Three CDs of the year

Schubert’s late piano works have long been some of the most important music of all for me. So one of the highlights of this last year was going to hear Imogen Cooper’s wonderful 70th birthday concert at Wigmore Hall, when she played the last three sonatas,  every bar revealing her deep and lasting engagement with this music. More recently, I’ve discovered Francesco Piemontese’s rightly much admired recordings of the same sonatas. But the most revelatory Schubert this year must surely be the second installment of Andras Schiff’s recordings made on a Franz Brodmann fortepiano, made in Vienna around 1820. Schiff’s performances are utterly convincing and make you hear these pieces anew; I was bowled over again, as I was by the preceding disks. Listen, for example, to the Drei Klavierstücke D 946 (favourites of mine): magical playing.

I have much admired Ivana Gavrić’s previous recordings, and praised them here. So I would have bought her new release, whatever it was. This new CD, Origins, starts with a sparkling performance of the Haydn D Major Concerto (it took me a few moments to adapt my ears to the orchestral texture, so used am I to listening to “period” performances of Haydn, but this is joyous playing). There follow the six short homages to Haydn for solo piano commissioned from French composers for the 100th anniversary of his death, and a seventh homage from Gavrić’s Cambridge contemporary, the composer Cheryl Frances-Hoad. And then there follows a performance of the piano concerto Between the Skies, the River and the Hills written for Gavrić by Frances-Hoad. This nods to Haydn (particularly his last movement thought sometimes to be based on  a Bosnian dance) and uses a Bosnian folk song in its own third movement: the connection here is that Gavrić herself was born and spent her early years in Sarajevo. There’s more about the CD in three short videos here. I’ve listened and re-listened with warm admiration — both for Frances-Hoad’s composition and Gavrić’s playing! — and I have enjoyed this CD a lot: well worth seeking out.

But the CD of the year has to be the Pavel Haas Quartet’s Shostakovich disk. This isn’t comfortable listening. As the reviewer on the BBC Radio 3 Record Review programme put it, “It’s absolutely gut wrenchingly intense. It’s almost unlistenable to, it’s so fabulous, it’s such committed playing, it’s such deep, deep sincerity.” That gets it exactly right: I’ve heard them play Shostakovich in concert with the same completely overwhelming mastery and emotional depth.  This is all quite extraordinary playing, intense indeed, but also in places heartstoppingly beautiful (listen to Veronika Jarůšková in the Adagio of the 2nd Quartet).   There’s a revealing interview with PHQ here that tells us something about how they prepare and rehearse and come to terms with the music with such concentrated attention: the result is stunning.

Teach Yourself Logic 2020 updated

Since I posted it on Dec 11, the newly revised Teach Yourself Logic Study Guide has already been visited a few thousand times — more than enough to confirm my impression that it is worth continuing to maintain and update the Guide when the spirit moves me.

Thanks in particular to some very useful comments from Daniel Nagase when I posted that initial version (see the comments here), I have now updated TYL 2020 again.

[Added. Updated with a couple of additional sentences again on Dec. 31.]

I can now bore for England …

The scaffolding for our loft conversion went up on June 3rd. The decorators finally left a few days ago. So we’ve been living with workmen around, with some short gaps, for over six months. But it has, in the end, all been really worth it.

And let me leave the story more or less there. I can now bore for England on the subject of loft conversions; but it’s the sort of thing which is of all-consuming interest if you are in the middle of it yourself, but of very little interest to everyone else (“is it still not finished?” friends say solicitously, before quickly moving on). If anyone local to Cambridge wants advice and recommendations, I’m your man! But here, all I’ll say is that things went more or less as smoothly as one could hope, and the result is quite terrific. Which is a mighty relief.

But the combination of almost continual low-level disturbance at home (and occasionally a lot more) and the energy-sapping business of knocking IFL2 into shape means I get to the end of 2019 having done a heck of a lot less than I’d have liked, in lots of ways, particularly on various logic matters. So some battery-recharging over the holidays next, and then I must fix on A Sensible Plan for 2020: I really don’t want to hang up my logical boots just yet … But I need to focus. So why have I just ordered a stack of books in the OUP sale?

Kirby, An Invitation to Model Theory

I very briefly noted Jonathan Kirby’s An Invitation to Model Theory (CUP, 2019) when it was published earlier in the year. I put it aside to look at later, and (I confess) forgot about it entirely when recently updating the TYL Study Guide! Belatedly, I have now dipped into  quite a lot of this short book; how does it compare as a first introduction to model theory?

The aim of the book is described like this: “[T]raditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, [the author] brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics ….” Now, one thing that usually isn’t familiar to undergraduate mathematicians is any serious logic: so, as you would expect, Kirby’s book is an introduction to model theory that doesn’t presuppose or seamlessly continue on from a first logic course. By contrast, in the TYL Guide, I suggest as a route into the area the long last chapter ‘Some use of compactness’ from Goldrei’s excellent logic text, and/or the more expansive but equally logic-based book by María Manzano.

