Term rattles on, leaving little time for doing much reading other than for the two logic seminars for grads (this term we looking at Mary Leng’s book on Mathematics and Reality in one, and Sara Negri and Jan von Plato’s Structural Proof Theory in the other). So the books that I’ve recently bought start to pile up on my desk. Perhaps if I briefly mention there here, they will feel slightly less neglected.
So at the bottom of the pile, there from just before the beginning of term, you’ll find the new Cambridge Companion to Frege co-edited by my colleague Michael Potter who came into the project late. The collection looks a bit of mixed bunch, as is the way of these things. But the three pieces I’ve read so far (by another colleague Alex Oliver, by Richard Heck, and by Peter Sullivan) are impressive. Though the high sophistication of these pieces makes me wonder a bit who the Companion is for.
Next up the pile is the Alan Weir’s Truth Through Proof: A Formalist Foundation for Mathematics. As you might expect if you’ve met Alan at all, this has the most engaging possible preface! — and it should be a provoking read. Formalism lives? In 2010??
Then there is Oded Goldreich’s P, NP and NP-Completeness: The Basics of Computational Complexity which has just come out too. Having read the first two chapters, this promises to be highly accessible, a sort of warm-up exercise to see if you want to tackle his ‘big book’, Computational Complexity. In fact I really must try to read the rest over the coming few days, as a refresher since I want to say something about P-vs-NP in my first year lectures (just for fun, and to keep the mathematically ept awake).
Next up is William Henry Young and Grace Chisholm Young’s The Theory of Sets of Points. Published in 1906. And reprinted last year in CUP’s “Cambridge Library Collection”. Why is that in the pile, you ask? Because I want to see what set theory — the actual theory that mathematicians use(d) — looked like after Cantor had been initially digested but before Zermelo. I very much enjoyed reading the first few chapters in a coffee shop after buying it, probably because the style is so very reminiscent of old maths books from the 30s and 40s from my father from which I learnt maths as a school boy.
Top of the pile, and only just published, is W. D. Hart’s The Evolution of Logic which promises to be an intriguing but bumpy ride. Here’s part of the blurb:
After World War II, mathematical logic became a recognized subdiscipline in mathematics departments, and consequently but unfortunately philosophers have lost touch with its monuments. This book aims to make four of them (consistency and independence of the continuum hypothesis, Post’s problem, and Morley’s theorem) more accessible to philosophers, making available the tools necessary for modern scholars of philosophy to renew a productive dialogue between logic and philosophy.
How well will Hart pull this off? He certainly hasn’t made things easy for the reader by going along with about the lousiest bit of maths typesetting I’ve seen since the days when books were done on electric typewriters. All the symbols are in the same roman font as the rest of the text (see what I mean by following the Google preview link on the CUP webpage for the book). It makes the symbol-heavy pages ludicrously and utterly unnecessarily hard going. What on earth were CUP thinking of? Still, Hart’s topics are central enough for me to still want to make the effort. But when term finishes.