Elisabeth Brauß at Wigmore Hall

The extraordinary Elisabeth Brauß played again last night at Wigmore Hall, to the warmest of receptions. The concert last night was live-streamed, and is available to watch for 90 days here. In an engagingly varied programme she offered us some rarely performed Hindemith, Brahms’ late four Klavierstücke, and Schumann’s Faschingsschwank aus Wien, all done with such verve and then wonderful delicacy, as variously called for — just a delight.

But the recital started Beethoven’s Op. 109 Sonata, which inspired Elisabeth to quite mesmerising playing with heart-stopping moments: transcendental music, and a performance to more than stand comparison with the very best I’ve heard. Extraordinary, as I say.

Proofs & Theories

I have been reading Proofs & Theories. This is not a weighty logical tome, but the (oddly titled?) very slim volume of short essays and occasional pieces by Louise Glück.

How little, I would have thought, there could be in common between the writing experiences of a Nobel-prize-winning poet and of someone putting together a few elementary logic books! Yet her words resonate. At the very outset, she talks of the anxieties and frustrations: “wanting to write, being unable to write; wanting to write differently, being unable to write differently.” It requires poetic licence, perhaps, to write here as she does of “various kinds of torment” (torment?)… but yes, I recognize the constant sense of striving, “not made serene by sensations of achievement”. When you make the writing public, “The work stands as a reprimand or reproach”, difficult to connect to. And then, very soon, “What strikes me is how far away all this work seems” — and I don’t necessarily mean the particular logical content (in my case) but often the tone, the style.

Which is a feeling that struck me again just now, when I had occasion to re-read a chapter of IFL. I didn’t like the authorial voice very much. I suppose I originally wrote most of that chapter some twenty years ago, but I have revised it in the last five years; but I’m sure I could now do better. Or at least write with a lighter touch. I’m increasingly tempted to have one more bash at that book! (Try again. Fail again. Fail better.)

The occasion for dipping into IFL was very belatedly putting online one more set of answers to exercises, and also adding to the  online page of corrections for typos. I’m probably getting to the point where I should update the file for the printed and downloadable book. (That’s in one way not that much of a palaver; the more time-consuming bit will be checking that I don’t inadvertently make unintended changes in the process!)

I have also updated the corrections page for GWT. 

Have I mentioned here Akihiro Kanamori’s relatively recent book Essays on Set Theory which brings together nineteen previously published essays?

Apart from a handful of more technical pieces, these are mostly historical and/or philosophical essays, or papers focussing on the development and work of particular set theorists of note. It is very good to have these widely scattered essays brought together like this. They are typically readable, interesting and enlightening. Lots about proofs & theories …

And three cheers to College Publications for re-publishing them (as a 600 page book!) so very inexpensively.

Beginning Category Theory: Chs 1 to 16 (etc.)

A short post, just to announce another update of Beginning Category Theory. I have significantly improved the chapter on equalizers and co-equalizers, and I have also split into two, and expanded, the old chapter 15 which covered both limits in general and pullbacks/pushouts in particular. So here is a version of BCT including these newly revised chapters.

Just as before, to keep things simple, there is one long PDF here, with both the reworked chapters up to Chapter 16 and also the remaining unrevised chapters from the 2015/2018 Gentle Intro, with the division between old and new clearly flagged. The same remark applies as before: revised chapters get posted when I think they are an improvement on what went before, not when they are polished perfection! All comments and corrections as always most welcome.

My plan over the next few weeks is to rework/expand the last four chapters in Part I of BCT , and then to go back to the beginning in order to try to smooth out the (sometimes considerable) unevenness in the level of exposition/style of presentation which inevitably creeps in as you are concentrating on local revisions. What fun.

Logic Works?

I can hardly complain about people adding unnecessarily to the over-supply of introductory logic books, having done it myself. But here’s yet another one, Logic Works: A Rigorous Introduction to Formal Logic by Lorne Falkenstein, Scott Stapleford and Molly Kao (published just six months ago by Routledge). I’ve been asked what I think of it. Having now taken a look at the book, I’ll save you the trouble of doing the same. It’s pretty bad. Not that I’ve struggled through all 645 pages. But you’ll forgive me that: life is short and patience limited.

That’s a strange subtitle, no? As if introductions to formal logic aren’t usually rigorous. Or at least, as rigorous as they need to be — and as they say, “sufficient unto the day is the rigour thereof”. You might be tempted to worry, then, that a book that especially advertises itself as “rigorous” is likely to be unnecessarily laboured. You’d be right. And actually it is worse than that. It’s not just heavy-handed in explaining the technicalities, but quite generally the long-winded prose is depressingly clotted and terminally uninviting. I pity the poor students who have this inflicted on them!

Two sample episodes. Chapter 6 presents a Fitch-style deduction system for propositional logic. Good choice (though the system isn’t as streamlined as it could be). But the authors plod through a turgid presentation, without zip and zest, making very heavy going of things. It is really pretty difficult to imagine a reader coming to appreciate that by doing things Fitch-style we can arrive at a really rather elegant, natural, and highly user-friendly system. Things aren’t helped by the printed pages being a typographical mess. 

The same applies in spades to the grimly laborious chapters introducing the language of predicate logic. Who would ever guess from these longueurs that the beautiful and compelling basic idea of a quantifier/variable notation for expressions of generality is so very neat and attractive once explained that it can be introduced well enough to convey a reading knowledge to any beginning mathematics student in half a lecture? (I was surprised to see that one of the authors does have some mathematical background — yet the writing throughout gives no sense of the aesthetic attractions of rigorous mathematical ideas.)

I could go into more detail, but I won’t. A rather depressing read, then, which I can’t recommend at all. If you want a good introduction to formal logic which also ranges quite widely, I’d stick to Nick Smith’s!

