Logic Matters

That isn’t quite a picture of our house, though it is a bit of a losing battle against books piled in every room (and often dangerously on the stairs too …). They are tolerably organized in my study, not because I’m naturally tidy but because I know the aggravation involved if I can’t lay my hands on a work book that I know I have somewhere. But elsewhere things are rather more haphazard. Why is Lichtenberg next to Wolf Hall, or the great Courtesans and Fishcakes snuggled up to a mildly embarrassed Alan Bennett? But such happenstance makes for good browsing when you are looking for the book, the one that fits the mood and the time of day and the weather outside and all those other mysterious factors that determine what is right for the occasion. I know there are people who catalogue their books and know exactly who has borrowed which. But it’s not like that here.

Nor for Susan Hill, as she recounts in her engaging Howard’s End is on the Landing which I’ve just finished. If you too have accumulated more books than you know what to do with and have eclectic reading habits, you’ll love her book, nodding in agreement here (as she explains why she keeps books she knows she won’t read again), and starting with surprise there (she doesn’t ‘get’ Jane Austen? Twelfth Night doesn’t make her Shakespeare shortlist??). Reading her book is like a one-sided conversation with a ridiculously well-read, gently opinionated, meandering friend.

And as you’d expect from a fine writer, Susan Hill is very keen on the virtues of slow reading. “Fast reading of a great novel … will not allow the book to burrow down into our memory and become part of ourselves, the accumulation of knowledge and wisdom and vicarious experience which helps to form us as complete human beings. It will not develop our awareness or add to the sum of our knowledge and intelligence.” Which, pace the po-mo loonies, is why serious reading matters.

The new Hans Rausing Professor of HPS here, Hasok Chang, is planning to run seminars in the mode of Peter Lipton’s much admired institution — and the plan for the first term, is to look at the collection of essays Scientific Pluralism, edited by Stephen Kellert et al. I’ve been having a quick browse, to see if I will want to go along. Well, I think not. The book seems a lightning tour ranging over far too much: I don’t find that kind of enterprise likely to be of much value.

I’m sad to say that this seems particularly the case with the essay by Geoffrey Hellman and John L. Bell on ‘Pluralism and the Foundations of Mathematics’ (complete in the Google Books excerpt linked above). I much admire both authors, but this is really ill-judged.

The essay divides into two parts. After a preamble, there are four pages — yes, just four pages — arguing to the conclusion that the “classicism-constructivism duality in mathematics” illustrates the need for a “pluralistic approach”. This is feeble stuff indeed. There is a bit of Dummett bashing that assumes that he just has a verificationist theory of meaning (as if e.g. Crispin Wright had never written). There’s the bald claim that “it is clear that classical reasoning is especially useful in scientific contexts” (so much for Neil Tennant’s defence in depth of the claim that good science only needs intuitionistic logic). There’s a long quote of David Lewis’s now too-familiar passage “I’m moved to laughter at the thought of how presumptious it would be to reject mathematics for philosophical reasons. Etc. Etc.” which, as a number have by now remarked, is dangerously near point missing (see for example Alexander Paseau’s essay in BJPS 2005). Fictionalists, predicativists, constructivists have their philosophical reasons for making philosophical claims, perhaps discriminating between different metaphysical statuses for different parts of classical practice: and sure, most mathematicians aren’t interested in reflecting on those discriminations. But so what? I’m afraid that Hellman and Bell’s breathless pages wouldn’t pass muster as part of a final year undergrad. dissertation.

The second part of their paper is mostly about topos theory as an alternative to set theory as a foundational framework. But again, as you’d expect from the fact that it is only seven-and-a-bit sides, this is far too fast and allusive to be of use to anyone who doesn’t already know a lot about this stuff (and even if you do, it is pretty unclear what the take-home message is).

Isn’t this kind of thing becoming more and more common? — pieces written for Yet Another Collection, maybe generated by Yet Another Conference, which don’t have to get past an anonymous refereeing process, and which just go too fast. I think it behoves philosophers, of all people, to take things slowly. Or am I just getting old?

If the header for this post means absolutely nothing to you, then read no further. But a few people might be interested in my impressions of these classy desktop speakers. Are they worth the not inconsiderable expense?

A bit of background first. I recently re-organized my very small study at home and bought a new iMac. And I’ve found myself listening to music a lot through the surprisingly-not-too-awful speakers on the computer. (I should say that, for someone with something like a thousand classical music CDs, I’ve put up with some really crap music playing systems, and the one I had in my study before rearranging stuff was pretty hopeless: even listening through the iMac’s speakers was about as good.) And I really liked a lot having the music coming from in front of me as I worked at the computer, rather than from shelves to my side. So I started investigating the options for improving things with desktop speakers actually designed for “near field” listening. The reviews for the B&W MM-1 are extremely good, with the price point being the only clear negative for many reviewers. I asked in the Apple Store, and — this is worth knowing, as it was a surprise to me — their “14 day open box returns” policy applies to everything they sell apart from software, including non-Apple kit. I knew from my experience of buying a 27″ iMac and then trading down to a 21.5″ that it really is a no fuss policy, and so it really is a no risk option to take home a pair of these speakers and try them out.

