Back to business …

A break from logical matters, away for half-a-dozen busy days in Athens, followed by visiting family on the island of Rhodes for a week. Both most enjoyable in very different ways. Then we needed a holiday to recover …

But I’m back down to business. The first item on the agenda has been to deal with some very useful last comments on the draft second edition of Gödel Without (Too Many) Tears, and to make a start on a final proof-reading for residual typos, bad hyphenations, and the like. I hope the paperback will be available in about three weeks. If you happen to be reading this while thinking of buying the first edition, then save up your pennies. The second edition is worth the short wait (and will be again as cheap as I can make it).

I’m still finding the occasional slightly clumsy or potentially unclear sentence in GWT. I can’t claim to be a stylish writer, but I can usually in the end hit a decently serviceable level of straightforward and lucid prose. But it does take a lot of work. Still, it surely is the very least any author of logic books or the like owes their reader. I certainly find it irksome — and more so with the passing of the years — when authors don’t seem to put in the same level of effort and serve up laborious and uninviting texts. As with, for example, Gila Sher’s recent contribution to the Cambridge Elements series, on Logical Consequence. 

Mind you, the more technical bits have to fight against CUP’s quite shamefully bad typesetting. But waiving that point, I really have to doubt that any student who needs to have the Tarskian formal stuff about truth and consequence explained is going to smoothly get a good grasp from the presentation here. And I found the ensuing philosophical discussion quite unnecessarily hard going. And if I did, I’m sure that will apply to the the intended student reader. So I’m pretty unimpressed, and suggest you can give this Element a miss unless you have a special reason for tackling it.

Another book which readers of this blog will probably want to give a miss to is Eugenia Cheng’s latest, The Joy of Abstraction:An Exploration of Math, Category Theory and Life (also CUP). This comes garlanded with a lot of praise. I suppose it might work for some readers.

But the remarks supposedly showing that abstract thought of a vaguely categorial kind is relevant to ‘Life’ are embarrassingly jejune. The general musings about mathematics will seem very thin gruel (and too often misleading to boot) to anyone who knows enough mathematics and a bit of philosophy of mathematics. Which leaves the second half of the book where Cheng is on much safer home ground “Doing Category Theory”.

So I tried to approach this part of the book with fresh eyes and without prejudice, shelving what has gone before. But, to my surprise, I found the level of exposition to rather less good than I was expecting (knowing, e.g., Cheng’s Catsters videos). She is aiming to get some of the Big Ideas across in an amount of detail, and I was hoping for some illuminating “look at it like this” contributions — the sort of helpful classroom chat which tends to get edited out of the more conventional textbooks. But I’m not sure that what she does offer works particularly well. Try the chapter on products, for example, and ask: if you haven’t met the categorial treatment of products before, would this give you a good enough feel for what is going on and why it so compellingly natural? Or later, try the chapter on the Yoneda Lemma and ask: would this give someone a good understanding of why it might be of significance? I’m frankly a bit dubious.

So that’s a couple of recent CUP books that I did acquire, electronically or physically, and am sadly not enthused by. But in their bookshop there is another new publications which looks wonderful and extremely covetable, a large format volume on The Villa FarnesinaOn the one hand, acquiring this would of course be quite disgracefully self-indulgent. On the other hand …

Time to send them home …

I confess to have given little thought in the past to questions of just when objects of problematic provenance in our museums should be repatriated. But, better late than never, I realize I can’t conjure any cogent reason why the “Elgin Marbles”, the Parthenon Frieze and the rest, shouldn’t now be returned by the British Museum and displayed in the beautiful Acropolis Museum. That museum, as we found last week, is already worth a trip to Athens in itself, and the huge gallery waiting for the originals of the rest of the frieze is just stunning. Time the marbles went home.

GWT2, Category theory, and other delights …

A last call for comments/corrections (please!!) for the draft second edition of Gödel Without Tears — I plan to finalize and publish a paperback version around the end of the month. You can download the draft here (though I imagine that anyone interested will have done so by now).

I’ve mentioned before that my three hundred pages of introductory notes on category theory are downloaded surprisingly often — frequently enough for it to be rather embarrassing, given their current ramshackle state. So, with GWT2 simmering on the back burner while I wait to see if there are any last minute suggestions to deal with, I’m getting back to thinking a bit about categories.

I was, for a while, stumbling over two things when thinking about how to revise/develop the notes. Firstly, I didn’t have a clear enough conception of where I wanted to get to.  Secondly, I’ve become increasingly unhappy with the way the very opening chapters are handled (with those distracting sermons about set theory!). But I think that things are now falling into place rather better.

