Glenn Gould recorded his 1955 Goldberg Variations a few months before his 23rd birthday. Now Beatrice Rana has recorded the same music when less than a year older. And this is another quite extraordinary performance. Utterly gripping from the beginning. From the Gramophone review: “The variations that in some hands become merely strong and affirmative are beguilingly multi-layered …. Gentler numbers benefit from Rana’s ability to conjure the most translucent of textures … In the famous so-called ‘Black Pearl’ (Var 25) she allows Bach’s tortured dissonances to speak for themselves … the tension finally released by the joyously airborne Var 26. In some hands, these last variations, which build on that sense of joy, can seem rather forced …. Not here, though, where they range from the bucolic to the transcendental. After a Quodlibet that rejoices in its simple good humour, the return of the Aria is as emotionally multifaceted as you would expect – mysterious, quizzical, noble, resigned, hopeful – setting the seal on a life-affirming disc.”

Ivana Gavrić‘s Chopin disc groups some of Chopin’s earlier Mazurkas, seperated by a couple of Preludes, a Nocturne and the Berceuse. This makes for something like a concert programme (you should listen up to the Berceuse — which is quite hauntingly played, her left hand rocking the cradle in a way that somehow catches at the heart — and then take an interval!). Some of the Mazurkas are very familiar, but many were (as good as) new to me. Her unshowy, undeclamatory, playing seems just entirely appropriate to the scale and atmosphere of the pieces, often tinged with melacholy as they are. She is across the room from a group of you, friends and family perhaps, rather than performing to a concert hall. And repeated listenings reveal the subtle gestures and changes in tone she uses to shape the dances; these are wonderfully thought-through performances.

Haydn’s inexhaustible humanity can be a comfort and inspiration in these dark times, no? So I have returned again and again to the Chiaroscuro Quartet‘s wonderful exploration of the Opus 20 quartets, completed this year. Four friends, occasionally coming together to play concerts and record, perform with delight and bold inventiveness and warm insight. Their use of gut strings makes for wonderful timbres, now earthy, now confiding, now echoing a viol consort. This is extraordinary playing, and not just from Alina Ibragimova who leads the quartet: the sense of ensemble and the interplay of voices puts some full-time quartets to shame. Richly rewards that repeated listening.

And here is Alina Ibragimova again, this time continuing her long-standing partnership with Cédric Tiberghien. They have now recorded four double CDs of Mozart Sonatas — in fact there are two sets from this year. The early pieces written by the very young Wolfgang are dispatched with affection and bring out the moments of musical magic that are scattered even there. The mature Mozart is played as well as I have ever heard. As the BBC Music Magazine said of one of the discs, “Tiberghien’s limpid phrasing, radiant cantabile and velvety, cushioned tone provides a continual source of pleasure, complemented ideally by Ibragimova’s silvery-toned exploratory zeal, as she delights in Mozart’s gentle textual interplay, as though discovering its special qualities for the first time.” A constant delight.

The Doric Quartet give us a driven, intense, performance of two of Schubert’s greatest works. From the Gramophone review: “Even in a work as familiar as the Quartettsatz the Doric lend character through elasticity of phrasing, which nicely counterbalances the piece’s inherent energy. … The main event, the G major quartet, is very impressive too, spacious without ever being ponderous. … The quartet build up their own kind of relentlessness, one that becomes more and more potent upon repeated hearings.” Convincing and emotionally gripping playing. (If you like the Pavel Haas’s take-no-prisoners Death and the Maiden, you should like this too.)

Others that almost made it: the very fine Schone Mullerin from Christian Gerhaher and Gerold Huber (but how often can you listen to that?), the second Scarlatti disc from Angela Hewitt, and for lighter relief, ‘The Italian Job’ from Adrian Chandler and La Serenissima.

Finally, what about the much hyped recording of the last two of Schubert’s sonatas from Krystian Zimerman? Try the opening of the first or second movements of D960 — I found the playing to be so affected, the hesitations and rushes forward so unnatural as to be simply unbearable.

]]>In fact, the only 2017 published novel I seem to have read this year — though with great enjoyment and at the warm recommendation of Mrs Logic Matters — has been John Banville’s *Mrs Osmond* (his sort-of-sequel to *Portrait of a Lady*).

What about new logic/philosophy of maths books? It seems to have been a relatively thin year (or again, have I not been keeping up?). I have mentioned over the year a couple of new books by Jan von Plato. First, his introduction to and translation of Gentzen’s shorthand notebooks (which seems a major achievement — and of considerable interest even if the history of logic is not your primary concern). And second, his partial and opinionated (but therefore interesting and instructive) history of theories of deduction and computation. As I said before, the book retains the flavour of a thought-provoking and engaging lecture course, which makes for readability.

