Peter Smith's Blog, page 85

Category Theory in Context

Congratulations to sometime Cambridge student Emily Riehl, now at Johns Hopkins. Her very illuminating lecture notes, aimed at beginners in category theory (albeit mathematically perhaps rather sophisticated beginners) have become a book, Category Theory in Context, published in a new series of ‘Modern Math Originals’ by Dover Books. This is available now in the US, and at the end of the year in the UK.

There has been a link to Emily Riehl’s evolving notes on the category theory page here for a couple of years, and the publishers have kindly allowed her to continue to host a free PDF copy of the book. So you can take a look already if you don’t know her work — but at this low price, it will be really nice to have a paper copy (and of course, tell your library).

Postcard from Paris

Raphael, La belle jardinière, 1507
The Louvre

So, as it happened, we left for Paris on the day of the Presidential Election, and woke up in our hotel to the grim news the next morning. At least, being away from home, with so much else to distract us, we haven’t been glued to the television, internet, and newspapers as we might have been. But the result is, assuredly, a catastrophe.

Depressed by all that, we have found ourselves repeatedly seeking out balm for the soul, especially in the Louvre and the Musée d’Orsay. Here’s just one painting that I find particularly affecting.  (Almost no one stops to look at it as the crowds push past into the adjoining room with the Mona Lisa — yet wouldn’t you rather live with the Raphael, if you could?)

Paris has been rainy and cold — thank heavens for the wonderful Metro! — but still as beautiful as ever.

Life’s choppier waters

My non-logical readings are rather random, except for one pretty firm rule — I try to alternate between reading something new (or at least, new to me), and re-reading something familiar (or at least something that would be familiar, if only my memory for novels and the like wasn’t so terrible). Otherwise, there is no method to it. When I finish one book, I just hunt around the house for something that seems to fit my mood and inclination to read next.  So just recently, I’ve read Sarah Perry’s much praised  The Essex Serpent (which I rather enjoyed, but thought lost its way towards the end), Giuseppe Tomasi di Lampedusa’s The Leopard (which I must have read at least twice before, and which I enjoyed even more this time) and Ian McEwan’s The Children Act (which will go straight back to the Oxfam shop where I picked it up a few weeks ago — a quite unconvincing waste of McEwan’s considerable literary firepower). And I am now re-reading what is surely the best work by one of the best English prose writers of the late 2oth century, namely Jonathan Raban’s remarkable Passage to Juneau. This is proving, if possible, even better than I remember; I am absolutely gripped again.

For those who don’t know Raban’s work, let me link to this sensitive short essay  from the Guardian, whose title I have stolen, which says something about why it is so fine, and which might well (I hope) encourage a few others to read the book.

In another troubled world …

In another troubled world, a young woman – enigmatically beautiful – forever wanders the streets of modernist suburban Rome.

In this equally troubled world of ours, Monica Vitti, who played her so unforgettably, is 85 today.

Which makes me feel rather old.

Back to IFL2

There is now, freely downloadable, a revised version of the first part of my Introduction to Formal Logic, the scene-setting chapters on informal logic before the book gets formal. So these chapters from the planned second edition explain a few logical ideas like validity, forms of argument, counterexamples, proofs, etc. Beginning students who want a logical helping hand might well find them useful (so please spread the word to any class that might profit).

A small number of very kind readers have made really useful suggestions that have improved these early chapters a lot. I will be posting shortly about how to get to see more chapters, but I though I would make these early chapters available, hot off the laptop.

The Greeks win (2)

On the question of metavariables — relaxed italics versus Greek letters. Which do you prefer? Those who voted in the poll  (and too late, I realized I should have had added a  “really don’t care” option), preferred Greek letters by 4 to 1.

Not just for that reason, I decided a couple of weeks ago (before my brain was shut down by a cold) to go for Greek letters. And returning now to the decision, yes, that is still what I am going to do.

Or rather, I am going to do something just a bit more complicated — but I hope even better than an always-italics or an always-Greek  solution.

In the very early chapters of my logic book where everything is still very informal, arm-waving, motivational, I continue to use talk of patterns of argument like  ‘All F are G, n if F, so n is G‘ in that familiar and relaxed philosophy-classroom way which is surely good enough for very introductory purposes. Though I soon point out it is of course arbitrary what we use for placeholders, so long as patterns of recurrence stay the same.

I also then point out quite quickly that it is a bit murky how such informal notation is used (are we representing patterns in the surface form of everyday arguments or patterns in some supposed underlying logical form or what?). We don’t have to worry about this matter much for very introductory purposes (just as we skim over issues about sentences vs propositions, for example).

However, after the half-dozen intro chapters, we very quickly go formal in IFL, saying that we are going to be dealing with everyday arguments by a two-step process: we regiment these everyday arguments into a nice suitable formal language, and then develop tools for assessing arguments in these formal languages. So we quickly find ourselves talking about formal languages and wanting to talk e.g. about patterns of argument in these formal languages — and now I adopt the convention that placeholders/metavariables added to English to help us talk about wffs and other expressions of our formal languages will be Greek letters. And we have a perfectly precise story about what these variables run over (everything is cleanly superficial and syntactic).

So, in short, italic letters used in a loose but good-enough way for relaxed pre-formal use (as in our philosophy lectures when sketching the form of an argument, say); Greek letters are used when we really are talking about formal languages. Neat and perspicuous. No? (Well the proof is in the pudding, but having done some rewriting along this plan, I think it works well!)

The Greeks win (1)

To the Cambridge Greek Play a dozen days ago. Every three years, student actors and a professional directing team put on one or two plays, in the original Greek — this year, a double bill of Antigone (predictably wrenching) and Lysistrata (predictably bawdy and funny) at the Arts Theatre.

