Wednesday, May 28, 2008

Postcard from Siena - 1

We have decamped back to Siena for the better part of a month. Or rather to a small village about 15km to the east. Siena is already bustling with tourists, but here things are very quiet. From one window, a few domestic sounds of village life; from another I can see half-a-dozen men slowly working in a line between the vines below the village walls.

I suspect that logic postings here might be infrequent for a while, though I've brought a laptop and some things to work on when the mood takes me. But I have, at last, belatedly finished a review of the Absolute Generality volume (I'd have finished it a lot sooner if I'd bothered to check the word length and realized that I'd already written too much by a factor of four). The headline is: if you read nothing else, read the paper by Shapiro and Wright. That is terrific. Otherwise, I found the collection rather disappointing and frustrating. The editors should have rapped the knuckles of the unclear and the prolix. (Search back through this blog for more.)

I'm also still trudging through my Intro to Formal Logic, with one last search for typos and small ways of improving things. As things have turned out, I've found quite a large number of small changes worth making: but I've only made one significant addition, to Sec. 9.3, where I first start talking about valuations of propositional logic wffs. I now say a necessary three paras more about the classical assumption that we are dealing with wffs that are determinately true or false. (By great good fortune, the chapter previously finished near the top of the page, so I've been able to add material without changing pagination downstream.) Overall, I think the book is much improved for the changes.

Now a difficult decision. Go for a walk locally? Or into Siena to people watch over a drink in the Campo? Life is tough sometimes ...

Wednesday, May 21, 2008

The delights of moving semicolons

I have been very distracted over the last week reading and re-reading IFL. The trouble with writing or tinkering with something like a logic textbook is that there is no obvious point where you should call a halt to the revisions. You can always make it just that little bit better. Even if it is merely changing a bit of punctuation to improve the structure of a sentence.

Still, on the whole, I'm quite enjoying the job. I certainly feel more warmly inclined to IFL than I did. But it has also made me want to rethink how I should run my first-year lectures based on the book. Our students are a bright bunch. Rereading IFL, it's mostly extremely clear (although I say so myself!). Given the back-up of logic example classes, students can actually teach themselves a lot of stuff just from the book. This year, I think I'll try using some of the lectures to range a bit more widely around and about what's in the book itself. More fun for me and surely more fun for the audience.

Wednesday, May 14, 2008

Revisiting IFL

I'm in the middle of rereading my Introduction to Formal Logic pretty carefully, from cover to cover. It's the first time really that I've looked at the whole book carefully since it went off to press almost five years ago. It is a slightly odd experience, though I'm finding it all rather less depressing, and I'm liking the book rather more, than I was expecting. The structure still strikes me as right (assuming, that is, you are going to do logic by trees), and some of the ways things are introduced and explained still seem felicitous. Well, I would say that, wouldn't I.

Since I've got the chance to make corrections, I might as well try to pick up any other infelicities or mistakes that aren't already in the corrections list posted on the book's website. So far I've found a few additional typos and quite a few tiny ways of improving readability: but -- given that I can't start writing a significantly different book -- there's not been too much major that I've wanted to change. In the propositional logic part of the book, I think the main shortcoming in the printed version is in not making clear enough the classical assumptions underlying the use of truth-tables. And there are constraints on what I can say, since I'd rather not change the downstream pagination. So sorting that is my task for tomorrow.

Monday, May 12, 2008

Good news re IFL, again

A reprint for my Introduction to Formal Logic is definitely on! Excellent news. I need to get corrections done before going to Italy, so that's all the spare moments in the next ten days taken care of. Anyone who has been meaning to tell me about some typo/thinko/'orrible 'owler/obvious occasion for improvement that isn't already noted on the corrections page, now is your chance to tell me!

(On the one hand, this is corrected reprint not a new edition so corrections theoretically should only be modest: on the other hand, I get to produce the PDFs, so I can rewrite easily rewrite where necessary.)

Sunday, May 11, 2008

Religion and evil, again

So he killed his daughter ... 'Death was the least she deserved,' said Abdel-Qader. 'I don't regret it. I had the support of all my friends who are fathers, like me, and know what she did was unacceptable to any Muslim that honours his religion,' he said. Again, comment is superfluous.

Thursday, May 08, 2008

Galois connections

In his classic paper "Adjointness in foundations" (1969), F. William Lawvere writes of 'the familiar Galois connection between sets of axioms and classes of models, for a fixed [signature]'. The idea might be familiar to category theorists, but it isn't easy to find a clear account of what it involves. So, inspired by a talk by Nathan Bowler last term, I've put together a piece on Galois connections to explain. All comments, corrections, suggestions for improvements/additions very welcome. It's part of a planned longer piece about order and ordinals.

