Year: 2021


Bringing to front again Lea Desandre’s new CD is, as you’d predict, terrific. She and Thomas Dunford are stars: if you haven’t seen them together then you’ve missed some real delight. For example, here they are in a concert recorded at the end of last year … try, for example, Monteverdi’s “Lettera amarosa” from 19.35 minutes in, and you will be captivated!

For more tasters from the new CD, here is a video of Lea Desandre singing with Cecilia Bartoli a duet by Giuseppe de Bottis, from his 1707 opera Mitilene, Regina delle Amazzoni. Yes, quite new to me and it will be new to you too, as it is (surprisingly, given the lovely music) a world premiere recording, as are most others on this CD. Both singers are in wonderful voice and enjoying themselves, we also get a little bonus wafting in the video from Lea Desandre who trained for thirteen years to be a ballet dancer!

And here’s another very short video of track from the CD: this time Lea Desandre sings “Sdegni, furori barbari”, an aria of Celinda from Pallavicino’s 1690 opera L’Antiope. As I say, the whole CD is indeed exceptional.

The revised Study Guide — elementary proof theory

Here is the draft final chapter of Part I of Beginning Mathematical Logic — so this is the last of the group of chapters on core topics at an elementary level. This one on proof theory is newly written; comments will therefore be particularly welcome.

Having got this far, I am well aware that there are now some mismatches in the level/breadth of the overviews in the various chapters, and also places which call for more cross-references.  For example, I need to go back to the overview on set theory to say just a paragraph or so more about ordinals, in order to make a better connection with the use of small ordinals in the current chapter when waving my arms at Gentzen’s consistency proof. So smoothing out the coverage of Part I of the Study Guide is a next task. But at least there is now a full draft to play with.

The revised Study Guide — intuitionistic logic

After the minor revisions of earlier chapters of the Beginning Mathematical Logic Study Guide, something more exciting! Here is a brand new chapter on intuitionistic logic.

The chapter starts by briskly outlining a standard natural deduction system for intuitionistic logic. Then there are two sections giving rough-and-ready overviews, one on motivation and the BHK interpretation, the other on some additional formal details and giving a sketch of Kripke semantics. There are then the usual sections suggesting main readings, followed by some additional reading options. The chapter ends with some pointers to a few pieces with a more historical/philosophical flavour. The usual chapter format, in other words.

Since this is newly minted, I’d very much welcome comments/suggestions — particularly about alternative/additional readings at the right kind of introductory level. (Also very welcome, advance suggestions for what should appear in the planned later section when we briefly revisit intuitionism at a more sophisticated level in Part III of the Guide.)

And in Big Red Logic Book news …

Brief version: There is now a hardback version available of the second edition of An Introduction to Formal Logic: ISBN 978-1916906327. It should now be available to order from bookshops (as well as from Am*z*n and some other online sellers). It is priced at £20/$25, about the minimum possible. I’ve just got a sample copy and it is very decently produced.

Longer version: You’ll probably recall that I recovered the copyright of the second edition of IFL a year ago so that I could make the PDF freely available (a pretty small gesture in these difficult times, but every little helps). Lots of students, though, do prefer to work from a physical book: so I also set up an inexpensive print-on-demand paperback (to minimise the cost, that is Am*z*n only). 

Now, as I’ve said before, self-publishing has the downside that the word doesn’t get out to librarians via a publisher’s fancy catalogue. But in any case, in last year’s lockdown, and more recently too, librarians were rightly concentrating on improving their e-resources, so it didn’t seem the time to fuss too much about getting physical copies into libraries. However, things are slowly returning to something more like the old normality for library operations. So I have now arranged for ‘proper’ hardback copies — printed by Lightning Source who do small-run/on-demand printing for some academic presses — to be available for library purchase at minimum cost from, inter alia, standard library suppliers. So do please ask your friendly local university or college librarian to order a copy or two (emphasizing, if you need to, that this is a significantly changed book from the first edition). Online resources are all well and good, though problematic for some students: to repeat, at textbook-length, many — like me — do much prefer to have real books available!

The revised Study Guide — set theory

Next week’s post on Beginning Mathematical Logic will be more exciting (promise!) — an all-new chapter on intuitionist logic. But before we get there, here is the revised chapter on set theory. Again, I have done some minor tidying since the last edition, but there is no real novelty, as I’m currently reasonably content with the chapter. But I’m sure that doesn’t mean it couldn’t be improved — so, as always, all comments gratefully received.

The revised Study Guide — arithmetic, etc.

Another revised chapter for the Study Guide. And again, there is little substantial change from the previous version, except to significantly cut down the length of the “overviews”, which were getting a bit out of hand! Anyway, here is the latest version of the chapter on computable functions, formal arithmetic, and Gödelian incompleteness.

These revised chapters I am posting are being downloaded a significant number of times, but comments (either here or by email) are few and far between. I‘m rather hoping that that’s because people aren’t finding my overviews on topic areas gruesomely misleading or my recommendations for reading too outlandish! But, as I’ve said before, if you do think I’m leading your students horribly astray (if you are a logic teacher) or think the Guide could be more helpful (if you are a student), now really is the time to say!

The revised Study Guide — model theory

The chapter on model theory in the Beginning Mathematical Logic Study Guide was last updated quite recently, in particular to take account of Roman Kossak’s nice 20221 book Model Theory for Beginners (College Publications). Rather little has changed, then, in this current revision, except some minor tidying (though I have dropped as unnecessary a previously footnoted long proof). But still, here it is, the revised Chapter 5 (as it is now numbered).

Elisabeth Brauß plays Schubert

I have only just noticed that a recording of Elisabeth Brauß playing the four Schubert Impromptus D.899 last year is available now and for another week on BBC Sounds (start at 10 minutes into the programme). [Added: Link no longer works, sorry!]

This strikes me as extraordinarily good and very moving — with so much thought gone into every bar, yet the playing utterly honest and direct and unmannered. I have more than a dozen wonderful recordings of the impromptus from Schnabel on; but these performances bear comparison (in that these too are such that, while you listen, you can’t help but feel “yes, this is how the Schubert should be played …”).

Judging from her Mozart and Beethoven too, one day — and I do hope that this is where her inclinations take her! — Elisabeth Brauß could become one of the very finest of Schubert pianists. And, with the clock ticking away, I hope I will still be here to hear her.

The revised Study Guide — second-order logic

What to cover in the Guide straight after standard classical FOL?

Theories expressed in first-order languages with a first-order logic turn out to have their limitations — that’s a theme that will recur when we look at model theory, theories of arithmetic, and set theory. You will find explicit contrasts being drawn with richer theories expressed in second-order languages with a second-order logic. That’s why — although this is of course a judgement call — I do on balance think it is worth knowing just something early on about second-order logic, in order to be in a position to understand something of the contrasts being drawn. Hence this next short chapter.

There are no very substantive changes from the previous version. But it is a little tidier in some respects. So here is Chapter 4: Second-order logic, quite briefly.

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