On the question of scope, of where to finish, I’m lowering my sights a bit. I had occasion, the other day, to be looking at the classic book on topos theory by Mac Lane and Moerdijk. It starts with a scene-setting fourteen pages of “Categorical Preliminaries” — a glorified checklist of what you need to bring to the party if you are planning to dive into the book. And that checklist more or less exactly corresponds to the topics sort-of covered (in rushed way towards the end) in the existing notes. So that’s persuaded me that maybe, after all, the notes do get to a sensible enough stopping point (and perhaps only need be rounded out with some brief pointers to routes onwards).

And on the question of how to start, I’ve decided that fussing at the outset about such issues as whether we should identify functions with their graphs just doesn’t make for a happy beginning. That’s largely got to go! But this makes for quite a bit of fiddly re-writing over the initial chapters.

I’m having a family break for a couple of weeks, so the new version of the first seventeen chapters or so won’t be ready for a few weeks. But I’m feeling decidedly cheerier about the project of improving those notes, at least enough for me to rest fairly content with the unambitious result.

The wider world continues to go mad and/or bad in various depressing ways. The most distractingly enjoyable novel I have read just recently? Perhaps Elspeth Barker’s atmospherically gothic O Caledonia. I dived in because of an enthusiastic recommendation by Maggie O’Farrell. I enthusiastically pass on the recommendation!

I have also been much distracted by Edmund de Waal’s The White Road, swept along by his obsession with porcelain and its origins (with walk on parts for Spinoza and Leibniz by the way). Strangely gripping I find!

Avigad on Mathematical Logic and Computation

A heads up, as they say. Jeremy Avigad’s new book Mathematical Logic and Computation has now been published by CUP (or at least, an e-version is already available on the Cambridge Core system if you have access — with the hardback due soon). Here’s a link to the front matter of the book, which gives you the Table of Contents and the Preface. Between them, they give you a fair idea of the coverage of the book.

As you’d expect from this author, this book is very worth having, an excellent addition to the literature, with plenty more than enough divergences and side-steps from the more well-trodden paths through the material to be consistently interesting. Having quickly read a few chapters, and dipped into a few more, I’d say that the treatments of topics, though very clear, are often rather on the challenging side (Avigad’s Carnegie Mellon gets very high-flying students in this area!). For example, the chapters on FOL would probably be best tackled by someone who has already done a course based on something like Enderton’s classic text. But that’s not a complaint, just an indication of the level of approach.

When the physical version becomes available — so much easier to navigate! — I’m going to enjoy settling down to a careful read through, and maybe will comment in more detail here. Meanwhile, this is most certainly a book to make sure your library gets.

Hilary Mantel, 1952–2022

From a photo by Richard Phibbs for Harper’s Bazaar, taken at Hampton Court Palace.

Such a wonderful writer. The Wolf Hall trilogy is the extraordinary work of our times, that only strikes you as all the greater on rereading. And the many touching tributes to Hilary Mantel’s human qualities make her untimely death seem all the sadder.

Another book, another disappointment

I picked up a copy of the very recently published A New History of Greek Mathematics by Reviel Netz in the CUP Bookshop a couple of weeks ago — an impulse buy, encouraged by the rave endorsements on the back cover.

This is the most irritating book I’ve read (well, not read to the bitter end) for a long time. On the positive side, it is extraordinarily interesting and illuminating about the intellectual and cultural milieus at various stages in the development of mathematics in the ancient Greek world. It told me a great deal about our fragmentary knowledge about the earlier figures, about the kinds of mathematics being pursued, when and why. That background story is told very readably, with zest and engaging enthusiasm. So Geoffrey Lloyd could be spot on when he writes that the book “brings to bear an extraordinary range of material from non-Greek as well as Greek sources, and develops original arguments concerning the fundamental question of why and how Western science developed in the way it did”.

So why the irritation, the great disappointment? Because the author, sad to say, gives no sense at all of having any real feel for mathematics. His accounts of ancient proofs (and actually there are surprisingly few detailed ones) are to my mind uniformly very poorly and unclearly done; they just don’t pass muster by normal expositional standards. I suspect that the author has zero significant mathematical background: and it shows badly. Having — only metaphorically, as I hate maltreating books! — thrown the New History across the room for the fourth or fifth time in frustration, I gave up after Archimedes. Though I took away this much: one day, I’d like to find out more about just what Archimedes knew about conics and the proofs he had available to him, as reconstructed by a competent mathematician.

