Peter Smith's Blog, page 61

The Pavel Haas Quartet — at Wigmore Hall



The Pavel Haas Quartet glimpsed rehearsing the Shostakovich Quintet for their Wigmore Hall concert on Wednesday with the terrific Boris Giltburg. The evening performance was wonderful, the best I’ve heard that piece played, full of ambiguities, tensions, life and colour. Indeed they rocked! (Or as the Times reviewer put it, they were at the top of their game. “The prelude was beautifully drawn, its counterpoint perfectly balanced. The sulphurous jig of the scherzo thickly painted, grimacing theatre music, while the intermezzo unfolded with magical transparency. There’s a volte-face in the finale to levity, a shift in tone that the quartet managed here with the grace of a master conjurer.”)

Here they are playing the intermezzo of the Quintet live on the BBC the previous evening  (starting 43 mins in).

And here are just the Quartet on Swiss Radio, a concert they played in Geneva earlier in the month (Schulhoff, Quartet No. 1; Dvorák, Quartet No. 12, ‘American’; Tchaikovsky, Quartet No. 3).

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Luca Incurvati, Conceptions of Set

Quite delighted to pick up in the CUP bookshop Luca Incurvati’s newly published Conceptions of Set and the Foundations of Mathematics. I saw some draft chapters some years ago when Luca was still in Cambridge, and this should really be very good. (Hopefully there will be a cheap paperback version sooner rather than later — but meanwhile do make doubly sure your library gets a copy, and/or gets e-access via the Cambridge Core system!)

I’ve dipped in a little, and plan to blogpost about the book  once I’ve finally sent off the camera-ready copy for IFL2 in a couple of weeks. (Yes, yes, you’ve heard it before; but the incremental revisions will come to an end, and Achilles will catch the tortoise, Zeno’s arrow will reach the target, and the my second edition will reach the publishers … the seemingly impossible sometimes happens.) In fact, I want more generally to get back to occasionally blogging about books as I read them, if only because I find it a very good way to fix my ideas. But in the meantime, it is back to fishing for typos and thinkos … What fun!

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A European moment



This was new to me, and was being shared by some at the moment of Brexit, making a sunny counterpoint to what I found a rather miserable evening. If you too haven’t seen it before then, whatever your views, enjoy!

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Natural deduction for quantifier logic

It’s very late in the day, as I hope to get IFL2 finally off to the Press within the next fortnight or so. But since the natural deduction chapters are new to the second edition it is understandable (I hope!) that I am still worrying away at them, tinkering here and there. Here then is the latest version of the three main chapters on QL proofs. Any last minute corrections and/or helpful comments (other than, perhaps, “use a different proof system”) will still be most welcome …

There is no real novelty here except perhaps by mistake: though one feature of the handling of QL proofs is the sharp distinction made between dummy names (parameters) and fixed-interpretation proper names, as I think this makes for conceptual clarity.

Some context for these chapters: As background, the reader will already be familiar with a Fitch-style system for propositional logic (pretty similar to The Logic Book‘s system, but with an absurdity constant and EFQ). The reader will also have done a lot of prior work on the language of QL, at least in an initial way,  hopefully coming to these chapters with a decent understanding of the quantifier/variable notation, and a lot of practice at translations. They won’t, however have met yet the identity predicate, and QL= proofs will come later.

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Category theory and quantum mechanics

My last link to something categorical turned out to be pointing to a less-than-splended online resource. I hope this is rather better!

I’d heard tell of people interested in quantum foundations and quantum information getting entangled (see what I did there?) with category theory. And by chance, I  stumbled a few days ago across details of a course currently being run in Oxford. The course materials are a late draft of Categorical Quantum Mechanics by Chris Heunen and Jamie Vicary which has recently in fact been published as a book by OUP. This strikes me (in contrast I fear to that book I mentioned by Fong and Spivak) as extremely lucid and well-organized; and you don’t in fact have to read very far to see why quantum theorists might indeed be interested in monoidal categories as a mathematical tool. My QM is very very rusty; but if you have a smidgin of knowledge, this does seem worth dipping into, if only to get a glimpse from the sidelines about what the cool kids are up to …

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Empty domains, again

Here’s a rewritten four-page chapter from IFL2 on empty domains. Difficult to know how to handle this topic. Many intro texts just skate over the issue. An earlier draft perhaps said a bit too much a bit too confusingly. Hope this strikes a better balance. Last-minute comments always welcome!

