Friday, May 29, 2009

The Wisdom of Wikipedia

Ye gods. The Wikipedia entry for Definite Descriptions until a moment ago read:

Bertrand Russell ... proposed according to his 'theory of descriptions' that when we say "the present King of France is bald", we are making three separate assertions:
1. there is an x such that x is the present King of France.
2. for every x that is the present King of France and every y that is the present King of France, x equals y (i.e. there is at most one present King of France).
3. for every x that is the present King of France, x is bald.
So Russell solved a problem about a sentence with a non-denoting description by analysing it into a conjunction of three sentences with the very same non-denoting description. Terrific.

I thought about leaving it as a bear trap for unwary students cribbing essays. But I couldn't, and it's been minimally corrected. It will interesting to see how long that lasts before some idiot changes it back.

Sunday, May 24, 2009

Praise where praise is due

I'm finishing marking a stack of dissertations and "assessed essays", submitted for examination in the Philosophy Tripos. I have some philosophical grumbles (of course!), but it is a beautiful late spring day, and I'm feeling cheerful, so let me give praise where praise is due. For I'm struck by the fact that so many are so well written. Students having to read a great deal of sharply written analytical philosophy; being forced to write supervision essays week in, week out; having essays ruthlessly criticized hour after hour for lack of clarity and cogency -- all that seems to produce after a couple of years some excellent writers of spare, readable, transparently lucid English prose. It's good to see we are doing something right!

Thursday, May 21, 2009

It's that time of year again ...

Things will continue to be quiet here for a while. Tripos starts tomorrow, with piles of marking to come. But in one way or another I've already been marking all week (reading dissertations and submitted essays, interspersed with looking at the work submitted by shortlisted candidates for the Analysis studentship). Let's just say it's been a pretty mixed experience.

To keep myself going, I've just got Angela Hewitt's new version of Bach's Well-Tempered Clavier to listen to between scripts. It seems to be the season for re-recordings by artists who have already made classic disks. As I noted here, Viktoria Mullova has released another version of the Partitas (stunning); Imogen Cooper is starting to release another Schubert cycle (very warmly reviewed, and I've just sent off for the first disks). And here Hewitt is giving us another version of the 48. Her previous version was about my favourite: this one might take some getting used to, as it is more ‘more expressive’, ‘more elastic’, than the earlier one. But on a first listen to the first couple of disks, I think I could warm to it.

Wednesday, May 13, 2009

Quantum computation again

The audience is thinning ... but we've got through Peter Shor's cunning quantum algorithm for factorizing numbers exponentially faster than the best classical algorithm. Fascinating stuff (even if the biggest number a real-world implementation has so far has managed to factorize is 15, which isn't yet too alarming for those worrying about the quantum algorithm being used for busting public key cryptography!).

Tim Gowers warmly recommended Michael Nielsen and Issac Chuang's book Quantum Computation and Quantum Information which does indeed seem very nicely put together, is pretty readable, and is distracting me from all the things I should be doing (like marking philosophy dissertations).

Maddy on logic

My blog postings on Maddy's Second Philosophy came to an early halt, largely due to the pressure of other commitments. But our reading group is continuing to work through the book. I liked the partly historical, scene-setting, first part of the book a good deal. But I think we all found the second part of the book, on truth, unsatisfactory (not least because it was unclear what was distinctively second-philosophical about this part of the enterprise). We are now discussing her treatment of logic in the third part of the book.

She aims to give what she regards as a naturalized version of a Kantian account of the status of logic:

As a first approximation, then, the Second Philosopher hopes to develop an account of logical truth with two components: (1) logic is true of the world because of its underlying structural features, and (2) human beings believe logical truths because their most primitive cognitive mechanisms allow them to detect and represent the aforementioned features of the world. As soon as these two ideas are laid down, it's natural to hope that they can be further reinforced by a connection between them: (3) human begins are so conīŦgured cognitively because they live in a world that is so structured physically.
But this way of putting things is surely going to ring alarm bells with well-brought-up logicians! Logic, we have learnt to say, is not about a special class of worldly truths, but is about what follows from what. Of course, regiment the rules about what follows from given assumptions in standard kinds of ways, and we'll find ourselves saying that certain propositions follow from no assumptions at all: call those the logical truths. But note that this account of the logical truths emerges as, so to speak, a spin-off from something else, namely a prior account of logical inference. And it's the account of logical inference which has to come first. So Maddy's Second Philosopher is starting in the wrong place. Or so it will seem to many.

Maybe Maddy could retort that her way of putting things is recommends itself just for simplicity and to make connections with an earlier tradition. She could -- couldn't she? -- have equally well started:
As a slightly better approximation, the Second Philosopher hopes to develop an account of logic with two components: (1') logical inference is reliably truth-preserving because of features of the way the world is structured, and (2') human beings accept certain inference rules because their most primitive cognitive mechanisms allow them to detect and represent the aforementioned features of the world.
But why is that supposed to be the obvious route for the hyper-naturalist Second Philosopher to take? After all there is a familiar enough alternative, much explored, which at a similarly broad-brush level runs:
However the worldly facts go, whatever structure the world has, our thoughts don't always track those facts. We get things wrong. And thoughtful agents need a way of explicitly acknowledging they've got things wrong -- we need a negation operator in our language.

