Peter Smith's Blog, page 48

Luca Incurvati’s Conceptions of Set

Almost a year ago, I started a sequence of what turned out to be fifteen blog posts on Luca Incurvati’s book Conceptions of Set. I never got round to returning to put everything together (after some comments from Luca himself) into a more careful and re-thought review. One day …! But meanwhile, if you were interested in those posts, you might enjoy Øystein Linnebo’s new review of the book.

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World Logic Day — a small contribution!

A small contribution for World Logic Day 2021 today: Gödel Without (Too Many) Tears is now available as a free PDF download — linked here.

Later in the year, I plan to put up a series of short podcasts, where I give introductory chapter-by-chapter chats about book. Many students are stuck in front of video lectures for far too long at the moment anyway, so I’m very reluctant to adding to the catalogue of full-scale lectures, quite apart from the time it would take me to record decent ones. So brisk arm-waving talks sketchings some Big Ideas which you can listen to while walking around or staring out of the window, followed by readings at your own pace of comparatively content-rich chapters, seems a format for teaching/learning worth trying out.

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Lea Desandre and Ensemble Jupiter, Lettres Amoureuses

Music for lockdown. And “without music, life would be a mistake”, as Nietzsche said.

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World Logic Day — a small contribution!

A small contribution for World Logic Day 2021 tomorrow: Gödel Without (Too Many) Tears is now available as a free PDF download — linked here.

Later in the year, I plan to put up a series of short podcasts, where I give introductory chapter-by-chapter chats about book. Many students are stuck in front of video lectures for far too long at the moment anyway, so I’m very reluctant to adding to the catalogue of full-scale lectures, quite apart from the time it would take me to record decent ones. So brisk arm-waving talks sketchings some Big Ideas which you can listen to while walking around or staring out of the window, followed by readings at your own pace of comparatively content-rich chapters, seems a format for teaching/learning worth trying out.

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Logic: A Study Guide now “launched”

I’ve now retired the mid 2020 version of the TYL guide, and marked the new year by officially launching a replacement, retitled as Logic: A Study Guide. (Although the Guide’s title has changed, its webpage address stays the same, so as not to break external links.)

The Guide now takes the form of two PDFs. The first contains the rewritten Chapters 1 to 7. That’s three preliminary chapters about the aims and structure of the Guide, and then four chapters on very-elementary (“naive”) set theory, FOL, elementary model theory, and arithmetic/Gödel’s theorems. These have already been posted here, and many thanks for the most useful comments so far.

The second PDF contains Chapters 8 onwards, renumbered but otherwise unrevised from the last version of TYL. As the weeks and months go by, the first PDF should grow as more newly revised chapters are added, and the second PDF will correspondingly shrink. Or at least, that’s the plan!

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Logic: A Study Guide — Naive set theory

I’ve decided to divide the coverage of set theory in the Guide into three different chapters. There will now be two chapters in Part I. A short initial chapter on naive set theory, meaning the bits and pieces of notation, concepts and constructions that are often taken for granted in even very elementary logic books. Mathematicians shouldn’t need the chapter, but it could well be useful for philosophers without much mathematical background. This chapter therefore now comes before the chapters on FOL, model theory, and arithmetic. Then, after those chapters, there will be the main chapter on elementary set theory (a first real encounter at the level of e.g. Enderton’s book or a little more). A later chapter on hard-core set theory (large cardinals, forcing, and the like) belongs in Part III.

So I’ve now inserted the draft chapter on naive set theory (and made a few changes too to other chapters, responding to a few comments and suggestions). Here then is the current version of Part I of Logic: A Study Guide, still lacking its main chapter on set theory, which I hope will follow fairly shortly.

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A Christmas card, from a small corner of Cambridge

From the Fitzwilliam Museum

So here we are. I don’t need to tell you that it’s been a troubling year in so many ways. Though as I have said before, compared with too many people, we personally are very fortunately placed — staying healthy (thanks for asking), no small children or very aged relatives to be deeply anxious about, in funds, well-housed, delightful walking on our doorstep (if you have to be locked down in a city, central Cambridge is one of the better options), and indeed with some gently lovely countryside still accessible not many minutes away. Friends and relations are there frequently on Zoom and FaceTime. The thing we miss most is being able to travel, and in particular to meet up in person with The Daughter who lives abroad. The weeks do drag, and the sameness can be enervating. But we mustn’t, and (mostly) don’t, complain. There is, in the circumstances, still much to be grateful for. But there is no question but that it is going to be a long,  long, winter.

The last months have certainly concentrated the mind on what really matters. Family and being in closer contact with nature seem to be very high on most people’s list: they certainly have been on ours.

Have any philosophers recently been writing particularly well on lockdown themes? I don’t know. But I wouldn’t entirely bet on it, given philosophers’ propensities for daftness of one sort or another. I was struck the other day by David Papineau’s report of Bernard Suits’s pretentious  The Grasshopper (a book I gave up on very quickly): “The overall argument of the book is that in utopia, where humans have all their material needs satisfied at the push of a button, what we would do would be play games, and therefore playing games is the ideal of human activity. Freed from all the necessities of having to do things we don’t want to do in order to get the material means of life, we’d do nothing but play games.” How profoundly silly is that? Not to say philistine. To be sure, some people sometimes enjoy games. But many of us, me for one (and actually most of the people of my generation I know well), have more or less zero interest in sports or games. And the idea of doing nothing but play games would fill us with horror — apart from spending time with family and friends, there are so many books to read, so much great music to listen to again, art to see, theatre to go to, wonderful countryside to be explored, new cities, new countries, to visit,  … Given the alternatives, spending time on games has very little appeal.

