Saturday, February 28, 2009

Maddy's Second Philosophy: Introduction

As announced, I'm (belatedly!) planning to comment here section-by-section on Penelope Maddy's Second Philosophy: A Naturalistic Method (OUP, 2007). Let me say straight away, having read on a hundred pages or so, that I have nothing but praise for Maddy's writing style, which I can only envy. This is a remarkably readable book. And perhaps I should add that I am also highly sympathetic to the kind of naturalistic project that she is pursuing: so it might turn out that my remarks here won't be that interesting (vigorous and acerbic criticism always being so much more fun to read!). But let's see ...

Who is the 'Second Philosopher'? She espouses a kind of 'naturalism' -- but that descriptive label has been used so variously, "to mark little more than a vague science-friendliness", as to become unhelpful. So over the opening chapters of the book, Maddy aims to characterize the Second Philosopher, not by giving a sharp definition of her position, but by means of a "character sketch", illustrating her philosophical disposition. But this much is clear from the outset: in her pursuit of truth, the Second Philosopher "rejects authority and tradition as evidence, she works to minimize prejudices and subjective factors that might skew her investigations." Rather, "she uses what we typically describe with our rough and ready term 'scientific methods'" though she avoids trying to give a definitive account of what that entails. She is open minded about how best to increase her knowledge; "she simply begins from commonsense perception and proceeds from there to systematic observation, active experimentation, theory formation and testing, working all the while to assess, correct, and improve her methods as she goes".

That perhaps makes it sound as if the Second Philosopher is just a scientist. But she has, as we will see in due course, a taste for some very general questions about the world and our epistemic relation to it and the concepts we bring to describe it, as well as for more local questions. And it is this (a matter of the range of her interests rather than of her intellectual methods) that distinguishes her from run-of-the-mill scientists. Unlike the working chemist, for example, she addresses "a wide range of questions we would ... typically regard as 'philosophical'" -- but she doesn't sense a crashing of the gears as she turns from narrower scientific questions to the more sweeping 'philosophical' ones. She has no criterion for sharply demarcating science from philosophy, and she aims to bring to bear the same methods of theory building and testing in her pursuit of truth, whether on the local or more global scale.

We recognize the tone of voice here! Here's Reichenbach (later quoted by Maddy):

Modern science ... has refused to recognize the authority of the philosopher who claims to know the truth from intuition, from insight into a world of ideas or into the nature of reason or the principles of being, or from whatever super-empirical source. There is no separate entrance to truth for philosophers.
The Second Philosopher, enlisting with Reichenbach, finds no place for a First Philosophy, prior to science, which can supply a priori principles of justification for science.

But in keeping with her anti-dogmatic stance, her open-minded willingness to test out any ideas that have some hope of advancing knowledge, it isn't that the Second Philosopher is refusing the very possibility of First Philosophy on the basis of some priori argument (after all, she isn't that keen on a priori arguments!). Rather, "[h]er reaction to extra-scientific philosophy is puzzlement; she asks methodically after its standards and goals, and assesses these by her own lights." She looks case-by-case at what is on offer from those who do have ambitions towards a First Philosophy and she finds herself quite unpersuaded by their offerings.

This is, in particular, her view of Descartes's project, as he engages in his Meditations on First Philosophy. He is promising, after all, a new method to put all future science on a firmer footing. So of course the Second Philosopher will sit up and take notice: she's all for anything that will improve science. As Maddy puts it,
When Descartes proposes that she adopt his Method of Doubt, she doesn’t reject it as 'unscientific'; impressed by the promised pay-off -- a firmer foundation for her beliefs -- she’s quite willing to give his proposal a try; she eventually discards it only as it proves ineffective.
The story is spelt out in more detail in Maddy's first chapter, so let's turn to that.

Friday, February 27, 2009

One hundred, not out.

I started contributing to the Ask Philosophers website just over a year ago. I've just posted my hundredth response -- not one of my most exciting efforts, but of course obviously true like all the rest! You can read my collected works here. Leaving aside my own contributions, though, there are some really excellent contributions to the site. Certainly well worth pointing philosophical beginners towards.

