how we manage to think about the non-existent, or the foundations of political liberalism, or on the nature of moral judgement (to pick a few local enthusiasms), they are doing philosophy, trying to get it right, trying to push things on. Of course they engage with what others have said, but not as commentators-from-the-sidelines but as fellow participants in the ongoing conversation of philosophy. They are most certainly philosophers as such.

At a time when humanities disciplines are depressingly undervalued and misunderstood, and indeed under some threat, it does my blood pressure no good to have the likes of the crashingly ignorant de Botton trying to piss on us as well.

Routledge go mad

I have on my desk my copy of Hartley Rogers’s wonderful Theory of Recursive Functions and Effective Computability. I’ve been checking my memory that he says that, for effective computability, the steps in a particular algorithm must be idiot-proof at least in the weak sense of being executable by a computing agent with a “fixed finite bound” on his/her/its capacity. And yes, he does say that. Which is good, because that’s what I said he said in a talk last week!

Inside the front cover, there’s still the June 1970 pencilled stock date of Heffers (the wonderful warren of a bookshop that used to be in Petty Cury), and the price, 149 shillings. I guess it is, relatively speaking, the most expensive book I’ve ever bought. Going by the retail price index, that’s about £87: relative to academic pay, rather more. But it is a unique classic (and already established as such when I bought it a few years after publication); it is almost 500 pages; and the costs of production must have been enormous.

Zip forward to the present day. My young colleague Ben Colburn has just published an elegantly written and exceedingly interesting slim volume Autonomy and Liberalism. In pages, it is about a third of the length of Hartley Rogers, in words very much less than that: and the production costs were minimal given Ben had to send them an electronic file to their detailed specifications. Routledge are charging a quite absurd and shaming £70 (yes seventy pounds).

Which is, as the youff say, simply taking the piss.

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