As I said, so many books to read. And re-read. Indeed, I mostly seem to have been re-reading since lockdown. But this is the season when all those lists of Books of the Year are published, depressingly emphasizing how few recent books have come our way. I certainly won’t be adding to those lists of obscure titles you mostly have never head of. Of books which were published this year, I’ve in fact most enjoyed two that very many others have equally enjoyed and recommended: Maggie O’Farrell’s Hamnet and (quite in a league of its own) Hilary Mantel’s The Mirror and the Light. I had just previously re-read with huge enjoyment the first two books in Mantel’s trilogy: but this final part is stunningly good.

On my desk too, dipped into at random times, have been some of Alice Oswald’s books of poetry. I do not find her at all easy or comfortable to read. But her work is deep and challenging and rewarding.

No concerts to go to. Wigmore Hall’s series of streamed concerts has included some wonderful occasions, most recently Mitsuko Uchida’s playing of two Schubert sonatas. Initially, being able to see so many concerts online in lockdown seemed terrific: but lately, I’ve been feeling that they somehow emphasized what we were missing by not being able to go to a live performance shared with an audience. Others have said the same.

Of CDs released in recent months, I’ve kept coming back to Supraphon’s boxed set of the Smetana Quartet playing the Beethoven quartets (recorded between 1976 and 1985), playing of the greatest humanity and insight. The tradition of Czech string quartets is indeed extraordinary.

A lot of reading and listening, then, in lockdown, while cautiously staying very close to home and trying to stay well. And on we will go, let’s hope, for more months like this. But still, the Tuscan wine selections for the holidays are looking very promising; we take our consolations where we can …!

With all good wishes for Christmas and for an eventually much better New Year. And stay well.

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Logic: A Study Guide — Computability, arithmetic, Gödel

I mentioned a couple of days ago that, in the last four months, the newly available PDFs of my Intro to Formal Logic and Intro to Gödel’s Theorems have both been downloaded over 3.5K times (and that’s ignoring an initial flurry of downloads of the Gödel book by people who clicked on a probably misleading link posted elsewhere). In the same period — without any advertising at all — the Teach Yourself Logic Study Guide has been downloaded 7.5K times. I mention this to explain again why I feel I ought to give the TYL project some love and spend some quality time updating the Guide: if it is being downloaded that much, with a big surge at the beginning of semesters, it must be being recommended as useful. So I guess I really ought to make sure it is as useful as it can be, and indeed make sure it reflects what I now think about which texts to recommend.  The last full version was a pretty rough-and-ready layered accumulation of bits and pieces of various vintages: it is well past time for an end-to-end rewrite. But heavens, it’s necessarily a slow job, as I revisit texts old and new!

Anyway … here now is the latest version of the new-style Guide up to the rewritten Chapter 6. This reworked chapter covers three inter-connected topics: (a) the elementary informal theory of arithmetic computability, (b) an introduction to formal theories of arithmetic and how they represent computable functions, which leads up to (c) Gödel’s epoch-making incompleteness theorems

My reading recommendations for this chapter haven’t changed a lot. But a feature of the revised Guide is that (after the preliminary chapters), each chapter has a section (or two) giving an extended overview of its theme, from five to ten pages long. These overviews are supposed to be elementary indicators of some of the topics covered by the recommended reading.  They can certainly be skipped (that’s clearly signalled): the overviews are included just for those who might find this kind of preliminary  orientation helpful. It is difficult to know just how to pitch them, and I will no doubt later revisit the set of overviews to make them more uniform in style and level (so comments appreciated!).

I realize now that the Teach Yourself Logic Study Guide has been so-called for over eight years. Maybe I shouldn’t change the “brand” name after all ….

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Gödel Without (Too Many) Tears published!

Brought to the front again — very short version: GWT is available on Amazon, print on demand.

Longer version: Gödel Without (Too Many) Tears is based on notes for the lectures I used to give to undergraduate philosophers taking the Mathematical Logic paper in Cambridge. Earlier versions were available here online, and have been much downloaded for a decade (and I know they have been used for seminars/lecture courses elsewhere). As occupational therapy in this time of pandemic, I have now very considerably tidied-up the notes into a book format — and many thanks to all those who have helped along with way with suggestions and corrections.

You can think of the result as a much cut-down version of my big Gödel book; it is just over a third of the length, but still aiming to explain some of the key technical facts about the incompleteness theorems. It should be rather more accessible too, as it cuts out some of the fancier digressions in the big book, and tries to make the rest of what it does cover as clear as possible.

The book is now available as a very inexpensive, at cost, print-on-demand book for less than $5/£4/€4.5. See e.g. US link, UK link; you can ‘look inside’ from the linked pages, which will give you a good impression of what the book covers. For other Amazons, use the ASIN identifier B08L5MQLRQ. 

(Small print: sorry about using Amazon; but they bought up the CreateSpace platform …! And they do a surprisingly decent production job at a very low price if you basically forgo royalties.)

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Mitsuko Uchida plays Schubert at Wigmore Hall

Of recent concerts live streamed by Wigmore Hall, this stands out. Mitsuko Uchida plays Schubert’s Piano Sonata in C, D840 ‘Reliquie’, and the great Sonata in G, D894. This, surely, is Uchida at her very best, bringing out the depths, with miraculous moments. Truly impressive Schubert.

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