Wednesday, February 25, 2009

Back to Gödel

I've foolishly agreed to give a mini-mini-course on matters to do with incompleteness at a Cameleon weekend that Thomas Forster is organizing in four weeks time. I ought to find some new Deep and Interesting Things to say that aren't in my book -- but that's a trifle difficult because if it was interesting and I knew it, I'd surely have put it in. I think I'm going to bluff my way through talking about iterated consistency extensions, but I need to do a lot more homework before I'll feel comfortable, and at least the next two weeks are going to be very busy before I can really get round to that. Going to be a close-run thing!

Meanwhile, Arnon Avron has just been in touch with a rather embarrassing question about the book. Why didn't I just point out that Theorem 30.10 (The truths of L, the language of arithmetic, aren't r.e.) follows from Theorem 21.5 (given a sensible system of Gödel-numbering, no predicate of L can express the numerical property of numbering-a-truth-of-L).

Suppose for reductio there is a recursive function f that enumerates (the Gödel numbers for) the truths of L. Then we know that any recursive function can be expressed in L (put together Theorem 30.1 and the last remark in Sec 4.7). So in particular there is a formal wff F(x,y) which expresses the enumerating function f, and then by definition the formal wff Ex(Fx,y) will be satisfied by a number if and only if it numbers a truth of L. But then this is impossible by Theorem 21.5. Which proves Theorem 30.10.

Why the heck didn't I say that? I guess I was so keen to make a connection with the informal proof in Ch. 5, and so motivate the discussion of Turing machines, that I forgot to mention the simple proof. Oops!

Tuesday, February 24, 2009

Constructive ZF

Just to note that there is a new entry in the Stanford Encyclopedia of Philosophy, on Set Theory: Constructive and Intuitionistic ZF, by Laura Crosilla. I'm out of my comfort zone here, but I found this a very interesting and helpful piece. The SEP really is going from strength to strength, and the logic/phil maths entries are most certainly of a fine standard.

Monday, February 23, 2009

The Leiter report is out

The new Leiter report is out. No real surprises it seems, at least as far as the UK rankings are concerned. In particular, no surprise that we (= Cambridge) come out markedly better than on the RAE, for reasons it would be perhaps be inappropriate to go into here. Still, quite cheering.

Wednesday, February 18, 2009

Forthcoming attractions: Second Philosophy

The last few weeks, since finishing Parsons, our Wednesday reading group has been talking about Jeffrey King's The Nature and Structure of Content. But I confess that, after three chapters, I've stirred up a rebellion (for I find King's project mystifying and am at a complete loss as to what the rules of the game he thinks he is playing are). So we are going to ditch King, and move on to read Penelope Maddy's Second Philosophy: A Naturalistic Method.

And I plan to comment here, section by section as I did on Parsons (at least that gets me to read the book carefully). Though I hope I finish the job rather more speedily this time. In fact, I predict I will, if I can project from my experience reading the first four chapters: for Maddy writes beautifully, with enviable clarity and style -- and I guess that I'm also intellectually much more at home with her naturalism. I'm looking forward to it.

So watch this space ...

Monday, February 16, 2009

Fools, damned fools, and the designers of online forms

I've a sabbatical coming up next Lent term, and I really ought to apply for matching "double your research leave" funding from the AHRC to have another term off. Not that I hold out much hope of getting it rather too near retirement, but it Looks Good with the powers that be to make the effort. But I'm struggling with the idiocies of the on-line application form, which seems purpose designed to raise your blood pressure to the point where you decide that it would be better for your health to give up and bang your head against a wall instead.

I'm planning to write a shortish book on matters to do with the consistency of arithmetic, which is just underway now, and should be very well-advanced by the end of next Lent term, given I've promised to talk about the stuff in various places in the meantime. But "if you are seeking funding for the completion of a monograph, you need to identify the chapter headings and contents in the Case for Support." Eh? Am I just supposed to lie? How best to organize and chunk up your material might only become clear pretty late in the game, especially if -- like me -- you favour rather short snappy chapters. I haven't a clue what the chapter headings will turn out to be. Have the people designing this form ever written a book? The hell they haven't.

