Peter Smith's Blog, page 66

IFL2 — at long last!

Some headline news. On Wednesday, at last — ok, at ridiculously long last — I’m sending off a full version of IFL2 to CUP. This is for proof-reading and then early production, I hope. Heaven knows I’d like to seriously tinker with the book more; but that way madness lies (not to mention the end of CUP’s sorely tried patience). Another read through some recently revised passages tomorrow, and then it is off.

But I have the next few weeks until the proof-reader’s corrections come back to make mini-corrections, so I will return to it after a week’s break. Meanwhile, if anyone would like to see a late version, with a view to spotting typos, thinkos, and other infelicities (very unclear sentences, English difficult for a non-native speaker, incorrectly commented proofs, etc., etc.), then I’ll happily send a copy on the strict understanding it goes no further. Drop me an email or comment here.

I have been in book purdah for the last month working more intensively and more systematically than for a long time (even giving up the chance of going up to London to see the Chiaroscuro Quartet performing live yesterday, though the video I posted is quite a good compensation for that). Working so hard has really been quite fun in a masochistic way, and rather embarrassingly instructive too. But I’ll be glad of a pause. So time for a few days off. And then I need — for a start — to catch up on emails (apologies to a number of people for radio silence!). But now tonight, time to pour a glass, and to watch again Alina Ibragimova and her friends at their inspirational best.

The post IFL2 — at long last! appeared first on Logic Matters.

Chiaroscuro Quartet, play Beethoven and Schubert



Today’s morning concert at Wigmore Hall. The Chiaroscuro Quartet playing Beethoven Op. 18 No. 4 and Schubert’s Death and the Maiden. Simply stunning.

The post Chiaroscuro Quartet, play Beethoven and Schubert appeared first on Logic Matters.

The 12 Ensemble play Mendelssohn



The Mendelssohn Octet on a summer’s evening, a short walk away down the river to the old Divinity School, takes a lot of beating for sheer enjoyment. And it was excellently played last night with verve and obvious relish — after some (Richard!) Strauss and Shostakovich — by the young 12 Ensemble. The audience rightly loved them: if you get a chance to catch them in concert, do so! Meanwhile, here they are with the first movement of the Octet from an Oxford concert last year.

The post The 12 Ensemble play Mendelssohn appeared first on Logic Matters.

IFL2: Quotation conventions

A small matter. But an intro logic book needs to have a policy on whether mentioned formulae get enclosed in quotation marks. IFL1 took a sternly conservative line on this, leading to somewhat unsightly rashes of quotation marks. I originally was going to carry this over to IFL2; but I have belatedly decided on a much more relaxed policy, which will be followed in future draft chapters (a policy more in keeping, indeed, with usual mathematical practice, which is a major plus). I was uncomfortable about the amount of quotational clutter in IFL1, and I was spurred on in part by some blunt remarks about not fussing over quotation in §9.1.2 of David Makinson’s Sets, Logic and Maths for Computing.

Having made the decision, I was interested to check back to see what other intro textbooks said about quotation, use and mention. There were some real surprises. For example:

My namesake Nick Smith, in his (in many ways excellent) Logic: The Laws of Truth, doesn’t use quotation marks round formulae. Fair enough — but he never discusses this decision: in fact in his long book, he rather oddly doesn’t talk about quotation conventions, use and mention at all.
Likewise, Barker-Plummer, Barwise and Etchemendy in Language, Proof and Logic also do not use quotation marks around formulae — and the only sort of quotes they actually mention in the book are scare quotes.
Greg Restall’s Logic an Introduction doesn’t use quotes either, and again doesn’t discuss the issue. He perhaps has the excuse of writing a short book, but …
Just the same goes for Virginia Klenk’s much longer, and quite popular, book Understanding Symbolic Logic. No quotation marks round formulae, and again no discussion of quotation conventions. The reader is just presented with lopsided sentences like this: The correct symbolisation for “Nixon is not president” would be ∼N. I can’t find any account of why the English sentence gets quotation marks and the formal one doesn’t!
Looking back at an older book which also eschews the use of quotation marks, Neil Tennant’s exceptional Natural Logic, I was surprised to find that he too — a serious philosopher of logic — again doesn’t explicitly discuss quotation, use and mention at all.
Just the same goes too, I think, for Jan von Plato’s much more recent Elements of Logical Reasoning.

I do find this sort of silence really quite strange, however. Ok, we can exaggerate the dangers of outright use/mention confusion: but equally, you would expect introductory texts to have something to say, at least a short Quinean sermon to the troops on the topic!

Here then are three intro logic texts that do use quotation marks round inline formulae (a lot!) and do say something about the policy:

Paul Teller’s A Modern Formal Logic Primer uses quotes but initially only gives a line of explanation on p. 5. It isn’t until p. 159 of the second volume that we get a fuller (and not wonderfully crisp) explanation of the books policy.
Warren Goldfarb is brisker and (as you would expect) very clear in §12, ‘Use and Mention’, of his Deductive Logic. He unusually uses double quotes round non-displayed, inline, formulae. (You might have predicted that this would lead to rather messy-looking pages, but such is the text design of the book that it manages not to.)
For our last example, let’s take Bergmann, Moor and Nelson’s weighty The Logic Book. In my third edition copy, they have a clear page-and-a-bit on object language and metalanguage, use and mention. And they adopt a consistent policy of using quotation marks round inline formulae.  To my eyes this makes for some messy pages (though to be sure, aesthetics isn’t everything!).