[Added And see Phil’s comment!]

One True Logic

There’s a new book out by Owen Griffiths and Alex Paseau, One True Logic: A Monist Manifesto (OUP). As the title suggests, this argues against logical pluralism. Yes, of course, there are myriad logical systems which we can concoct and study as interesting mathematical objects. But what about the logic we actually use in reasoning about them and about other mathematical matters? Is there in fact one correct logic which tracks what really does follow from what? Our authors take a conservative line, in that they are anti-pluralist: there is indeed one true logic for in-earnest applications. They are unconservative in defending a highly infinitary logic in that role.

I’ve read the first few chapters with enjoyment and enlightenment. But I’m going to have to shelve the book for the moment, as it will be too distracting from other commitments to engage seriously with the rest of it for a while. One of the delights of somewhat senior years is finding it more difficult to think about more than one thing at a time. (“But what’s new?” murmurs Mrs Logic Matters from the wings.)

For a start, I must continue cracking on with the category theory project. I have now revised Chapters 1 to 15 of Beginning Category Theory. So here they are, in one long PDF which also includes the remaining unrevised chapters from the 2015/2018 Gentle Intro.

In this iteration there are quite a few minor changes to Chapters 1 to 13 (correcting typos, clarifying some phrasing, deleting an unnecessary section, adding a new theorem in §12.2, etc.), though there is nothing very significant there. I have also now revised Chapter 15, the first of the two general chapters on limits/colimits. This and the preceding chapter on equalisers/co-equalisers could surely do with more polishing and lightening-up in places. But as I’ve said previously, I’m including revised chapters when they are at least an improvement on what went before (I’m not waiting for final-draft perfection!).

If you are like me, you are looking for the more-than-occasional consoling distractions from the state of the wider world. Let me share one.

Of the great pianists I have had the chance to hear live over the years, the one I perhaps find the most emotionally engaging of all is Maria João Pires. Her unmannered directedness goes straight to the heart. So here she is, playing Schubert, Debussy and Beethoven, in a video recorded in Gstaad last August.

Not Thinking Like a Liberal

For over ten years, Raymond Geuss and I were both members of the Cambridge Philosophy Faculty. But apart from one year when, like two unbelieving bishops, we had to co-examine a metaphysics paper, I doubt we spoke more than a few hundred words. I suspect he thought I was simply an uninteresting unphilosophical philistine. In fact, we might have had just a little more in common than he suspected, apart from contrarian tendencies — stretching from being both brought up as Catholics to both being amused by the racier ancient Greek epigrams (indeed the first things I ever read by him were his versions in his Parrots, Poets, Philosophers and Good Advice).

I have now just been reading Geuss’s new and very personal short book Not Thinking Like a Liberal (Harvard UP) with great enjoyment and some enlightenment too. He starts by recounting his strange out-of-its-time education, at a Catholic boarding school in the USA, largely staffed by Piarist priests, many Hungarian emigrés. This taught not a narrow authoritarian Catholicism, but a wide-ranging European culture transplanted to Pennsylvania. And Geuss finds — especially in the remembered teaching of one Fr. Krigler — the roots of his own distancing from the shallow “liberalism” of the kind he discerns in much political thinking. The earlier parts of the book are indeed fascinating and insightful.

Later pages found me a bit less carried along. Geuss does no better than others, for example, in conveying what was supposed to be so impressive about his teacher Sydney Morgenbesser at Columbia (Morgenbesser sounds pretty irritating to me). And the concluding pages about unclarity are rather too arm-waving, and the pages about negativity rather too negative, for my liking. But I still very warmly recommend this book as perhaps the most engaging of his writings (apart from those epigrammatic poems, that is!). It got me thinking about scripture and religious traditions, about authority, about education … and about liberalism and the tenor of our times.

Beginning Category Theory: Chs 1 to 14 (etc.)

Back from Cornwall, and I have now revised Chapters 1 to 14 of Beginning Category Theory. So here they are.

As before, to keep things simple, there is one long PDF with both the reworked chapters and the remaining unrevised chapters from the 2015/2018 Gentle Intro. I have added a little to Ch. 2, and tidied up Ch. 12. But the main revision this time is a much improved version of Chapter 14 on equalizers and co-equalizers. I’m still not entirely happy with it, but it is a heck of a lot better than it was. Enjoy!

Famous last words, but looking ahead, I think the next few chapters will be an easier job to revise, so I hope to now pick up speed again.

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It is a delight to see that, with thanks to Tim Crane, there is now a new website in memory of Hugh Mellor, who died almost two years ago on June 21, 2020. The site collects Hugh’s philosophical work, downloadable papers, memoirs and obituaries (and some photos, including this one by Mrs Logic Matters).

I do miss Hugh a good deal, so I’m much looking forward to looking round the site. I’ll let you know about particularly interesting things I find in the unpublished lectures and talks etc.

Postcard from Cornwall

The first time back in St. Mawes since the beginning of the pandemic. A magical place. It has been wonderful to look out over the harbour even on wetter, greyer days: a delight from early morning to the very end of the day. And we have walked and walked hereabouts. Cobwebs blown away. For a couple of weeks, the dire mess of the wider world seems particularly far away.

Soon, it‘s back to Cambridge, to category theory (I’m promising a much better chapter on equalizers/co-equalizers), some musings on a philosophical view from Terence Tao, some potshots at a recent rather dreadful intro book on formal logic. But just for now, logic can look after itself. The sun is going down over Roseland. Calm sea. Peace.

New Brahms album from the PHQ

The Pavel Haas Quartet’s recent performances of the Brahms quintets with their friends Boris Giltburg and Pavel Nikl (I’ve caught some online) have been just stunning. And now there is a new album released today. Extraordinary.

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