Oh well, set that aside for the moment: let's try to tackle the easy stuff. "You must state the reason why relief is required from the teaching, administration, examining and/or managerial duties detailed." Ah, that's straightforward: because I can't do two things at once. But then they know that, and my reason is exactly the same as everyone else's. So why the hell are they asking? Are they idiots?

Ah, now I have to list my current teaching. Fair enough. Make a list of current lecture courses. "Hours per week?" And what on earth does that mean? Official contact hours? Contact hours plus preparation time? Contact hours plus preparation time plus time going to grad seminars that aren't exactly duties but it would be a Very Bad Thing if no lecturers turned up to? Contact hours plus preparation time plus grad seminar time and background reading to be able to talk informally to various grads? Where do "teaching" hours stop? Who is to say? I press "Help". Which doesn't give any clue at all. More idiocy.

Well, I'll just have to see if our Faculty admin officer -- who is of a very calm and reasonable disposition, and knows about such things -- can hold my hand through the process tomorrow without me blowing a gasket.

Fortunately, I guess the dolts at the AHRC responsible for these forms don't read academic blogs.

Saturday, February 14, 2009

Another week goes by ....

A busy week. A short but interesting talk by Bob Hale at the Moral Sciences Club on Tuesday on the very idea that there might be possible worlds where the laws of logic are different -- what idea of possibility does that involve? Then on Wednesday afternoon, we've moved on from reading Charles Parsons to looking at Jeffrey King's The Nature and Structure of Content. I can't say I'm much attracted by his project, or by his theory of propositions -- but I don't think I'm exercised enough about the issues to put the energy into blogging about it here.

On Wednesday evening, a fun talk from Rob Trueman, one of our M.Phil. students, at the Serious Metaphysics Group. Suppose you reject the composition-is-identity thesis (as Rob thinks you should), so the train can't just be identified with the carriages. Then why does moving the train take no more force than moving the carriages? Rob was arguing that the natural answers we might try have surprising consequences. I wasn't convinced, but it was a fun evening (as 'Serious' certainly doesn't mean 'Solemn').

I've been trying to keep the Thursday Logic Seminar accessible to the handful of undergraduate students actually doing our Math Logic paper. So this week and next we are looking at four chapters from Marcus Giaquinto's The Search for Certainty, discussing Hilbert's Programme and the impact of Gödel's theorems on the Programme. I slightly disagree with Marcus's reconstruction of Hilbert (see my discussion of two routes for getting from the consistency an ideal theory to its real-soundness on p. 256 of my Gödel book): but that's very minor. Marcus's book is terrific.

On Friday, a prolonged Staff-Student Committee meeting. Every so often, for one reason or another, the disconnect between what many students think they want ("more continental philosophy") and what most professional philosophers in serious departments think they should get becomes dramatically evident. That's happened from time to time everywhere I've been. Most departments engineer some muddled compromises, but the strains can tell.

Monday, February 09, 2009

Top 50 philosophy blogs?

Here's a new list of philosophy blogs -- a bit random, but such lists can turn up serendipitous finds, so I pass on the link.

Saturday, February 07, 2009

Pohler's Proof Theory

I've started struggling through Wolfram Pohler's recent Proof Theory: The First Step Into Impredicativity. And it is, I'm afraid, a struggle -- for a textbook exposition "pitched at undergraduate/graduate level", it is really quite unnecessarily hard going. For example, I can't imagine that anyone who hasn't already encountered the idea would have much hope of cottoning on to what is going on with the Veblen hierarchy from the discussion in Sec. 3.4. And even if you are very familiar with completeness proofs for first-order logic, it's made ridiculously hard work to see what's going in the completeness proof in Sec. 4.4.

I'll certainly keep ploughing on through, given the book's coverage. But not with relish. Why on earth write like this, without the introductory informal motivating comments and explanations of concept definitions and proof ideas that you'd give in lectures? I'm quite baffled that anyone can think that this is the right way to write a book intended for a student readership.

Anonymous comments: I think this is the usual way of writing a math book. Most, if not all, math books are written this way.