One or two reviews had  mentioned their performance on classical music at relatively low volume being particularly good: this recommendation certainly ticked the boxes for me, because that conforms exactly to my study listening habits.

But of course ‘classical’ could mean anything from Bruckner symphonies to early Venetian lute music (well, both are “classical” in the all-embracing sense that seems to be used in hi-fi reviews); and my tastes are nearer the latter — which is pretty exposing stuff. How do the speakers fare in practice on the kind of music I listen to? Here’s some reactions. The warm positives (just a selection of examples):

• Brendel playing Schubert impromptus (his later, digital recording): amazing, revelatory sound (whether playing the CD or imported into iTunes with AAC at 192Kb).
• Perahia playing the Goldberg Variations: similarly excellent.
• Felicity Lott singing Schubert (the old IMP CD): again, revelatory.
• Mullova playing Bach partitas — jaw-droppingly good quality sound.
• Lindsays playing Haydn Op.54, no.1 (which I happen to be listening to as I write this): extemely real, natural sound. Difficult to fault.
• Haydn, Symphony 35, AMA conducted Hogwood. Again quite excellent.

Sort-of-negatives:

• I happen to have 128KB MP3s of the Alban Berg Quartet playing Beethoven: these didn’t sound at all good. Not the speakers’ fault of course, but they do expose less-than-high-quality digital sources.
• I wouldn’t normally sit at the computer listening to opera, but I did try the speakers on some opera CDs. With the speakers only a couple of feet from your head, the opera seems to be taking place in an odd location and felt uncomfortable (you can in real life sit very up-close and personal to chamber music and even small classical orchestras, as you might do e.g. in the Sheffield Crucible Studio’s ‘music in the round’; but you want opera coming from further away! Oddly I preferred listening on headphones, where there is no definite location. I got the same effect with Solti’s recording of Schubert’s Great C major — but again not what I’ll be listening to at my desk.

So my summary verdict: if you want decent reproduction of chamber music, piano, song — small intimate music — then these small speakers made for intimate up-close listening seem pretty wonderful: as I suppose they should be for the price. They do certainly seem to live up to reviews like this one. As, as I said, I’m no hi-fi buff, and it wouldn’t have taken a great deal to beat what I was using before hands down and cheer me up: so your mileage could vary. However, I’m very happy with them. They certainly won’t be going back to the Apple Store …

I have been rather quiet here, not because life has been so wildly over-exciting as to distract me from blogging but for the opposite reason. Nowt much happening.

My Faculty office is, at the moment, out of bounds as the builders are in my end of the Raised Faculty Building stripping out and replacing the heating system. (“Why wasn’t it done when the building was refurbished not so many years ago?” Jolly good question. And next summer they are going to replace all the windows, so that will mean more disruption and another round of covering everything up and cleaning after … Brilliant money-saving efficiency, eh?) But an upshot is that I’ve found myself working in the Phil. Faculty library, for the first extended period in … what? … forty years?? Which all seems a bit strange. Though very quiet and congenial with no students around.

Anyway, as I’ve said here before, my plan was/is to write a book which says enough to explain what is going on in Gentzen-style proofs of the consistency of arithmetic (how do they work? what do they show given that we all think that PA is consistent anyway, don’t we?). But it isn’t going quite according to the original plan, as I found that there wasn’t anything that I could point to as giving the background theory of small countable ordinals in the way that I’d want to have it presented. There are aspects I really like about Wacław Sierpiński’s old Cardinal and Ordinal Numbers (from 1958); and the short treatment in my friend and colleague Thomas Forster’s Logic, Induction and Sets (CUP, 2003) is very helpful. But all the same, I find myself spending the time writing a long tutorial on small ordinals as the first part of the book as now re-planned. More precisely, this is a tutorial (addressed to myself as much as anyone!) on small-ordinals-without-set-theory. And as always with these things, doing it carefully with (I hope) total transparency about what depends on what takes for ever (or at least, takes me for ever).

Perforce, then, I’m taking it slowly. I just hope that when this part of the book is done someone else will find my route through this stuff an interesting one to take. Anyway, when it is gets to a natural division point and is sufficiently polished, I’ll make this tutorial available here (perhaps 120 book pages?) for no-doubt much-needed comments. Watch this space, though don’t hold your breath.

By the way, talking of Sierpiński, Rafal Urbaniak has pointed me to a whole list of books by Polish mathematicians which mentions another nine by him (gotta admire the energy!), including a seemingly rather nice book in English on the Theory of Numbers, available online .

Oops. I’ve now sounded off over two hundred times on Ask Philosophers.

Well, doing that is a more productive form of procrastination than some alternatives that I could mention. And Ask Philosophers is a Good Thing. I can warmly recommend the philosophical good sense and humanity of many of my co-panellists (particularly Louise Antony, Richard Heck, Thomas Pogge, and Allen Stairs).