The other book I have highlighted here is Neil Tennant’s *Core Logic*, the result of some forty years of wrestling with entailment, the transitivity of entailment, the avoidance of explosion, and related matters. Some (many?) will think we should just keep things simple, allow that a contradiction entails anything, and not fuss. Neil has much to say about the gains in being fussy.

Just in the last few days I have got two newly published books, Cezary Cieśliński’s *The Epistemic Lightness of Truth*, and Elaine Landry’s edited collection *Categories for the Working Philosopher* (both, by the way, outrageously expensive, even after discounts). The latter seems to be a *very* mixed bag (of the three papers I’ve read, one bad, one no real news at all, and one very helpful). The former, however, looks good. If, like me, you are (a) interested in formal theories of truth, and (b) are inclined to some deflationist/minimalist view about truth according to which ‘It is true that *p*‘ shouldn’t get you much further than plain ‘*p*‘, then you will be very interested in Cieśliński’s project: and the opening chapters are promisingly crisp and clear and accessible (though probably presuppose a bit more from the reader than the author thinks).

So what have I forgotten/overlooked? What are *your* logic/phil maths picks of 2017?

Foundations in Mathematics: Modern Views (Munich, April 2018)

Philosophy of mathematics: objects, structures, and logics (Mussomeli, Sicily, May 2018)

Logic Colloquium 2018 (Udine, Italy, July 2018)

My conference-going days have to be over. But I’d have relished any of those!

]]>Looking ahead a few weeks, I am not planning to do a serious in-depth revision of the *Teach Yourself Logic Study Guide *for 2018, as I really, really, must concentrate on the second edition of my intro book. But I may well do a very modest ‘maintenance upgrade’, in particular updating links where other books have become freely (but legally!) available.

Occasionally people try to post comments here noting that this or that book is electronically available at the-file-repository-of-which-we-shall-not-speak, comments which I have to delete. But I am always pleased to hear about cases like this where authors listed in the Guide have themselves made their work free-to-download: so are there any more cases I should know about?

]]>I must have listened a few dozen times over the years to the Verdi on CD (particularly the old Karajan recording with Tebaldi/Bergonzi/Simianato). Every note was familiar. But I’ve never seen it before, and always feared that on stage, the opera could not live up to the Aida of the imagination. Perhaps nowadays, the only thing that would really work is a wonderfully sung but very abstract bare staging calling on the audience’s own imagination to fill out the public scenes. This staging, I fear was the opposite — not wonderfully sung and rather too old-fashioned in style (which made all too obvious the underlying clunkiness of the drama). Indeed, some of the half-hearted dancing sometimes teetered on the comical. The evening was only really saved by a stellar Amneris from Veronika Hajnová.

Rusalka a couple of nights later couldn’t have been a happier contrast. And completely new to me. The staging was rather magical, and the singing outstanding (with Veronika Hajnová again, doubling as the witch and the foreign princess). And what made the evening even more delightful was the very mixed local audience, ranging from the glamorously attired to ordinary-looking families with children. A fairy story, yes, but a dark one, so heaven knows what the young girls who come dressed as water nymphs made of it all! But the reception was rapturous, and the sense of being there for a very Czech occasion made it really rather special.

]]>(And if anyone can think of a nicer title than the uninspired ‘Logical snippets’ then I’d be very pleased to hear it!)

]]>How very fine the centre of the city is, street after street! And beautifully looked after too. (It has to be said how very, very shabby English cities can look in contrast.)

Away from the tourist traps, the cafés and restaurants we have been to have been good to brilliant — in particular, the quite exceptional Field. Eyes have been feasted at various sites of the Prague National Gallery, the Lobkowicz Palace, and a lot of churches. But just wandering around the city, from the Jewish Quarter up to Prague Castle and around and back is all a delight in itself. We are bowled over.

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You would have thought so! But oh, how you can be setting yourself up for disappointment when you order one (at least here in the UK).

