The Logic of Number

Having been so very struck by Russell and Frege as a student —  a long time ago in a galaxy far, far away — I have always wanted some form of logicism to be true. And the deviant form canvassed by Tennant back in his rich 1987 book Anti-Realism and Logic (I mean, deviating from neo-Fregean version we all know) is surely worth more attention than it has widely received. So I’m looking forward to reading Tennant’s latest defence of his form of logicism, in his new book The Logic of Number, published a few weeks ago at a typically extortionate OUP price.

On a quick browse, the book goes in a somewhat different direction to what I was expecting, having read Tennant’s 2008 piece ‘Natural Logicism via the Logic of Orderly Pairing’. The additional new apparatus for developing arithmetic added in that paper seems not to be in play again here. Rather, the book doesn’t (I think) develop arithmetic as far, but instead goes on to discuss logicist accounts of rationals and reals.

I’ll perhaps try to say something more about the book in due course, when some other reading commitments are done and dusted. Meanwhile you might well in fact be able to take a look if interested. For The Logic of Number, I’m glad to say, has just been also made available at Oxford Scholarship Online. So if your university library has a suitable OUP subscription, it should be free to read.

Beginning Category Theory: Chs 1–8

Here now are Chapters 1 to 8 of Beginning Category Theory

The new chapter is on initial and terminal objects; there have only been minor changes to other chapters from Chapter 4 onwards. These new chapters 1 to 8 are I think a significant improvement to the corresponding Chapters 1 to 6 of the old Gentle Introduction. Or at least, they are a significant improvement in clarity of content. But I don’t think I have yet quite hit the mark as far as tone/reader-friendliness is concerned. So I need to let these pages marinade for a few days, and then return to them (particularly to the last couple of action-packed chapters) to make them a little more relaxed. Onwards!

Beginning Category Theory: Chs 1 to 7

Here now are Chapters 1 to 7 of Beginning Category Theory

The new chapter is on kinds of arrows. I have also revised Chapter 3 (now preferring to talk about implementing structures in set theory, rather than to talk of set-theoretic surrogates or proxies — the change of rhetoric isn’t really a change of view, but will I hope slightly mollify some readers!).

I should say that Beginning Category Theory is very much a work in progress, and I can imagine these early chapters getting significantly revised to better fit the later ones in content and tone. But, for all that, I’m putting them online as I go along, when I get to the point of thinking that a new chapter is at least better than the corresponding old one in the Gentle Intro!

Online mini-conference on logical pluralism

Just a reminder that I’m very happy occasionally to announce here new books, online conferences, etc., that are likely to be of interest to enough readers of this blog. Just let me know if you have something suitable you want to publicise.

So: there is an online three-paper conference Logical Pluralism:  One logic, or many logics? announced for Friday April 1st (from 10 am, EST), from James Madison University:

  • “Perspectival Logical Pluralism”   Roy T. Cook (Minnesota)
  • “Logical Pluralism: Boring Truth? Exciting  Falsehood?”  Erik Stei (Utrecht)
  • “Logical Pluralism and Logical Disputes”  Teresa Kouri Kissel (Old Dominion Univ.)

Zoom links etc. available from the conference webpage here.

Beginning Category Theory: Chs 1 to 6

Slow progress, but some progress is better than none. So here are Chapters 1 to 6 of Beginning Category Theory. The chapters are

  1. Introduction [The categorial imperative!]
  2. One structured family of structures. [Revision about groups, and categories of groups introduced]
  3. Groups and sets [Why I don’t want to assume straight off the bat that structures are sets]
  4. Categories defined [General definition, and lots of standard examples]
  5. Diagrams [Reading commutative diagrams]
  6. Categories beget categories [Duals of categories, subcategories, products, slice categories, etc.]

Both Chs 2 and 3 are mildly revised from the posting a week or so back. Chapters 4 to 6 are tidier versions of what were Chapters 3 and 4 in the old Category Theory: A Gentle Introduction. And so these six chapters taken together replace the first four of the Gentle Intro.

The Stage 1 plan over the coming weeks is to correct/smooth the existing content from the Gentle Intro. Stage 2 will then be to round out that content (same or closely related topics, same level, but improved examples, etc.). Stage 3 will be to push on to a look at a few more topics I want to cover.

Updated: The definition of a commutative diagram improved.

The Pavel Haas Quartet play Haydn Op. 42

From photo by Marco Borggreve [Click for full original image]
Grim, grim days.

For fifteen minutes of consolation, here is a wonderful performance of Haydn’s Op. 42 String Quartet by the Pavel Haas Quartet. It is on the BBC website, a late night programme from a few days ago: the Haydn starts at 4:59:30.

This must, I think have been recorded from a Wigmore Hall concert some years ago now, when the violist was Pavel Nikl. So the cheering photo, from the quartet’s latest gallery from the fine photographer Marco Borggreve, doesn’t quite fit! But I thought I would post it anyway …

Beginning Category Theory: NOT Chs 1 to 3

I wanted to be reminded of a different Russia. And so picked up our old Penguin copy of Turgenev’s Home of the Gentry to start re-reading. And it has fallen quite to pieces. Which somehow seems rather symbolic.

We must all distract ourselves from the dire state of the world for some of the time as best we can. Mathematics still works for me: as Russell remarks, “it has nothing to do with life and death and human sordidness”. So I have been starting working again on my notes on category theory which, as I’ve said before, are downloaded rather embarrassingly often given their current half-baked state. It will help keep my mind off other things, trying to get them into better shape.

Things are going slowly, as I need to do a lot of (re)reading. But for those who might like the distraction, here are the first three chapters (under 30 pages). Chapter 3 is mostly new, and the previous chapters have been significantly revised.

[Update: the Preface has now been revised too.]

[Further update: Hmmmmmmmm. I think a more radical rethink of the opening chapters is needed …. so I’ve dropped the link, and am banging my head on the desk ….]

War plates

From a series of six at the Ai Weiwei exhibition in Cambridge. Extraordinarily evocative, appallingly timely.

Schubert for dark days

[Video recording no longer available.] Dark days. For consolation, inspiration, a reminder of better things, a great performance of Schubert’s G major Fantasy Sonata D894 by Pavel Kolesnikov at Wigmore Hall a couple of weeks ago.

The first movement starts at 5.00; the remaining movements start at 1.17.00.

Kolesnikov’s full programme, as if a musical evening with Proust, is very worth listening to; but the Schubert is stupendous. Here is Frances Wilson on her fine blog: 

Kolesnikov … launched into the serene first movement of Schubert’s ‘Fantasy’ Sonata, D894, a mesmerizingly spacious account so carefully, subtly nuanced that as each new subject was introduced it took on a special character of its own, as if one was opening a little secret door into another room, another world where we glimpsed, momentarily, people dancing a gentle waltz, unaware they were being observed, or overheard the delicate tinkling sounds of a music box…..Kolesnikov flexes tempos, applies stringendo, pulls back again, allowing the music to ebb and flow, creating an extraordinary sense of time suspended, yet never once sounding contrived nor insincere; this was coupled with a powerful intimacy, as if we had exchanged the Wigmore Hall for an elegant Parisian salon. For a composer for whom pauses and silences are so meaningful, this for me was some of the most sensitive Schubert playing I have ever encountered.

That seems exactly right.

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