Wednesday, November 28, 2007

Boolos, Burgess and Jeffrey, 5th edn.

It seems only yesterday that the fourth edition came out: but -- as I found in the CUP bookshop today --- there's now a fifth edition of Computability and Logic. The preface announces that the main revision in this addition is a "simplification of the treatment of the representability of recursive functions". And the material on Robinson Arithmetic has been rewritten, and there's a more explicit discussion of the two uses we can make of Church's Thesis (essential and eliminable).

I confess to still perhaps preferring the more spartan elegance of the early editions. And I think that the book has always been, then and now, rather harder for students than the authors intended (which was one reason that I imagined that there was room for my Gödel book, even though it criss-crosses over quite a bit of the same territory). But credit where a great deal of credit is due: this is still a lovely book, full of good things and with some terrific explanations of tricky stuff. So hasten to your bookshop ...

Tuesday, November 27, 2007

Logic lives?

Well, this is moderately cheering (about logic matters, at any rate). First, about fifteen people have said that they are interested in a reading group working through the shorter Hodges on model theory. And now, about a fifth [update: over a quarter] of our second year undergrads already have said they are interested in another reading group working through Bell, DeVidi and Solomon (I've warned them it isn't a doddle). So despite my despondency about the state of logic in the UK more generally, interest does seem to live on here (bright students will see there's perhaps more serious sustenance than in e.g. worrying about how they know there's a coffee cup in front of them, which is a game which palls for most of us after about twelve minutes). It's just that we don't have enough people to sustain a proper logic teaching programme.

Losses

To Edinburgh yesterday, for the funeral of John Davidson, an old friend going back to early Aberystwyth days, who died far too young. The funeral was done with great aptness to the man. The poet Jeffrey Wainwright read 'Stoic', which he had written some ten years since for and about John. "The brook's lullaby" from Die Schöne Müllerin to conclude (for John found endless solace in Schubert's songs). Then later glasses were raised at The Scotch Malt Whisky Society members' rooms in Leith, and old acquaintances seen whom I suppose we are not likely to come across again with a last link gone. A hard day.

And on getting back to Cambridge I was shocked and saddened to hear of the sudden and quite unexpected death of Peter Lipton here.

Sunday, November 25, 2007

ACA0, #7: The last word

At last. If you go to my Gödel book's website, and click on the link under "Latest Additions" then the link no longer takes you to a rambling, unfinished essay but to a much crisper extended version of the talk I gave in Oxford a week ago. I argue that ACA0 strictly speaking overgenerates, and that the official conceptual motivation for the theory in fact favours a weaker theory (a theory that doesn't threaten to inductively inflate, yet which is as competent at generating proxies for theorems of classical analysis). And I make a similar claim about a different family of extensions to first-order PA as well, i.e. extensions by adding truth-theories. Here too I suggest that a familiar weak theory also overgenerates. (I suggest that this matters if we are concerned to evaluate and perhaps defend Dan Isaacson's Thesis that first-order PA sets a limit to what can be established from purely arithmetical considerations plus logic alone.)

Friday, November 23, 2007

I'm with Turgenev

Figes tells us that Turgenev wrote a famous bit of verse about the critic Stasov: the penultimate lines are ...

Argue even with a fool:
You will not gain glory
But sometimes it is fun.

I confess I've been spending a few minutes here and there blasting off again at a few fools on sci.logic. The highminded justification is that, given the thousands of people who do visit that group each day, someone ought occasionally to say "enough is enough" faced with streams of garbage. But let's be honest, Turgenev is right: sometimes it is just fun.

Thursday, November 22, 2007

Looking on the bright side, logically speaking

Heck, advancing years are a terrible thing. Apart from the obvious drawbacks -- and let's not go into those -- you start forgetting stuff that once upon a time you kinda knew a bit about. Ok, the things that you've regularly lectured on/written about sort of stay in place, more or less. It's the more peripheral stuff that you find has been dragged to trash by the passing of time. Humppphh. So there I was, sitting like an idiot in the math logic seminar, not having had time to do enough homework, and just not able to recover what I once knew(?) from Bell and Slomson's Models and Ultraproducts. Duh. But then I suppose I can look on the bright side. There will be the fun of rediscovery rereading the book (which I recall as very good) before the math logic seminar gets a bit serious next term. Though I'm not sure that is much compensation.