I don't think that's entirely true. I'm sitting here surrounded my shelves of relatively recent maths books, both pure and applied maths (dating from when I was writing my chaos book ten years ago, or teaching the philosophy of space-time theories). They do illustrate a whole spectrum of modes of presentation from rather relaxed to take-no-prisoners relentless formality. To be sure, there are too many of the latter kind -- but it is possible to do better!

Wednesday, February 04, 2009

Pro-vice-chancellorian bollocks

Once upon a very long time ago, I spent a year or more of my life doing nothing else much but mathematics problems, preparing for the then entrance scholarship to get into Trinity to do maths. The standard was fairly stratospheric, and it was quite difficult to find enough practice questions on e.g. projective geometry. But one source was selected questions from various university examinations. Yes, degree-level questions from elsewhere being used as Cambridge entrance paper practice ... which rather undermined any belief I might have had in the myth of close equality of level of enterprise across different universities.

Well, things have no doubt changed in all sorts of ways since those distant days. But one thing remains the same. As almost everyone knows perfectly well, there are wide differences between what is intellectually required to get (say) an upper second-class degree in a particular subject at different UK universities.

But there are always those concerned to deny the obvious. Thus, in the correspondence column of the Guardian today, the Pro-vice-chancellor of London South Bank University writes

All universities work to a common understanding of degree classification (supported by an external examiner system which is common to all).
And another correspondent writes
There is, in fact, close equivalence of degree-level standards across institutions. It is effectively maintained through the Quality Assurance Agency, which asserts that the standard "should be at a similar level across the UK". The much-admired external examiner system is a major feature of this.
Which is all, of course, complete bollocks.

For a start, external examiners are very largely swapped between universities at similar levels in the pecking order. I bet, for example, that London South Bank University rarely uses examiners from Cambridge, or vice versa. And moreover, even when you do act as an external examiner for another university, your main job is to certify that the examining board there is behaving properly in following its own rules, and is behaving in a transparent and principled way. You might hope, where appropriate, for some rough comparabilities -- but only pretty rough. And rough comparability is patently not transitive. Standards at A might be roughly comparable with standards at B, and standards at B might be roughly comparable with standards at C, and so on down the chain. But standards at A may of course be in a different ballpark to standards at Z.

And so they certainly ought to be. For example, here in Cambridge we spend a great deal of effort in trying to recruit the brightest and best; we then give them maybe seventy hours or more one-to-one 'supervisions' (i.e. tutorials) in philosophy over three years, not to mention all sorts of other formal and informal small group teaching on top of lectures -- a quantity and quality of provision that most universities can only dream about. It would simply be a scandal if our students by the end weren't in general performing at a level a good few notches above what it is reasonable to expect in many other places. And what we demand of them in Tripos quite rightly reflects that. That "close equivalence of degree-level standards" remains a myth.

Logic matters website updated

I've not been at all attentive to the Logic Matters website recently -- it's one of those things that sometimes I'm quite in the mood to do, and at other times it seems to drop right off the bottom of the "to do" list.

Anyway, there is now a new page "Other logic" linking to some recent papers and expository handouts. There's more to be added, which I'll want to tidy very slightly before irrecoverably letting them lose onto the net. Putting this page together was a rather cheering experience -- I seem to have done more recently than I remembered!

I hope to get round to finishing the port of the LaTeX for Logicians pages from the old form to the new one sooner rather than later -- at the moment some internal navigation is a bit flakey, though the requisite info is mostly in there somewhere.

Monday, February 02, 2009

Tim Crane moving to Cambridge

Since it is now announced on the Leiter blog, I guess there is no reason now not to say here that we're delighted that Tim Crane is moving to Cambridge from UCL as the new Knightbridge Professor, from the autumn.

Parsons, the whole story, at last

I have been blogging on and off for quite a while about Charles Parsons's Mathematical Thought and Its Objects, latterly as we worked through the book in a reading group here. I've now had a chance to put together a revised (sometimes considerably revised) version of all those posts into a single document -- over 50 pages, I'm afraid. You can download it here.

I've learnt quite a bit from the exercise. I'll be very interested in any comments or reactions.