When I moved to Cambridge a dozen years ago, people asked why I wanted to leave Sheffield which was and is such a good department. “But aren’t the attractions of Cambridge obvious?”, I’d reply, “it’s more work, less money, and astronomical house prices.” (There’s an explanation, then, for the noted tendency of Cambridge to appoint people who already have strong Cambridge connections: we are the ones daft enough to want to take the deal!)

The Bertrand Russell Professorship of Philosophy has now been advertised. The title is now wonderful: but as to the work/money/living costs … well, it will be very interesting to see who is still susceptible to the other inestimable attractions of Cambridge.

There’s a new page on this site, linked on the right, for anyone interested. And for the rest of you, I’ll try henceforth to keep the blog an iPad-free zone.

Mind you, I’m only saying try …

[Added] Well, since that page was accessed over 1400 times in the first two days, maybe there is rather more interest than I thought!

To London yesterday. We had to be near Sloane Square, so we took the opportunity to visit the Saatchi Gallery. We were most impressed. With the Gallery. Unfortunately the contents are mostly a pile of crap. We can recommend the restaurant for a light lunch though. Especially if the sun is shining and you can sit under one of the umbrellas outside.

Later we spent a very enjoyable and instructive hour at the (sparsely attended, so pleasingly very quiet) free exhibition at the National Gallery, Close Examination: Fakes, Mistakes and Discoveries.

One room, ‘Being Botticelli’, raises something of a philosophical question. There, side by side, are two paintings bought by the gallery in 1874, from a sale of pictures collected by one Alexander Barker. The first is the wonderful ‘Venus and Mars’. The other picture, ‘An Allegory’ is a crude travesty (though it isn’t a fake — scientific investigation shows that it wasn’t painted long after Botticelli’s masterpiece.)

Yet at the time, this too was confidently attributed to Botticelli, and indeed at the sale commanded the higher price. But now, seeing them together, even the most casual gallery visitor (counting myself as one) must think how was that possible?. How was it not just obvious at the time that the paintings were of utterly different quality, technically and aesthetically? — well perhaps that’s not quite so obvious from the small reproductions here, but stand in front of the pictures, and the difference is startling. The proud buyers of ‘An Allegory’ for the nation must have seen the picture differently: what is it about aesthetic perception that can allow such extraordinary shifts?

I’m sure some philosopher must have written interestingly about such things. Suggestions?

Just a few thoughts, after five or six weeks of happy togetherness with my new iPad …

It is no wonder that we love our books: in reading them, we cradle them close to our heart.¹

Yes. And we similarly cradle an iPad. Even the Apple cover, with which we lovingly protect it, is designed to make the iPad’s hard shell seem softer and warmer in the hand — more like a book in fact. And the experience of reading on the iPad is as good as the tactile feel. Even those PDFs of articles you’ve downloaded from JSTOR, or scanned older books acquired one way or another, are at least as readable as your crumpled print-outs; and proper ebooks or modern PDFs of academic books are a delight. It was no surprise to me, then, that a recent study suggests that people find the experience of reading on an iPad (or indeed a Kindle) comparable with reading a printed book, and both much to be preferred to reading on a computer screen.

And that’s not to mention the ease of reading e.g. Anna Karenina in bed, rather than that handsome but massive hardback of the wonderful newish Pevear and Volokhonsky translation (about which more another time).

So — as someone who spends a lot of the day reading on screen — I haven’t had a moment’s regret about getting an iPad. On the contrary, I get more pleased as the days go by. Of course, it isn’t a laptop substitute for when e.g. you want to do extended writing in LaTeX (though I can imagine that soon enough we’ll even be able to do at least modest amounts even of that, adding a paragraph or two to a paper-in-progress: imagine the next version of DropBox has a built-in text editor, you can send source files to be compiled to some server which sends the result back to DropBox, and you can flip between source and PDF …). But for reading papers in the almost-awesome Papers², or reading books in PDF form, for internet trawling, keeping tabs on your emails, jotting down a few notes in Evernote (automatically synced to your computer), updating appointments and other low-key writing tasks — and even maintaining a blog! — the iPad is fantastic. I find myself taking the it around more and more instead of a laptop.

Of course, those of you who prefer hair shirts to cashmere can buy a cheap-as-cheaps netbook, become Linux geeks, and feel superior: but I’d rather have the aesthetics and delights of the iPad, thank you very much.

^{1. I steal this thought from http://craigmod.com/journal/ipad_and_books/}

^{2. Why oh why is the long promised Papers v.2 so alarmingly delayed? We just want (a) Papers to be aware of PDF books as well as articles, and perhaps (b) to allow a bit of highlighting/annotating of PDFs. Is that too much to ask?}

One to watch if you are a philosophical LaTeX geek? —  PhilTeX, a fairly new group blog on possibly relevant LaTeX matters. I’ve added links on the blogroll here and on the LaTeX for Logicians pages.