Something very different I'm currently devouring for the first time as my late night reading -- something I wanted to read when it came out, but I've only just got round to -- is Orlando Figes' Natasha's Dance. I'm only about a quarter through but it is simply fantastic. He writes with a novelist's flair, building up a multilayered picture that throws so much light on what is going on in Russian literature. It's wonderfully readable. I'm bowled over in admiration. So back to it ...

Tuesday, November 20, 2007

Back from Oxford

I'm back from Oxford where I was giving a talk at Dan Isaacson's philosophy of maths seminar. I was a bit anxious about the occasion in advance as I knew that Michael Dummett still tends to go. In the event he did come, and nodded and smiled encouragingly from time to time, and said he enjoyed the talk as he left at the end of the discussion. Which has certainly made my week. The discussion was helpful (Dan was pressing me hard to be clearer), but the basic line of argument seemed to survive. Phew. So I'll write up a version of this stuff over the next week and put it on my website. Watch for a link.

I'd not been to Oxford since The Daughter left about eight years ago: and I'm always struck anew how wonderful the place looks (even on a rainy late-autumn night). Cambridge really hasn't anything to compare with Radcliffe Square, or indeed the streets around and about.

I spent more than I should have done in Blackwell's. I've made a start since on James Ladyman and Don Ross's Every Thing Must Go: Metaphysics Naturalized which I bought despite the outrageous price, gripped by reading the first twenty pages or so in the shop. Having now finished the first long chapter, I find myself in considerable agreement with their basic line. Indeed, I'd say they rather pull their punches in criticizing arm-chair metaphysics based -- if based on science at all -- on a grasp of science that stops round about A-level chemistry (as they rudely but fairly put it); and some of the discussion so far is a bit oracular. Still, there's a lot of the book to come, so we'll see how well they sharpen their points and hammer them home. So far, so rather good!

"We segwayed"

An article in the Times today: "We segwayed in to a conversation about the au pair ...". Truly, the barbarians are already inside the gate.

Saturday, November 17, 2007

Ahem .... Leopard stacks icons

It is seriously sad to care about these things. I know. But for those who are equally miffed by the Leopard update's failure to sort the stack icon flaw -- ok, it's not exactly a bug but everyone thinks it is a quite daft design choice -- I've just found a very elegant solution here. (Apologies to all those who haven't the foggiest what I'm talking about!)

Friday, November 16, 2007

Homeopathy

A wonderful piece in today's Guardian, reprinted here, by the estimable Ben Goldacre, on quack science and the moral bankruptcy of professional defenders of homeopathy. Read it.

CMS at twilight

I was coming out of CMS this evening and was struck, not for the first time, how terrific it looks in twilight or at night. In daylight, the buildings look relatively sober, though very handsomely done. But later it can look almost magical.

The small image here links to a slide show of very atmospheric photos by Stefan Meinel, a grad student in DPMMS. They seem to me to hit off the place excellently.

(I bumped into Thomas Forster there, and the plans for a serious model theory reading group for philosophers/mathmos/compscis next term indeed look to be a runner. Excellent news.)

Thursday, November 15, 2007

Logical excitements ...

A day that didn't quite go to plan in a couple of ways, but still, three good logical things happened.

First, I'd been given the task of updating and expanding the logicky part of the entrance test done by undergraduates applying to read philosophy at Cambridge. It would be giving the game away to say very much about this. But I did have quite a bit more fun than I was expecting trawling around to see how others -- like USA grad schools -- manage these things, and putting together some suitably testing questions. (I'm not sure I'd have ever got in to Cambridge with all these new fangled tests, and interviews to find out if you are a well-rounded human being: in my day I just did a lot of nasty problems in projective geometry very fast, and bingo ...)

Second, it seems that -- thanks to Thomas Forster -- my plan to learn some more model theory by running a reading group with some hard core mathmos joining in seems as though it will come off next term: that should be terrific. The default suggestion is that we do the shorter Hodges (though the Marker book looks a possibility too).