So, folks, as everyone knows, you *do* use a proper thick china espresso cup of the traditional shape (there’s a reason it’s traditional). Warmed, yes: but you *don’t* scald the cup first with boiling water. You most certainly *don’t* use some fancy “artisanal blend”, since they are mostly crap and too bitter and only suited to flavouring those milky drinks that the British seem to love (for straight espressos or macchiatos, they will be beaten hands down by Illy or Mokarabia or the other good Italian brands). You *don’t* make a mini-cappuccino: “macchiato” means “marked” or “stained”, not “drowned” — so two or three teaspoons of silky foamed milk is enough. And yes, for heaven’s sake, learn to make decently textured milk: filling the cup with wet bubbles is just evil. *Do* supply a proper coffee spoon so we can scrape the last remnants of crema from the cup (wooden sticks? no!!!). And *do*, without being asked, add an elegantly sized small glass of water (not a paper cup, not a half pint mug, not lukewarm, not lemon-flavoured, …).

Now, that wasn’t too difficult, was it?

]]>The first chapter on natural deduction motivates/introduces the rules by talking through some worked examples. The second chapter looks at some issues, about explosion, the best disjunction elimination rule, vacuous discharge, etc, and takes with another look at the negation rules. First, we note equivalents to (DN), including (EM), excluded middle. Then — at the very end of the chapter — I briefly touch on the status of (DN)/(EM).

I want to say *something* about this last issue. But equally, in the context of an introductory book I can’t say much. Here below is a draft of the relevant page-and-a-half. I’d very much welcome comments (perhaps not so much about philosophical doctrine, as about the expositional clarity given the intended audience! — can I put things better?).

In §21.4, we noted that the negation rules (RAA) and (Abs) make a nicely harmonious introduction/elimination pair. Which leaves the remaining negation rule (DN) and its equivalents out on a limb. As we asked before: what, if anything, is the significance of this? The issues here quickly become complex and contentious; but here are a few introductory remarks.

- We ordinarily distinguish being
*true*from being*warrantedly assertible*. The naive thought is that whether a proposition is true depends on how the world is — and how the world is may be beyond our ken, even in some cases beyond our capacity to find out. Hence, we suppose, a proposition can be true without there being any available warrant or grounds for justifiably asserting it. - But on reflection, for some classes of propositions, perhaps there is after all no more to being true than being warrantedly assertible. So-called ‘intuitionists’ and other constructivists hold that mathematics is a case in point. Mathematical truth, they say, does not consist in correspondence with facts about objects laid out in some Platonic heaven (what kind of objects could these be? how could we possibly know about them?). Rather, being mathematically true is a matter of being warrantedly assertible on the basis of a proof.
- We can’t discuss here whether an intuitionist view of mathematics is actually right. But we can ask: what should be our principles of correct informal reasoning
*if*we accept such a view? For the intuitionist, correct inferences in mathematics are those inferences that preserve warrant-to-assert-on-the-basis-of-proof. Which inferences involving the connectives are these?

If you have a warrant for*A*and have a warrant for*B*, then you surely have a warrant for their conjunction,*A**and**B*. Likewise, having a warrant for*A*(or equally, a warrant for*B*) is enough to give you a warrant for*A**or**B*, when the ‘or’ is inclusive. And if you can show that supposing*A*leads to absurdity, that is enough to put you in a position to justifiably reject*A*, i.e. to give you a warrant for*not*–*A*.

So even if we are thinking of good inference as a matter of preservation of warranted assertibility, versions of the now familiar introduction rules for the three connectives — with (RAA) as negation-introduction — will still apply. And since the harmonious elimination rules simply allow us to extract again from a wff what the introduction rule for its main connective required us to put in, the elimination rules will continue to apply too. - What, however, will be intuitionist’s attitude to the rule that we can cancel double negations or to equivalent rules? Take the law of excluded middle. The intuitionist won’t endorse this as a generally applicable principle. Suppose that
*A*is a mathematical open conjecture, not yet actually proved or disproved. Must it all the same be provable or disprovable? There is no obvious reason why so. Hence, according to the intuitionist (who holds that all there is to truth in mathematics is provability), we have no warrant to suppose that mathematically things are one way or the other with respect to*A*, so no warrant for*A or not-A*. - Now going formal again, imagine you are an intuitionist who wants to encapsulate the inference rules you accept into a variant of our natural deduction system. Then you will adopt all the same rules as our PL system minus (DN) (since that’s equivalent to the unwanted excluded middle). Such a system, at least once we add the rules for the conditional too, is said to define
*intuitionistic propositional logic*. And arguably, this intuitionistic logic is the right formal logic for arguing with the connectives when dealing with any domain where truth is warranted assertability/provability. - Imagine alternatively that you conceive of truth in a more naively ‘realist’ way for some domain. So you think of the truth-values of (non-vague) propositions of the relevant kind as being determined one way or another by the world, independently of whether we can warrantedly judge whether they are true or false. You will then think of negation here in the classical way, as simply swapping the value of a proposition, taking you from a determinately true proposition to a false one and vice versa; and every proposition of the relevant kind determinately has one value or the other, ensuring that excluded middle always holds. Going formal, you will therefore adopt (EM) or equivalently (DN) as one of your rules for the connectives. The classical logic of our
**PL**system reflects that classically realist view of truth.