The Invitation is divided into six parts, each comprising five or six short chapters (the main text of the book is only 176 pages long), with dependencies very well signalled — the book is a model of clear structuring.  The first part ‘Languages and structures’ gives the logic-less student some basics about the ideas of a first-order language and interpretation in a structure, and then introduces the ideas of embeddings, substructures etc. The next part proves a compactness theorem and gives some first applications. Part III, ‘Changing models’ proves downward and upward Löwenheim-Skolem theorems, gives some applications, gives examples of theories which are countably categorical (or categorical in other cardinals), and in particular use the back-and-forth method to show that countable models of the theory of dense linear orders with endpoints are isomorphic. Part IV starts by proving some results about quantifier elimination …

And we are now about 100 pages into the book. Is this perhaps beginning to sound a bit action-packed?  Manzano, for example, takes over 200 pages to get about as far. And I do suspect that for self-study Kirby’s book would make for tougher going for many students. Not that Kirby is unclear in what he does say; on the contrary, he writes beautifully clearly. But he could/should have said at least a little more. A few more classroom asides, a few extra illustrative examples of key concepts, etc.  could have made a significant difference.

For example, Part V is on types; and surely the student reader would have welcomed more explanation and motivation for the introduction of the notion than they get in §23.1. An  extra paragraph or two here would have helped a lot. And as this part of the book continues, the level of difficulty seems to me to ratchet up markedly. I would have thought that by the time we get to §26.3 on zero-stable theories, or to a sudden invocation of strongly inaccessible cardinals in §27.3, many student readers could be losing the plot. (It’s not that the relevant notions aren’t clearly defined: but the motivations and significance may well pass them by).

The book finishes with five short chapters on the model theory of fields, applying earlier techniques, and leading up to a proof of Hilbert’s Nullstellensatz: interesting for algebraists, and pointing forward towards an important area of model theory — but maybe more than the logic-oriented reader will want in a first introduction to model theory.

Overall, then, I will stick to the TYL recommendations: those such as the likely readers of this blog, coming from a logic background, should begin model theory in company with Goldrei and Manzano. Kirby’s book will then make for useful revision/re-inforcement material as necessary.

The Rise of Analytic Philosophy, 1879–1930

It is very good to see that my friend and one-time colleague Michael Potter’s book The Rise of Analytic Philosophy, 1879–1930: From Frege to Ramsey (Routledge) is now out. And given it is over 500 pages, the paperback is pretty reasonably priced by modern standards.

I suppose some might complain that there is a slight  suggestio falsi in the title, for the thematic route through the concerns of Frege, some time-slices of Russell, early Wittgenstein, and then Ramsey, is only part of the story of the rise of what we now think of as ‘analytic philosophy’. But let’s not argue about that! This familiar route is certainly of quite central interest and importance, and students need an accessible, readable, and reliable guide taking them along it. The interpretation of all four philosophers is a contentious business, so no doubt those who know more about the debates than I do will find things to cavil with. But I enjoyed reading quite of the bit of the book in draft, often found it illuminating, and can warmly recommend it.

Teach Yourself Logic 2020!

Short version: there is at last, after three years, an updated version of the TYL Guide. Click on the cover picture for links!

Long version: The title gives it away! — this is an annotated guide to logic books  and other resources suitable for self-study, starting a step up from ‘baby logic’ and going though to quite advanced stuff. It is a PDF, now over 90 pp., formatted for onscreen reading, with a lot of live links.

The TYL page is the most visited page here on this site (with 70K visits last year), with the Guide getting thousands more visits too at its academia.edu location. So there is evidently  more than enough interest in the Guide to make it well worthwhile maintaining it, and trying to improve it.

This new version is a ‘maintenance upgrade’. Its overall structure has been clarified by dividing it into three parts, some entries have been revised, and a few new recommendations added. But there are no new sections, and I haven’t found myself wanting to change many main recommendations this time. Have any stand-out books been published in the last three or four years which really ought to have shot to top of any reading list? As always, comments and suggestions are most welcome.

Book sale! — including a fine book on Ramsey

Far be it from me to encourage you to add yet more books to your groaning shelves, but … You might well find something of interest in the “cyber sale” from Palgrave Macmillan — each and every title is now £9.99. Given the usual list price of many of their books is around £80, this  means that there are some real bargains here.

Or at least, there are bargains if there are books in their massive catalogue which are actually worth having. Looking through their philosophy backlist, I didn’t find much to appeal to me, other than perhaps some of the titles in the history of analytic philosophy series. But I will mention one book which I know to be really very good indeed, Steven Methven’s Frank Ramsey and the Realistic Spirit (2015). Don’t take my word for it: read Cheryl Misak’s very warm review.

The sale is only on for a few days, until 3rd December. If you spot other titles you’d like to recommend to readers of this blog, then do comment below!

Clive James

Clive James’s death at his home in Cambridge on 24 November has just been announced. He survived to his surprise and gratitude ten years after a first terminal diagnosis, thanks to the wonders of the hospital here. He leaves, along with much else, a wonderful late flowering of poetry. Here, for now, “Japanese Maple” (2004).

Your death, near now, is of an easy sort.
So slow a fading out brings no real pain.
Breath growing short
Is just uncomfortable. You feel the drain
Of energy, but thought and sight remain:

Enhanced, in fact. When did you ever see
So much sweet beauty as when fine rain falls
On that small tree
And saturates your brick back garden walls,
So many Amber Rooms and mirror halls?

Ever more lavish as the dusk descends
This glistening illuminates the air.
It never ends.
Whenever the rain comes it will be there,
Beyond my time, but now I take my share.

My daughter’s choice, the maple tree is new.
Come autumn and its leaves will turn to flame.
What I must do
Is live to see that. That will end the game
For me, though life continues all the same:

Filling the double doors to bathe my eyes,
A final flood of colors will live on
As my mind dies,
Burned by my vision of a world that shone
So brightly at the last, and then was gone.

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