And third, not least, it was Logic Seminar day -- the highpoint of the academic week really. At the moment, at Michael Potter's instigation, we are thinking about later Dummettian arguments against realism in mathematics. Or rather Michael and some of our grads are thinking, and I'm trying to keep up. Today we were looking at Peter Sullivan's contribution to the new "Schillp" volume on Dummett, where he seeks to locate in Frege: Philosophy of Mathematics a really rather simple argument for anti-realism. Applied to arithmetic, we have Premise One: The logicist claim that arithmetic is broadly analytic, its true claims being made true by the character of our concepts. Premise Two: what is given in our concepts does not suffice to fix the truth-value of every claim in the language arithmetic . So there is nothing to fix it that every such claim is determinately true or false.

This is an argument against realism in mathematics which (a) doesn't threaten to sprawl in ways that are difficult to handle to become a general anti-realism, and (b) doesn't depend on problematic claims about indefinite extensibility. Peter Sullivan certainly seems to show that the argument is indeed a thread running through the later Dummett, and his exploration is very illuminating (even if I think I lost the plot a bit towards the end of this long paper). I learnt a lot from the discussion. Great stuff.

Monday, November 12, 2007

Who needs an iPhone? ...

... but I sure hope that this rumour is true! That would be so very useful to have.

Soothing the troubled brow

I needed a bit of distraction after another faculty meeting. Inevitably, in my experience, as soon as departments start talking about root-and-branch reorganization of degree structures, it quickly becomes clear that the existing tolerance, more or less, of current arrangements in facts hides really quite deep disagreements about what we should really be doing, and why. The more you talk about possible changes, the less chance of coming to a happy consensus. Still, twenty minutes playing around making a few desktop pictures helped sooth the troubled brow afterwards. This is the view from San Gusmè near Siena, very early on an August morning this summer. 


Now back to ACA0 ...

Sunday, November 11, 2007

No names, no pack-drill

I've just been reading four or five assorted recent articles (as it happens, a bit away from my usual logical/phil. maths stamping ground: but sometimes I feel masochistic). They were tedious, unexciting, ephemeral stuff, on issues that is difficult to take very seriously, and all were about three times the necessary length. They were also all written by evidently very clever people, and were probably more or less right -- or at the very least, the pieces made sane-seeming moves in the scholastic game -- and they will give their respective authors brownie points for promotion. But I just couldn't see the point. Maybe I'm not cut out for this philosophy malarky. But I'd rather say: they just illustrate how philosophy loses its way when it stops engaging with serious foundational issues in logic, mathematics and science. I've quoted Steve Stich here before, but it's worth repeating what he wrote: "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. ... The results of philosophy done in this way are typically sterile and often silly." Indeed.

ACA0 again

I'm coming round to see things like this. Despite its centrality in the reverse mathematics programme, ACA0 is in fact (as it were) conceptually unstable. For take any open sentence F(x) of the language of second-order arithmetic which may embed set-quantifiers. Then ACA0 proves ∀x(Fx v ¬Fx). But if, from ACA0's viewpoint each number indeed determinately falls under F or doesn't, then what good reason can someone who accepts ACA0 have for not allowing F also to appear in instances of induction? But following that reasoning inflates ACA0 to the much stronger full ACA.

So in fact, I want to argue that the usual conceptual grounding for ACA0 in fact shouldn't take you quite as far as that theory: roughly, it takes you to a more restricted theory with parametric (rather than quantified) versions of induction and comprehension and lacking formulae with embedded set quantifiers, though you can allow prenex existentials. That still -- or so it seems to me at the moment -- gives you all the usual constructions for proving proxies of theorems of analysis: it's just we can lose the unwanted stuff like ∀x(Fx v ¬Fx) when F embeds set-quantifiers.

I'm going to talk about this and related matters in Oxford in about a week's time. If the suggestion survives its outing, I'll put a souped-up version of this stuff on my webpage. Fingers crossed.

Friday, November 09, 2007

Such a rarity, this blogging lark!

The Guardian today estimates that there are four million bloggers in Britain alone. Yes, four million -- i.e. about 15% of the twenty six million web-active people in the country. Ye gods. So much for that famed British reserve ...

Wednesday, November 07, 2007

So, not Manzano ... but who?

