Logic Matters

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.

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.

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!

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.

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 …

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.

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.