GWT2 — a third (near-final?) full draft

There is now a third complete draft of the forthcoming new edition of Gödel Without (Too Many) Tears. You can download it here.

What’s changed this time, since the last full draft? There has been some more typographical micro-adjusting (you won’t notice!). A few more typos have been fixed, and there have been some scattered very minor changes in phrasing for clarity’s sake. I plan to do a bit more work on the index, but I hope the rest of the book is now in a near-final state.

Corrections and suggestions for local improvements will still be extremely welcome for another few weeks. I’ll then be getting back to GWT after a planned holiday and family time. To be definite: I’ll be calling a halt to further tinkering the weekend of October 29th, with the aim of getting a second edition out in print in November. So all comments, including — especially including! — quick notes of the most trivial typos, will be most welcome until then. (And many thanks to those who have emailed comments so far.)

Added Sept. 25: Minor corrections/revisions in Ch. 14, Ch. 17 and Appendix.

Saul Kripke, 1940–2022

Much will be written, no doubt, about the man (whom I never met), and here I remember only the impact that Kripke had on logic-minded philosophers of my generation and the next. That was immense, from the time of his absurdly precocious first papers on modal logic (the first JSL paper published when he was nineteen), through the 1970 Princeton lectures on Naming and Necessity, and the later 1970s papers — such as the “Outline of a Theory of Truth”. And there was so much more too. Those 1970s papers struck me, still strike me, as a paradigm of philosophy — imaginative but full of good sense and straight talk, with forceful arguments appealingly written with great clarity, and in the background a real depth of technical logical knowledge lightly worn.

Unlike some, I wasn’t such a fan of Kripke’s 1981 long paper on Wittgenstein and rule-following, which indeed perhaps marked the end of his extraordinarily fertile great publishing period. But there is a very large amount of still unpublished work from then and later, with significant pieces to appear in further volumes of his Collected Papers if the first volume, Philosophical Troubles, is anything to go by. I look forward to that. And look back now to so many rich hours spent in Kripke’s intellectual company.

Postcard from Cambridge to … Bulgaria

Wren Library, Trinity College Cambridge

As I have said before, it is difficult to know quite what to make of the absolute numbers given in the stats for this website (supposedly there are about 35K ‘unique visitors’ a month). But the relative numbers can surely be trusted. Every month, the largest number of visitors come from the US, followed by Germany and then GB. And there are no surprises in the next few countries down the list.

But regularly about the tenth on the list, ordered by numbers of page views, is Bulgaria. And this really is a surprise, at least to me. The population of that country is less than a fifth of that of Poland, for example, yet supplies a dozen times as many visitors. Indeed, there are over a quarter as many visitors from Bulgaria as from here in GB. In fact, relative to size, it seems that’s where Logic Matters is most read!

A little googling suggests that logic has a very substantial presence in the University of Sofia, with a large department. So maybe some students from there find their way here. And I guess free resources are always going to be particularly appreciated by those in relatively poorer countries. Anyway, warm greetings from Cambridge, if you are exploring Logic Matters from Bulgaria!

GWT2 — a second full draft

There is now a second third complete draft of the forthcoming new edition of Gödel Without (Too Many) Tears. You can download it here.

What’s changed? There has been a fair bit of typographical tidying (which you no doubt won’t notice, but I might as well try to make things consistent!). The index has grown a bit, though there is more work to be done there. Some typos have been removed, there have been some scattered minor changes in phrasing, and further changes to tidy the way topics in different chapters are linked together. But the main update has been to the chapter on the Diagonalization Lemma: I’ve hopefully much improved this by re-arranging the material in a more logical way.

So that’s enough by way of updating to be worth putting on line now. The first full draft has been downloaded about 650 times. If you are one of those actually reading it, you might want to download the new improved version.

To repeat what I said before: It is too late to write a very different book, and after all this is supposed to be just a revised edition of the seemingly quite well-liked GWT1! This is not the moment, then, for radical revisions. But otherwise, all suggestions, comments and corrections, including quick notes of the most trivial typos, will be most welcome! Send to the e-mail address on the first page of PDF, or comment here. (Just note the date of the version you are commenting on.) Comments will continue to be welcome for the next month or so.

Added Sept 17: revised version of second draft posted, with minor changes to Preface and Chapters 1 to 4.
Added Sept 18: revised version posted, this time with minor improvements to Chapter 5.
Added Sept 21: revised version posted, with mostly very minor improvements to Chapters 6 to 15 (the one substantive correction is at the very top of p.76 where I’d made an unnecessary assumption that we are dealing with a consistent theory).
Added Sept 22: second draft now replaced by a third draft

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