[Later] Thanks to Luca Incurvati for catching a daft thinko and a few typos too!

[Later again] I've replaced the previous version with a notationally slightly prettier version.

Wednesday, May 07, 2008


I was sitting at tea at CMS yesterday listening to Martin Hyland and Thomas Forster talking about set theories, and it struck me -- not for the first time -- how important a certain kind of informal discussion is to the mathematical enterprise.

You'd miss some fun ("fun" in a rather stretched sense, but you know what I mean) if you didn't ever have face-to-face philosophical discussions. But you wouldn't necessarily miss out on a lot of philosophy. Because in written philosophy, you do still get the to and fro of ideas, the false starts, the dead ends, the conjectures, the refutations -- often in the writing of a single author as she wrestles with objections and counter-objections. The dynamic is there on the pages (not in its untidiest and rawest form, to be sure, but still very evident). With mathematics published in the approved conventional styles, on the other hand, you get the end-product, some results and their proofs. But the dynamic that led to them, the whys and the wherefores, can be very hidden, and informal commentary can often be very laconic (or altogether missing). So a few arm-waving remarks over tea that might never get into a written paper can make all the difference to your understanding of how some bits of maths fit together. Conversely, missing out on picking up the folklore of maths is arguably a much bigger loss than missing out on "live" philosophical discussions.

Monday, May 05, 2008

Three cheers for Alan Sokal

Alan Sokal's Beyond the Hoax has been out a few weeks, but I've at last got a copy. It reprints his wonderful "Transgressing the boundaries" parody with a running commentary of annotations on the opposite pages (or at least, the commentary would have been on opposite pages if he'd got the LaTeXing right!). And it has a selection of other papers, all written with his characteristic verve, directness and good sense. There is better philosophy of science here than is purveyed by some philosophers of science.

And incidentally, I was amused by Sokal's cheerful abuse of the intellectual pretensions of religion -- witness e.g. his description of the Pope as "the leader of a major pseudoscientific cult". Agree or disagree, you are at least very clear where Sokal stands (which is more that can be said for some writers on religion ...).

Sunday, May 04, 2008

Believing in

Provoked by some remarks of Tim Crane's at the last meeting (where he was drawing on a paper by Zoltan Szabo), I gave a talk on Wednesday at the local Serious Metaphysics Group on whether a distinction between "believing in Fs"/"believing that there are Fs" can do any serious work for us. My answer was "no". This was dashed off the previous Saturday afternoon, and I'm outside my comfort zone here. But the talk survived the discussion: so for what it is worth, here it is.

Saturday, May 03, 2008

The hollow halls of academe

A Canadian reader of this blog kindly send a link to this depressing article on the effects of the drive to push ever more and more students through some kind of university education. It has the ring of truth.

Though the effects, I hasten to add, don't really apply so much here in Cambridge where we can be exceedingly picky about those we admit, and a decent number of our undergraduates are still very clever, very committed, and very hard working. Though my sense is that at least some serious departments here, like mathematics, keep up the old standards by taking increasing numbers of undergraduates from abroad, casting the net ever wider. (Hardly a surprise that they can't get enough suitably qualified homegrown students when maths teaching in the English state education system is in a terrible state. For more depressing reading, see this report about UK maths here.)

Friday, May 02, 2008

Good news re IFL?

The annual royalty statement implied that my Introduction to Formal Logic sold pretty modestly last year (I was of course an idiot to write it, given all the competition, but there you go: I wouldn't be told!). But an e-mail from CUP today said that it had in fact sold many more than I was told, the initial big print run is almost exhausted, and there might shortly be a reprint. I won't find out till next week now which is right, the royalty department or the editorial department: but fingers crossed (as it seems rather less likely that their central computer stock system is wrong). [Later: Ahah, both departments were right -- the royalties were for 2007, and there had been a sudden surge of sales in the last couple of months. Hooray.]

That would be terrific if I do get the chance of a corrected reprint, because the first printing has some horrible typos/thinkos. Getting things sorted would make me feel a lot happier about the book.

I typeset the book myself -- so yes, the printing errors were my fault entirely -- in my pre-LaTeX days, using FrameMaker which only runs under OS9. Fortunately, I've still got a working Mac with OS9 installed, and I've just checked that it all seems to be running smoothly (phew). So it shouldn't be a pain to update the files if I do get the go ahead. So here's hoping.