The plan has been to post a weekly link to share some performances, ones that you too might find really worth pausing over for a reflective moment one evening. As I said at the outset, they might be old or new, maybe just part of a concert, perhaps just half an hour more or less — and available online at least for the next couple of weeks, so you can find a chance to stop to watch and listen.

This sixth week — in particularly grim days — let’s turn to Bach, who else? Here is the wonderful Beatrice Rana playing Bach BWV 1052 with the Amsterdam Sinfonietta in 2019. [22 min.]

I particularly like the way the small-forces orchestra is standing closely gathered round the piano as she plays. It seems to engender such engaged performances from both pianist and band. The result surely is a stunningly good interpretation of this great music.

The old chapters on products (pre-categorial reflections followed by the categorial story) have been considerably tidied up, with the more tedious intricacies rather better corralled into a separate optional chapter, and other chapters giving the main conceptual news re-organized.

This takes us to roughly the half-way point in the planned coverage of Category Theory I. As always, the usual invitation applies — comments on this work in progress most gratefully received!

Moving on through Greg Restall and Shawn Sandefer’s Logical Methods, Part II is on propositional modal logic. So the reader gets to find out e.g. about S4 vs S5 and even hears about actuality operators etc. before ever meeting a quantifier. Not an ordering that many teachers of logic will want to be following. But then, as I have already indicated when discussing Part I on propositional logic, I’m not sure this is really working as the first introduction to logic that it is proclaimed to be (“requires no background in logic”). I won’t bang on about that again. So let’s take Part II as a more or less stand-alone treatment that could perhaps be used for a module on modal logic for philosophers, for those who have already done enough logic. What does it cover? How well does it work?

Part I, recall, takes a proof-theory-first approach; Part II sensibly reverses the order of business. So Chapter 7 on ‘Necessity and Possibility’ is a speedy tour of the Kripke semantics of S5, then S4, then intuitionistic logic. I can’t to be honest say that the initial presentation of S5 semantics is super-clearly done, and the ensuing description of what are in effect unsigned tableaux for systematically searching for counterexamples to S5 validity surely is too brisk (read Graham Priest’s wonderful text on non-classical logics instead). And jumping to the other end of the chapter, there is a significant leap in difficulty (albeit accompanied by a “warning”) when giving proofs of the soundness and completeness of initutionistic logic with respect to Kripke semantics. Rather too much is packed in here to work well, I suspect.

Chapter 8 is a shorter chapter on ‘Actuality and 2D Logic’. Interesting, though again speedy. But for me, the issue arises of whether — if I were giving a course on modal logic for philosophers — I’d want to spend any time on these topics as opposed to touching on the surely more interesting philosophical issues generated by quantified modal logics.

Chapter 9 gives Gentzen-style natural deduction systems for S4 and S5. Which is all technically fine, of course. But I do wonder about how ‘natural’ Gentzen proofs are here, compared with modal logic done Fitch-style. I certainly found the latter easier to motivate in class. So Gentzen-style modal proof systems would not be my go-to choice for a deductive system to introduce to philosophy student. Obviously Restall and Sandefer differ!

Overall, then, I don’t think the presentations will trump the current suggested introductory readings on modal logic in the Study Guide.

Chamber music can be profound, difficult, emotionally wrenching. But much can be more fun, a delight for friends or scratch ensembles to play just for the enjoyment of it.

Last year, while in Manchester to play concerts as a soloist with the Hallé, Elisabeth Brauss got together with the orchestra’s Sergio Castelló López and Simon Turner to play Beethoven’s Piano Trio in B-flat major, Op. 11 for piano, clarinet and cello (known as the Gassenhauer Trio). The Hallé have just newly put a video recording online, and it is captivating, with the players’ enjoyment indeed shining through. So I thought I would share! [Just 22 minutes]

It is an odd business writing books (other than research monographs which get reviewed in the journals and perhaps with luck discussed by a few colleagues).