(By the way, “sets*” with a star is my usage in the book for when I really mean sets as objects in their own right — the ones that play a starring role in full-blown set* theory — as opposed to when I’m occasionally using lightweight talk of virtual classes which can be translated away.)

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Programming with categories, again

Well, I started watching the on-going series of lectures which I’d linked to a couple of blogposts ago. Frankly I can’t say the lectures are at all good, and can’t now recommend you try them. They all seem, to put it kindly, very underprepared, underpowered, undercooked, low in nutritious content!

I’d say more, but I’m saved the effort because there’s now a long comment to that earlier post sent by Peter F. which well expresses some of my concerns about the whole thing.

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Imogen Cooper plays Schubert’s last three piano sonatas

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Programming with categories

One of the books I’d set aside until the main work on IFL2 was done and dusted is Brendan Fong and David Spivak’s An Invitation to Applied Category Theory (CUP, 2019 — there’s a late version freely available here). I’ve now had a first proper look. I can’t say that the book overall works very well for me. When the authors are talking about things I already know a fair bit about, I find there are indeed interesting approaches and illuminating comparisons. But when they are introducing new-to-me material it, all goes by too fast to be very helpful. That could of course just be a comment on my inadequacies as a reader! — but I’d be quite surprised if mine weren’t a common reaction. Chapter 7 on sheaves and toposes, for example, is surely going to pretty impenetrable to someone who doesn’t already have some handle on this stuff.

However, there are obviously lively minds at work here, and so I’m encouraged to take a look at another of their projects — an MIT course of lectures with the estimable Bartosz Milewski (whose Category Theory for Programmers I think is terrific). The course, Programming for Categories, has a web page here with planned links to videos of each lecture and also links to lecture notes. The lectures are just starting, and new videos/notes should appear five times a week for four weeks. I’ll hope to learn a lot!

 

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Logic: another “Five Books”

There is an entry I hadn’t noticed before (a recent one?) on the always interesting though sometimes annoying Five Books website, this one suggesting five books on logic.

The recommendations come from Tom Stoneham (a professor of philosophy at York). And they do seem to me to be a somewhat rum collection. I wouldn’t have dreamt in a month of Sundays of starting with Colin Allen and Michael Hand’s Logic Primer (this very brisk and to my mind dull effort may or may not work as a back-up to a suitably tailored lecture course, but as a teach-yourself book there are surely dozens better). Wilfrid Hodges’s Logic, Stoneham’s other mainstream textbook recommendation, is a vast improvement; but has its quirks. While the idea that you’d recommend Wittgenstein’s Tractatus to someone wanting to find out about logic and why it matters strikes me as frankly perverse.

But it is very easy to carp! So what would I be recommending to the same intended readership?

Well, why not start off with Graham Priest’s typically zestful Logic: A Very Short Introduction (OUP), which should intrigue and tantalize.

And then I’ll suggest — well, forgive me, but of course I will! — the forthcoming second edition of my Introduction to Formal Logic (CUP) as a gentle introduction with a natural deduction flavour, followed by Nick Smith’s longer and more discursive Logic: The Laws of Truth (Princeton). My namesake’s book engagingly re-covers the same ground as mine and rather more as it highlights trees, with more side-discussions along the way (lots of interesting endnotes!).

I’ll follow Stoneham in rounding off the introductions to formal work with two more books that look sideways at related philosophical issues (rather than pushing on with more technical logic — the TYL Guide will give someone more than enough pointers on that!). But which two books? Stoneham recommends Quine’s short Philosophy of Logic as being “all about the philosophical arguments that underlie the decisions to do logic in one way or another”. But my book and Nick Smith’s already say quite a bit of that. So let’s set Quine aside, good though it is. As an alternative, how about Stephen Read’s still zippy, but more expansive and more adventurous, Thinking about Logic (OUP)?

Stoneham also recommends Mark Sainsbury’s Paradoxes, but this revisits topics already touched on in Graham Priest’s little book and in Read’s. So why not have some very instructive logical fun with Raymond Smullyan (to be read in parallel with the worthy books by the Smiths!)? How about starting with his old What is the Name of this Book? (now republished by Dover)?

So there you have Stoneham’s five (if you’ve clicked the link, you can also read his reasons, which I’d certainly want to challenge), and you have my five (as of this evening!). What would be your five, still bearing in mind the intended audience?

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