Likewise, sometimes we can only narrow down the facts to some options. And thoughtful agents need a way of expressing the options without committing to any -- so we need a disjunction operator as well. We need negation and disjunction, then, not because the world is full of negative and disjunctive facts which we have to track (whatever such facts might be), but because of our cognitive limitations. And so it goes, mutatis mutandis, for other logical operators too.

Now, what makes something a negation operator, a disjunction operator, etc.? Meaning is use! It's what we do with the operator (in the jargon, the practice codified in the introduction and elimination rules) that fixes which operator is which, and shows it is apt for rejecting something as wrong, for narrowing down options, or whatever. Of course there are constraints -- we can't pair up introduction and elimination rules willy-nilly: that's the lesson of tonk. But the constraints aren't so to speak external, world-imposed, ones: in a naturalistically anodyne sense, they are a priori constraints of harmony imposed by sensible conservativeness requirements etc., needed to keep the enquiry game from falling apart.

The harmonious inferential rules, then, are meaning-fixing -- we read off the content of complex sentences involving the operators from the rules in just such a way as to ensure that the rules are truth-preserving. So we don't need to look at the way the world is structured to determine that they are truth-preserving. But there's nothing naturalistically suspect about all this: we've indicated why limited cognitive agents have need of the likes of negation and disjunction working in the way they do.
Of course, I'm not saying that such an inferentialist story is utterly unproblematic. Far from it. But it is the obvious foil to Maddy's sort of story. So good Second Philosophy methodology might suggest she should at least be taking the stories in parallel and devising some nice "crucial experiments" to decide between them.

But that isn't how Maddy proceeds. In fact, she just doesn't mention the well-trodden inferentialist path at all. Maybe she associates it with e.g. Dummett, who she would have marked down as a modern First Philosopher par excellence. But I don't see that there is in fact anything especially first philosophical about inferentialism (in Tennant's hands, his inferentialist treatment is bound up with what look to be rather Second Philosophical concerns -- evolutionary considerations, thoughts about the inferential practices necessary for good science).

So I'm left rather puzzled about Maddy's confidence that treating logical laws like particularly general laws of nature is evidently the way to go for the naturalist. It surely isn't.

Monday, May 11, 2009

Gowers online!

Tim Gowers's lectures are being recorded: the first five lectures are now fully online in various formats (including iPod friendly video) here, with the rest presumably to follow.

Wednesday, May 06, 2009

Quantum Computing Since Democritus

Tim Gowers this morning recommended Scott Aaronson's notes for a lecture course 'Quantum computing since Democritus.' I'm half way through, and the notes are a great read and highly illuminating. So I add my recommendation, if you want to get to know more about computational complexity and about quantum mysteries too. (Aaronson also has a fun blog.)

Monday, May 04, 2009

The State of the Nation

I've just finished helping do the shortlisting for the Analysis Studentship. Without inappropriately giving things away, what have I learnt about the state of the nation, philosophically speaking? (A reminder: the studentship is intended for those who are finishing or who have recently finished a PhD in the UK, to give them another year in which to have a second stab at applying for JRFs, post-docs, or other posts that will keep them in philosophy. So the applications give a partial snapshot of what finishing/recently completed UK-based grad students are up to.)

  • The good news is that there are some really rather impressive-looking young philosophers starting out, already publishing in good places.
  • The bad news is that there are a lot of good but not quite so impressive-looking philosophers starting out. Surely far too many to ever get permanent jobs in this country. To be sure, some of the applicants are of overseas origin and might eventually want to return home. But I can't help feeling that there are going to be an increasing number of people who have given (say) seven or eight years of their lives to postgraduate work in philosophy, doing a MA and a PhD followed by some temporary employment, and who are then faced at 30 with an unenviable and depressing choice between hanging on in a sequence of very temporary jobs or starting over in some other career. (That would still be the situation even if everything were rosy in the economy, given the numbers now coming out of UK grad schools: but things are only going to be made worse by the financial plight of universities here and in the USA.)
  • I would have predicted that one effect of the drive for early publications would be a kind of scholasticism. There were some signs of this -- philosophers who seemed to know a lot about rather little (Professor X's views about Y) and coming at it from a narrow angle too. But in the event, this happily wasn't too much in evidence.
  • Some topics were over-represented. Predictably, issues to do with consciousness and knowledge of one's own mental states loomed large (the hottest topics of a decade ago evidently became the routine topics of starting graduate students four or five years back). Other topics were rather unpredictably under-represented. For example, mainstream philosophical logic or indeed straight philosophy of language surprisingly featured hardly at all.
Overall, though, the future of UK philosophy looks cheeringly bright.

Friday, May 01, 2009

Tim Gowers's lectures

I'm going to Tim Gowers's graduate course on Computational Complexity, and we're four sessions in. It must be the first time I've followed a full-blown maths lecture course since I was a Part III student (once upon a time, when the world was young), and I'm enjoying it hugely. Partly because the topic is fascinating, and I'm being prompted to read around a bit. And partly because the performance is terrific.

At five past the hour, Tim Gowers picks up a piece of chalk, and -- without notes, it seems -- proceeds to explain ideas and proof-strategies and outline proof-steps. Not using overheads or a data projector means that things go at a pace you can take in, and there's a sense of the proofs being re-created in real time which is very engaging. And his running commentary of incidental comments can be extremely illuminating. For Tim Gowers characteristically wants to show that proof-ideas aren't just rabbits to be pulled out of the hat in a mysterious way, but are in fact rather natural ideas to try. And that -- I warmly agree -- is how mathematical proofs should be presented.