So on the one hand, books in the first group  say nothing about use/mention, and don’t using quotes; and books in the second group both say something about use/mention and adopt a policy of always using explicit quotes when we are mentioning formulae.

But there’s obviously another possible line. Give  the Quinean sermon, saying  something about use/mention; say something about the official convention of using quotation marks on Sundays when we feel the need to be fully explicit that what we are doing is mentioning formulae; but then avoid ugly rashes of quotes by adopting a more relaxed weekday policy, and allowing ourselves to drop explicit quotation marks in practice when it is clear what is going on.

For example, suppose we follow Barker-Plummer, Barwise and Etchemendy in using a characteristic font for formal expressions —  e.g. using sans serif for all formal expressions, as against ordinary roman font for our English metalanguage. Then an English sentence that embeds expressions in sans serif font can, by default, be  taken as mentioning those expressions (this is, in effect, BBE’s policy — though I think unannounced, and not quite consistently applied ): it is then overkill to use quotation marks as well. (It is perhaps not an accident that the three books I mentioned that do use quotation marks to set off mentioned formulae do not have a special font convention for formal expressions, so there is more need for some way of setting off mentioned inline expressions from the surrounding text.)

In IFL1 I was guilty of overkill — using sans serif font for expressions in formal languages, and putting these sans serif expressions in quotes when embedded in English text (where they must be being mentioned, not used). In IFL2, I again use sans serif font for expressions in formal languages. But after talking about object language and metalanguage, use and mention, I propose a default convention that such expressions occurring inline, embedded in metalinguistic text, are mentioned. Quotes are kept for use when a explicit reminder that expressions are being referred to is helpful. The resulting text looks cleaner and in line with the usual practice in more advanced mathematical logic. What’s not to like?

Here’s the revised Chapter 11 where the policy is spelt out.

The post IFL2: Quotation conventions appeared first on Logic Matters.

PHQ play Beethoven Op 59/3 and Schubert Trout Quintet

To Wigmore Hall, to hear the Pavel Haas Quartet again. A matchless evening.

In the second half of the concert, they played the Trout Quintet with the pianist Boris Giltburg and Enno Senft on double bass. This is joyous music, and the five of them were obviously enjoying themselves enormously; you kept catching shared half-smiles as they played with such verve, without ever losing their subtle colouring and wonderful ensemble. Giltburg in particular was dazzling but never dominating as he wove in and out of the other four. We loved it, the audience loved it, and the musicians happily beamed back as they took the waves of applause. Great stuff. (Boris Giltburg has posted a short video of them rehearsing earlier, which gives a flavour, but the sound isn’t terrific and the evening performance was much more magical.)

But a chance to hear the Trout Quintet wasn’t the main reason I’d been looking forward to this concert for months. Because, before the interval, PHQ played Beethoven’s third Rasumovsky Quartet. I fell in love with this piece, particularly the Andante, when a student — first heard, indeed, in Godard’s film, Une Femme Mariée where snatches of Beethoven keep recurring. As odd chance would have it, I had never before heard it played live, even by a good quartet let alone a great one: the time had come! And, oh heavens, it was a stunning performance — more than bearing comparison with the greatest recordings. Veronica Jarůšková’s phrasing, bar by bar, is a thing of wonder. The Andante was played at the edge of melancholy, with the cello’s plucked notes (which can be too dominant in some performances) in perfect balance. The final Allegro then performed with such speed and drive but also such control, to bring cheers as the four raised their bows at the end. Astonishing indeed.

Ten years ago, the BBC Music Magazine had a cover CD of the PHQ playing three of the Beethoven Quartets (when they were BBC New Generation Artists). These are fine performances, full of youthful adventure. But ten years on — and now with Marek Zwiebel, who is surely just a superb second violinist — their Beethoven playing is in a different league again. In my dream world,  they will one day (sooner rather than later) get back to the studio and record e.g. all three Rasumovsky Quartets. That would be quite something.

Not quite the same, perhaps, but here are the PHQ on BBC iPlayer from a concert recorded last year, with Dvořák’s String Quartet No.14, Op.105 (something else they haven’t yet recorded). No one plays Dvořák better. 

The post PHQ play Beethoven Op 59/3 and Schubert Trout Quintet appeared first on Logic Matters.

PHQ play Beethoven and Schubert (and some Dvorak)

To Wigmore Hall, to hear the Pavel Haas Quartet again. A matchless evening.

In the second half of the concert, they played the Trout Quintet with the pianist Boris Giltburg and Enno Senft on double bass. This is joyous music, and the five of them were obviously enjoying themselves enormously; you kept catching shared half-smiles as they played with such verve, without ever losing their subtle colouring and wonderful ensemble. Giltburg in particular was dazzling but never dominating as he wove in and out of the other four. We loved it, the audience loved it, and the musicians happily beamed back as they took the waves of applause. Great stuff. (Boris Giltburg has posted a short video of them rehearsing earlier, which gives a flavour, but the sound isn’t terrific and the evening performance was much more magical.)