You send your best efforts out into the wider world to take their chances and have precious little idea of how they are really received. For example, the second edition of IFL is downloaded over 10K times a year. I don’t think one reader in a thousand lets me know how they found the book.

So I take comfort and encouragement where I can! And I’ve just spotted a new review on Amazon for Godel Without Too Many Tears (the first for its second edition, though the review is linked to the original edition, which I’ll try to get changed):

Clearly the best concise introduction to Gödel’s theorems ever written. I bought the first edition and found in a very few places errors and margin for a more felicitous presentation. Nothing, however, that could stump an astute reader. In the second edition … this is all corrected. The book really does accomplish the miracle of being self-contained, though, of course, a reader may come up with questions not covered in the book. In that case it may be helpful to consult the author’s more complete treatment in “An Introd. to Gödel’s Theorems” (also cheaply available from Amazon) or a book like Boolos, Burgess & Jeffrey.

I recommend the book not only to students but also to academic teachers. It is a model of how logic ought to be taught.

I have been listening to a couple of CDs by the violist Dana Zemtsov. And I thought I’d also share this video of a relaxed and very engaging short concert she gave with friends a couple of years ago. I particularly enjoyed the opening two pieces by Beethoven and Lutosławski, and the final pieces (starting at 51.40) by Shostakovich.

What took me to exploring Dana Zemtsov’s recordings was finding that she is to be the violist with the Pavel Haas Quartet for the coming months. She is obviously a very fine player, but also (or so it strikes me) her approach and playing style should be a terrific fit. [Added: And a review of their Madrid concert, a couple of days ago, comments that they were “perfectamente integrados”, mentioning particularly Dana Zemtsov’s viola as something “fantástico” given how new she is to the quartet.] I really do hope this works out for them all — we so need the PHQ to settle into a happy new line-up and then feel able get back to the recording studio!

Meanwhile, here are two BBC radio recordings from PHQ concerts at last year’s Bath Mozartfest. First, the Prokofiev’s String quartet No 2 (which they recorded on a prize-winning CD a dozen years ago) and Schubert’s String quartet in G major, D 887 (starting at 6.14). [You might need to use a VPN pointed to the UK to access BBC sounds.]

And some other PHQ news, in case you missed it. In the BBC Radio 3 Record Review programme last Saturday, their “Building a Library” episode was surveying recordings of Shostakovich’s String Quartet No 8 in C minor. Surely one of the very greatest pieces of chamber music of the second half of the twentieth century. The reviewer’s top recommendation was the PHQ recording. So yet another accolade for them. You can listen to a podcast of the episode here. And then their recording of the Shostakovich was broadcast here (starting at 17.00).

The ‘I’ in the new title signals that I am carving the old notes into Part I and Part II, and I am planning to work up Part I into a decent shape, while quite putting aside Part II for a good while. (Lichtenberg: “Just as certain writers, after first dealing their material a rough blow, say it naturally falls into two parts”.) And ‘Notes’ is a frank admission that the material still won’t be very smoothed out, and I’ll not be aiming for a polished book-style finish. ‘Gentle introduction’ means that it goes no doubt far too slowly for some.

I’d be really interested in comments on Chapter 3, which has given me a lot of grief.

Not my usual kind of music! But, this week, here is a performance of Grażyna Bacewicz’s Double Piano Concerto of 1966. The soloists are Peter Jablonski, who last year released a very well received CD of Bacewicz piano works, and Elisabeth Brauss. And since this concert in December, they have recorded the Concerto together for another CD to be released in the spring. Visit the concert page here, press Katso (play), and go to about 22.30 for the Concerto (which last less than twenty minutes). I’m not sure what to make of the music, but I much enjoyed watching them play!

Peter Jablonski and Elisabeth Brauss also play a very short and delightful encore by Ligeti, at 42.10. And then, if you want something a lot calmer, here is another very short piece, this time by Hindemith, quite beautifully played by Elisabeth. Hopefully a trailer for a DG solo disk by her.