And if you think this is bound to be of minority interest, just try to get tickets for one of the eight performances if you don’t book weeks ahead (and if you get tickets, you’ll find yourself in perhaps the most age-mixed audience of any night of the year). There is no attempt to recreate a fake antiquity. The plays are re-imagined, the stagings are modern. In comedies, contemporary references are freely updated, so in  Lysistrata, a messenger and magistrate become Donald Trump and Boris Johnson  (who end up tap-dancing — don’t ask!). But there is every attempt to get the complex rhythms of the ancient language to sing again (and indeed the chorus does sometimes burst into song), in a way that can be spectacularly effective.  Translations-by-surtitles mean you don’t have to rely on  dim memories or sneaky glances at the programme, and work brilliantly.

Again, as with the previous Prometheus/Frogs double bill,  a  fantastic night at the theatre. Creon, who doubled as Donald Trump, and Lysistrata herself were quite outstanding. Though it was just a little sobering to realize that the last time the Cambridge Greek Play  did Antigone, a performance that I saw as a schoolboy, was over fifty years ago.

(We thought, though, that we might have been coming down with “a bit of a cold” that evening. And oh heavens, yes. Hardly been able to stir from the house since. Which in my case goes with a woolly brain, and logic not even on the back burner — the light turned right off until today. Apologies to those to whom I promised some revised chapters of IFLs to look at. I hope to get back to light logical duties tomorrow!)

“My heart in hiding/Stirred for a bird”

Photo from BBC website

When we lived in Aberystwyth, long since, there was only a handful of pairs of red kites left in the whole of Britain, living in the remote mid-Wales hills. But we would see kites occasionally gliding down the Ystwyth valley, to scavenge on the town tip next to the sea. The birds are now much more common in Wales, and have been re-introduced into various parts of England too with great success. But it was so surprising, the sheer delight to be driving out to a pub near Cambridge along a back way, turning a slight bend in the road, and — not a dozen yards from the car — a kite was swooping to the grass verge, grabbed its lunch, and magisterially flew slowly on.

How stirring such moments still are.

The Pavel Haas Quartet at the Wigmore Hall

Another extraordinary concert from the Pavel Haas Quartet last night.

They began with Webern’s Fünf Sätze of 1909 — extraordinarily condensed, emotionally unsettling music, which for me works better in a live performance than it can ever do listening to a recording. Certainly I have never got anywhere as much out of this Webern, as from this characteristically intense but totally controlled performance from the PHQ.

Next, the Shostakovich String Quartet, No. 2. Again, this is unsettling music, emotionally torn and veering from dissonance (even violence — and a resulting broken cello string) to the simply melodic and back.  Compared with the couple of recordings I know best, this again was extraordinarily intense playing last night.

Reviewing a recent DVD of Schubert quartets by Cuarteto Casals, Michael Tanner remarks in passing, “One always speculates – at least I do – about the dynamics, artistic and personal, of string quartet performers”. I speculate too. Was it just my romantic imagination, or at the centre of the slow movement of the Shostakovich, when the first violin has a particularly yearning melody set against the background of chords from the others, didn’t Veronica Jarůšková play directly to her husband and father of their small child, the cellist Peter Jarůšek? It was difficult not to feel that.

After the  interval, the PHQ were joined by the young Dutch cellist Harriet Krijgh for Schubert’s  String Quintet. I think this was the first time that they have performed the piece together in a concert: so the first thing to say is that the ensemble, the stylistic unity, between the five of them was somewhere between superb and miraculous. And as for the interpretation, it is as you would have expected from the PHQ’s award-winning CD (with Danjulo Ishizaka). There was again  an overarching sense of the piece as a whole (so not at all one of those performances where the last two movements come as a disappointing let-down after the extraordinary heights of the first two). There was a particularly driven and emotionally taut third movement, so good that it drew premature applause. But, as always in great performances, the slow movement was transcendental: when it finished, the audience sat in total silence, not a murmur, not a rustle, not a cough.

If I am ever again present at a performance of the Quintet as good, I will count myself blessed.

How do you like your metavariables?

Ok, logic people: it’s time to vote on a Grave Matter of Great Pedagogic Import!

So here I am, revising my intro logic book — which, recall, is intended for first year philosophers. I try to get things fairly precise, at least when we get down to formal business after the initial informal faffing around, but I  also aim to keep things unscary.

I’m still a bit torn about what to use as metalinguistic variables.

In the first edition of my book, I use a sans serif font for wffs in the formal languages, as in: ,  .

Then I use serif italic for metavariables, e.g. as in ‘A’, ‘Fn’.  Though on the board in class, some years I’d actually use Greek letters for metavariables.

Pro using italics: Familiar italic type  makes the book look rather less mathematical, rather less daunting (most philosophers are neither classicists nor mathematicians — so initially is about as friendly as ‘squiggle squoggle’).
Pro using Greek: It’s the convention in more advanced texts so you might as well get used to it straight away. And for lecturers writing on the board, and for students taking notes, keeping track in your handwriting of ‘ordinary letters’ (for formal languages) vs Greek letters (metalinguistic) is much easier than trying to mark the distinction between e.g. upright and sloping letters.

In writing the first edition, friendliness-on-the-printed-page was the winning consideration. I still lean in that direction. But I’m interested to know what you think. So here is a poll (vote thinking of the interests of likely readers of an intro text!).

Note: There is a poll embedded within this post, please visit the site to participate in this post's poll.

By all means add further thoughts in the comments below, as obviously this is a Very Serious Issue.