I’ve just finished writing a short paper with the title “Santa’s singleton” (think about it …), of which I’ll post a version here in due course, once I’ve tried it out in a talk or two. Try to contain your excitement. Meanwhile, you might like to know about five logic books that have turned up on the new books shelves in the C.U.P. bookshop fairly recently. Or then again, if like me you have a dauntingly high pile of recent books you’ve been meaning to read which is already growing too fast, maybe you won’t like to know. But here’s the list anyway, in order of appearance …
- Bernard Linsky, The Evolution of Principia Mathematica, (subtitled ‘Bertrand Russell’s Manuscripts and Notes for the Second Edition’ which gives you a good idea what it is about). OK, this is a scholarly effort aimed at specialists and very expensive: but I’ve sat in the shop and dipped at length and found parts of it very interesting. A definite ‘must’ to order for the library, and well worth looking at when it arrives. In fact, that goes for the rest too.
- Matthias Baaz et al., eds, Kurt Gödel and the Foundations of Mathematics
Horizons of Truth is one of those large mixed-bag collections of papers emerging from conferences. But it has a starry line-up of contributors, and — dipping again — some of the papers look good or very good. I’m going to be reviewing this for Philosophia Mathematica, so when I get to work I’ll perhaps blog about this collection here.
- Juliette Kennedy and Roman Kossak, eds, Set Theory, Arithmetic, and Foundations of Mathematics is a collection whose “inspiration is the work and interests of the logician Stanley Tennenbaum, and through Tennenbaum the work of Kurt Gödel”. It happens that Tim Button and I have just written a short paper forthcoming in Philosophia Mathematica on the philosophical significance (or lack of it) of Tennenbaum’s lovely theorem about non-standard models of arithmetic: so I’ve seized on this with real interest. Again, I’ll report back in the blog when I’ve had a chance to read more.
- Harold Simmons, An Introduction to Category Theory has the expository virtues you’d expect from the author. I’m not so sure that it is the One First Book On Categoty Theory that is perhaps still to be written. But having read a largish initial chunk in a couple of sittings, I can certainly recommend it.
- Sara Negri and Jan von Plato, Proof Analysis. From the blurb: “This book continues from where the authors’ previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic.” I very much liked the previous book (it worked well in a grad reading group, and we learnt a lot from it). The work on axiomatic theories is original, and this looks likely to be a very rewarding read.
So there they are. I’m sure most of us will knock them off in just a few days. Next!!