Not too much serious work has got done the last couple of weeks, what with touristy visits and finishing Christchurch teaching. But I have been dipping into two recent books.
Leila Haaparanta’s The Development of Modern Logic (OUP 2009, weighing in just under a thousand pages) is a curious tome. Eighteen essays by various hands, of widely varying lengths and widely varying depth. There’s a sixty seven page essay on “Late Medieval Logic” and just seven pages on “Gottlob Frege and the Interplay between Logic and Mathematics”; “The Development of Mathematical Logic from Russell to Tarski, 1900–1935” gets a hundred and fifty three pages; but “Set Theory, Model Theory, and Computability Theory ” (yes, all three!) are supposedly polished off in just twenty eight. (The last of these chapters is by the usually entirely admirable Wilfrid Hodges; quite unsurprisingly, he fails to pull off the impossible task of covering all that in a useful way in so short a space).
This all suggests, I’m afraid, a lack of editorial vision, shaping, and direction, and a lack of a clear sense of who the volume is intended for. Still, even if the several essays don’t add up to a coherent book, they mostly look pretty interesting, and I’ll try to blog about them, chapter by chapter, here, when I get back to the UK.
I’ve also started reading Kenneth Kunen’s The Foundations of Mathematics (College Publications, 2009). Kunen’s book on set theory is a classic. This one is much more introductory:
This book grew out of some notes for a beginning one semester graduate level course in logic … The course, and this book, provide an introduction to set theory, model theory, and recursion theory. (p. vii)
But given Kunen’s expository abilities on technical matters, I’m hoping this one too will prove an illuminating read. I’m not so sure, though, about his philosophical asides. But I suppose you have to admire the imperialist confidence in claiming
All abstract mathematical concepts are set-theoretic. All concrete mathematical objects are specific sets. (p. 14)
(That quote, followed by “Discuss”, would make a nice tripos question for the Math Logic paper …). Again, I’ll say more about this book here when I’ve got through more. But it should certainly be in your uni. library.