I have now had a chance to read the first part of Greg Restall and Shawn Sandefer’s Logical Methods, some 113 pages on propositional logic.

I enjoyed this well enough but I am, to be frank, a bit puzzled about the intended readership. The book’s Preface starts “Welcome to Logical Methods, an introduction to logic for philosophy students …”. And the text does indeed seem to start right from scratch. But Restall’s web-page for the book says “The text was developed through years of teaching intermediate (second-year) logic at the University of Melbourne.” While their Amazon blurb says “suitable for undergraduate courses and above.” Which suggests a rather unstable focus. And indeed, a significant amount of the material here, as we’ll see in a moment, is at what strikes me as a decidedly non-introductory level.

Certainly, things that can (and often should!) give pause to a philosophy student encountering formal logic for the first time are often skated over at speed. For example, when we do propositional logic, just what is the relation between the formal systems and our everyday inferences using the ordinary-language connectives? So, exactly what are these dratted “p”s and “q”s doing? On p.8 we are told that “declarative sentences express propositions”, and that we are going to be looking at propositional languages “where there are declarative sentences”. But then are also immediately told that our formal language is just designed “to express the forms of propositions combined with [the connectives]” (my emphasis). So do the “p”s and “q”s get interpretations as expressing propositions or not?

On p. 9 we are baldly told that “disjunctions will always be inclusive in this text” without a moment’s discussion of how things might or might not stand in ordinary language. And later, the much more vexed question of how the logician’s conditional might be related to the ordinary language conditional is relegated to a “challenge question” on p. 32. I wonder: if we don’t say rather more about the ordinary-language logical apparatus, how do we rack up a persuasive score sheet of the costs and benefits of various alternative formal choices? (Teachers using this book with real beginners might well be adding quite a bit of appropriate classroom chat on such matters as they go along — but I’m thinking here of a student reader taking the book “neat”.)

Again, the beginning reader is given just one worked example of a truth-table test for validity in action. And nothing is said e.g. about standard heuristics to speed things up (as in “you don’t need to work further on a line where the conclusion is true because that can’t give us a counterexample”) Yes, yes, of course truth-table testing complicated examples is as boring as heck. But surely(?) we do want our beginning students to be just a bit more au fait with how things can work out in practice.

So already, I’m not sure how well this is going to work with real beginners. But there are more serious worries. Restall and Sandefer advertise their book as presenting “proof construction on equal footing with model building” — but in fact that briskness over truth-tables is just one sign that their presentation is really skewed to emphasize proof-theoretic ideas. And so, long before we ever hear about the classical truth-functional interpretation of the connectives, we are tangling with why we might want detour-free proofs in a Gentzen-style natural deduction system. (By the way, much as though I like the elegance of Gentzen trees, I’m yet to be really persuaded that they trump Fitch-style proofs for introducing ND to students.)

And now, not only is the — I agree! — reasonably intuitive idea of a detour-free proof canvassed, but we actually get a full-on, ten-page, proof of normalizability for intuitionistic propositional logic (starting as early as p. 53 in the book). I honestly can’t imagine too many thinking that this is where they want their beginning philosophy students to be concentrating, so early in their logical encounters!

Now, I don’t want to carp, so let’s now recalibrate our expectations, and think of this as in fact a second-level text with some brisk reminders of the more elementary stuff. Then, on positive side, it can be said that the normalization proof and other parts of the discussion of Gentzen style ND are very accessibly done. So I can e.g. well foresee the relevant sections getting into the next edition of the Study Guide as warmly recommended reading on entry-level proof theory. But yes, for me at least, that is where this material really belongs, a step or two up from a first introductory text for philosophers. Call me old-fashioned!

I note that the text was typeset by the authors (and some of their aesthetic choices are a bit wonky!). But that does raise a question. I do wonder why, in 2023, since they have a nice PDF to hand, they have gone done the route of conventional publication when they could have got the book into so many more students’ hands by going down the free-PDF-plus-cheapo-print-on-demand route? Just saying.