OK, I’m back from Cornwall (and very nice it was too, thanks for asking), and am trying to get the philosophical corner of my mind back into gear. Now, as I mentioned a couple of posts ago, Charles Parsons has published a new collection of some of his essays, *Philosophy of Mathematics in the Twentieth Century*, which (sensibly or otherwise) I’ve said I’ll review for *Mind*. So I better make a start on the reading. On the principle that telling people you are going to do something is a good way of keeping yourself up to the mark, I said that as I read through I’ll start posting some comments here. Please do chime with and thoughts and comments of your own.

If you want to be reading along, now I’ve had a first skim through the beginning of the book, here’s the plan for the first few instalments. For my opening effort — which I’ll post at the end of the week — I’ll look at Parsons’s *second* essay ‘Realism and the Debate on Impredicativity, 1917-1944’ (originally published in the Feferman festschrift edited by Sieg et al.).

Parsons’s first essay, new to the present volume, is on ‘The Kantian Legacy in Twentieth-Century Foundations of Mathematics’, and perhaps the most interesting bit of this not-very-exciting essay is on Bernays, so it seems a good notion to discuss that alongside the third essay ‘Paul Bernays’ Later Philosophy of Mathematics’ (published in Dimitracopoulos et al., eds, *Logic Colloquium 2005*).

Then for my third instalment I’ll look at Parsons’s next two pieces, a short piece on Gödel from the *Dictionary of Modern American Philosophers*, and then the substantial piece on Gödel’s essay ‘Russell’s Mathematical Logic’ written as an Introductory Note for Gödel’s *Collected Works*, Vol. II.

So watch this space!

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Alex RegueiroI’m looking forward to your future thoughts on this collection. As a student of mathematics (and somewhat of computer science), with some decent experience in logic, I’ve been thinking of picking up a book on the philosophy of mathematics for some time now. Ideally one that is largely self-contained in its philosophical aspects, but gives a nice overview of the history and philosophical views on mathematics and logic. Perhaps this compilation of essays would be an appropriate thing to have a look at? If not, my (rather passive) search shall continue.

Peter SmithI don’t think the Parsons collection would be the best place to start for a reader coming from where you currently are. However, there are two wonderful textbooks on phil. maths that I always used to recommend to students; Stewart Shapiro’s “Thinking about Mathematics”, and Marcus Giaquinto’s “The Search for Certainty”. (The links allow you to “look inside” which will give you an indication of their contents. The books are different enough in emphasis and content for it to be worth looking at both.)

Alex RegueiroPerfect. Thank you for these recommendations. I think I’ll leave Parsons’s collection aside for now, as you suggest. Presumably these two books should be of reasonable interest to someone like myself with some mathematical maturity in logic, but only minimal exposure to the philosophical side thus far.