(For new readers: in our math logic reading group, we are working through Maria Manzano's Model Theory, as a warm-up exercise to tackling Hodges's Shorter Model Theory.)

Writing logic books involves all kinds of comprises and trade-offs between approachability and absolute precision, between breadth and depth; and all kinds of decisions have to be made about coverage, the amount of more philosophical commentary that you give, and so on and so forth. It is, as I found writing my two logic books, a horribly difficult business making sensible decisions -- which is not to say that there is just one way of getting them right. So I'm now pretty reluctant to get too critical (am I mellowing with age?). Still, I have to say that I've come to think that Manzano's book really isn't terribly good. I certainly wouldn't recommend anyone following our example, and using the book. True, Manzano is not at all well served by her translator, but that's only a small part of it: key ideas are far too often just not sufficiently well-motivated and clearly explained. Which is a pity because there are certainly some nice sections. But it is all too uneven in execution to be the helpful introductory guide we were looking for. Though it is certainly not obvious who, at this sort of level, we should have been reading instead.

I hereby bag the title Model Theory without Tears: A Philosophical Introduction for the book which my counterpart in some more or less close possible world is beginning to wonder about writing before the equally not-yet-started Ordinals, Cuts and Consistency. Choices, choices.

Callas, Tosca ... and YouTube

There are some astonishing finds on YouTube, amongst all the trivial dross. Someone -- no doubt breaking all sorts of copyright law, but in what a cause! -- has posted the whole of the astonishing 1964 television film that was made of Maria Callas and Tito Gobbi in the second act of Tosca at Covent Garden, in seven parts. The first two parts 1, 2, are followed by the torture scene 3, 4, then 5 , followed by Vissi d'arte, and finally the last ten minutes of the act.

The style is indeed from a different era ... yet the visceral impact remains however many times you see these legendary performances (past their vocal prime though, by all accounts, Callas and Gobbi were). Words fail me. Except to say that, if you have never seen this film, you must and now can. (Start with Vissi d'arte, then backtrack to watch the whole in sequence.)

Sunday, November 04, 2007

Oh no .... more geekery

I've just discovered -- about eight months after everyone else -- that Wordpress (the cool alternative to Blogger for hosting/managing a blog) can handle LaTeX code, so can do nice looking logic stuff. I was already trying to resist following the daughter's lead and migrating there, but this might tip the balance. Watch this space ...

More books -- free this time

In his nice blog, Words and Other Things, Shawn Standefer helpfully notes that CSLI publications have digitalized their backlist, and put the PDFs online for free here. The list includes e.g. Peter Aczel's Non-well-founded sets, Jon Barwise and Lawrence Moss's Vicious circles: on the mathematics of non-wellfounded phenomena, and other very good things.

Friday, November 02, 2007

Leopard, second impressions

I'm still dosed up to the eyeballs and so finding it annoyingly difficult to concentrate on work. I am supposed to be thinking more about issues related to ACA0 -- especially as I'm due to talk about this sort of stuff at Dan Isaacson's seminar in Oxford in a couple of weeks. I certainly hope that normal brain functioning is restored sooner rather than later. Meanwhile, apologies for the consequent lack of any very interesting content here recently!

Still, I've been able to play with Leopard more than perhaps I'd have otherwise been able to. I'm still rather impressed. As well as the obvious things, there are lots of neat little improvements. To mention just one, being able to write yourself notes and handle reminders inside Mail turns out to be just very useful (more so than I'd have ever predicted). Of course, it is all very sad to get excited about things like that. But there it is. I'm sure I'll get better soon.

Spread the word!

Ah well, sales for the first three months of the Gödel book are not exactly on a Harry Potter scale. But my editor does seem reasonably pleased. Still, sales in North America are (proportionally) nowhere near as good as those in the UK and Europe. So c'mon, people, some serious spreading the word is needed out there! The Gödel book is terrific: every grad student should have a copy, and every library should have three .... You know it makes sense.

Ray Gravell

Ray GravellI was sad to read that Ray Gravell, a stalwart of the great Welsh team of the 1970s, has died. Reading some of the obituaries brought back memories of those glory days. Here are J.P.R. Williams, Gerald Davies, Ray Gravell and Steve Fenwick. What heroes!