But a chance to hear the Trout Quintet wasn’t the main reason I’d been looking forward to this concert for months. Because, before the interval, PHQ played Beethoven’s third Rasumovsky Quartet. I fell in love with this piece, particularly the Andante, when a student — first heard, indeed, in Godard’s film, Une Femme Mariée where snatches of Beethoven keep recurring. As odd chance would have it, I had never before heard it played live, even by a good quartet let alone a great one: the time had come! And, oh heavens, it was a stunning performance — more than bearing comparison with the greatest recordings. Veronica Jarůšková’s phrasing, bar by bar, is a thing of wonder. The Andante was played at edge of melancholy, with the cello’s plucked notes (which can be too dominant in some performances) in perfect balance. The final Allegro then performed with such speed and drive but also such control, to bring cheers as the four raised their bows at the end. Astonishing indeed.

Ten years ago, the BBC Music Magazine had a cover CD of the PHQ playing three of the Beethoven Quartets (when they were BBC New Generation Artists). These are fine performances, full of youthful adventure. But ten years on — and now with Marek Zwiebel, who is surely just a superb second violinist — their Beethoven playing is in a different league again. In my dream world,  they will one day (sooner rather than later) get back to the studio and record e.g. all three Rasumovsky Quartets. That would be quite something.

Not quite the same, perhaps, but here are the PHQ on BBC iPlayer from a concert recorded last year, with Dvořák’s String Quartet No.14, Op.105 (something else they haven’t yet recorded). No one plays Dvořák better. 

The post PHQ play Beethoven and Schubert (and some Dvorak) appeared first on Logic Matters.

Sorolla at the National Gallery

Last week, the slates were stripped off our roof (preparing for a loft extension). This week has of course started with the very wettest of Cambridge days. Option (1): sit at home, fretting and listening out for more leaks through the tarpaulins (after an initial one last week was sorted). Option (2): go up to London for a long-planned concert. We sensibly if nervously went for option (2).

London outdoors was miserably wet too. But indoors at the National Gallery there was such sun and light and warmth at the exhibition Sorolla: Spanish Master or Light. Joaquín Sorolla y Bastida (1863–1923), prolific and once greatly popular, was quite new to us: and we enjoyed this exhibition hugely — there is something life-affirming here. As the Guardian review put it, “It is hardly possible to stand before these enormous canvases, thick with paint, without feeling at least something of their appeal, a combination of the obvious and comfortable relish in their making, and the irreducible beauty of sunlight itself.” The exhibition is on for another month: the next time you are in London on a wet  and cheerless day, see it!

The post Sorolla at the National Gallery appeared first on Logic Matters.

IFL2: Natural deduction for quantifier logic

Here is a tranche of draft chapters for IFL2. Chapters 25–30 are revised chapters on QL languages (informal syntax and semantics, how to translate in and out). Chapters 31–34 are newly drafted chapters on natural deduction for QL proofs (the system is standard, and I hope contains no surprises).

The following chapters will give a more formal semantic story, define q-validity etc.; but I think it is good to get natural deduction proofs up and running in an intuitive way first (after all, they are supposed to be fairly natural!).

All comments, especially on the new Chapters 31–34. In particular, chapter 34 is a stand-alone short chapter on empy domains, which significantly revises an earlier draft section in response to some very just comments.

The post IFL2: Natural deduction for quantifier logic appeared first on Logic Matters.

IFL2: Chapters on propositional natural deduction (revisited)

Here is an improved version of the five chapters on propositional natural deduction for IFL2. (Exercises to be added, which will fill some gaps, like noting the equivalence of DN and Classical Reductio, given the other rules, or dealing with biconditionals.)

As I have said before, one advantage of basing an intro logic book on trees (as in IFL1) is that people don’t get very exercised about how a tree system should be developed. By contrast, people get decidedly heated about the best form of natural deduction to adopt. And I have changed my mind more than once about how to do things (having explained things rather differently in classes over the years). I have ended up with a more conservative Fitch-style system than in previous drafts. But that is still probably not going to satisfy half of those who urged me to go for natural deduction in the second edition: it doesn’t even fully satisfy  me. But just is there’s no meeting all the desiderata!

As always, all comments (other than variants on “you have written the wrong book!”) and all corrections will of course be very gratefully received.

The post IFL2: Chapters on propositional natural deduction (revisited) appeared first on Logic Matters.

Postcard from Cornwall

Evening sun at St Mawes in Cornwall, where we have been again for a while. So no logic matters for the last fortnight (the book has not been nagging away insistently enough to the break the spell). And we’ve been trying to ignore Brexit too (which all looks even madder than ever). So a lot of walking along coastal paths, visits to some great gardens, and more walking. Or just sitting in the apartment watching the quiet comings and goings in the harbour below. All balm to the soul.

Back to real life and builders, not to mention IFL2, in a couple of days …

The post Postcard from Cornwall appeared first on Logic Matters.