So, at any rate, goes one often-told story. But it goes without saying that there is a great deal to wrestle with here. Does the apparently attractive logic of **PL**, with its immediately appealing rules, really presuppose a particular realist conception of truth? Are there really areas of enquiry where the appropriate notion of truth is non-realist, more akin to an idea like ‘warranted assertability’ or ‘provability’. If there are, is intuitionist logic really the right logic for such domains? Does it then make sense to think of different logics as being appropriate to different domains? Or should we rather think of the law of excluded middle — if it doesn’t apply to reasoning in general — as not part of core logic at all? Should we perhaps think of excluded middle, when it applies, as really more like a very general *metaphysical* claim about the determinacy of some parts of the world?

It also goes without saying that we can’t begin to tackle such intriguing but baffling issues in this book!

And there the chapter will end, apart from the usual end-of-chapter summary and exercises. As I said, all comments (or rather, all comments which bear in mind the intended introductory role of these remarks) will be very gratefully received!

]]>A collection of essays on

I can’t honestly recommend that you do the same.

At my not-so-tender years, I’m just not very willing to spend my limited time reading papers that are badly written or unclear where they are going. So I didn’t get very far with the first two pieces in the collection, by Penelope Rush herself and by Jody Azzouni.

The next paper by Stewart Shapiro is predictably three steps up in terms of clarity, focus, and lightness of touch. He is writing about ‘Pluralism, relativism and objectivity’. But if you have read his interesting 2014 book *Varieties of Logic *then you won’t find much new here.

There follows a typically thought-provoking paper by the late Solomon Feferman on his so-called conceptual structuralism. But it is available on his website here: Logic, mathematics and conceptual structuralism.

Penelope Maddy follows with ‘A second philosophy of logic’, again written with her characteristic clarity. But as with Shapiro’s paper, if you have been keeping up with this author’s recent work, there will be no surprises. Maddy herself says that the paper “reworks and condenses the presentation” of Part III of her earlier book *Second Philosophy. *So while the paper here might serve some as a useful introduction to her thinking, it doesn’t really add anything new.

The next paper is at least new, but I’m not sure what other virtues it has. Curtis Franks is out to defend the idea that ‘logic, in the vigor and profundity that it displays nowadays, does and ought to command our interest precisely because of its disregard for norms of correctness’. So he aims to ‘lead the reader around a bit until his or her taste for a correct logic sours’. (Note the ‘a’.) Well, the therapy didn’t work on this reader (though there some interesting but hardly original remarks on the relationship of classical and intuitionist logic). But you can try for yourself here: Logical nihilism.

There follows a piece by Mark Steiner on ‘Wittgenstein and the covert Platonism of mathematical logic’. Wittgenstein seems to make both radical criticisms of classical ideas and to want to leave everything as it is. Steiner explores how to reconcile these tendencies. Just how much you get out of this will depend on how much residual interest you have in Wittgenstein on the philosophy of the mathematics-he-really-seems-not-to-have-known-much-about.

And that’s all the papers in the first part of the collection, ‘The Main Positions’. These are all papers by old hands, Rush apart, who have already contributed books on logic and foundations of mathematics. It would have been much more interesting to hear new takes on old positions from younger philosophers.

The next part of the book consists on four random papers cobbled together under the catch-all ‘History and Authors’. The only interesting one is Sandra Lapointe writing about Bolzano’s Logical Realism.

Finally we have three papers on ‘Specific issues’ (now the editor is *really* struggling to find an organising principle for her heap of contributions). Graham Priest has a short and thin piece on Revising Logic. Jc Beall, Michael Hughes, and Ross Vandegrift contribute another short paper, on Glutty theories and the logic of antinomies (how is this relevant to the volume? — ‘We shall argue that [the logic] LA reflects a fairly distinctive set of metaphysical and philosophical commitments, whereas LP, like any formal logic, is compatible with a broad set of metaphysical and philosophical commitments’). Finally, Tuomas Tahko writes on The Metaphysical Interpretation of Logical Truth: you’ll only like this paper if you think there is anything to be said for slogans like ‘A belief, or an assertion, is true if and only if its content is isomorphic with reality.’ Which I don’t.

So a pretty disappointing collection, one way or another. Save your pennies for some good haddock.

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