It is always pleasing to be able to warmly recommend a new book. So let me enthusiastically draw your attention to this newly published book by Tim Button and Sean Walsh, *Philosophy and Model Theory*, just published by OUP. (The pbk is £30 — but this is xvi + 517 larger-format and action-packed pages, so we certainly can’t complain!)

This is a unique book, both explaining technical results in model theory (eventually at a pretty non-trivial level), and exploring the appeals to model theory in various branches of philosophy, particularly philosophy of mathematics, but in metaphysics more generally (recall ‘Putnam’s model-theoretic argument’), the philosophy of science, philosophical logic and more. So that’s a *very* scattered literature that is being expounded, brought together, examined, inter-related, criticised and discussed. Button and Walsh don’t pretend to be giving the last word on the many and varied topics they discuss; but they are offering us a very generous helping of first words and second thoughts. It’s a large book because it is to a significant extent self-contained: model-theoretic notions get defined as needed, and many of the most philosophically significant results are proved.

The book only arrived yesterday, so at this point I have to report just having read the opening four chapters (two carefully, two more quickly) and dipped very speedily in and out later in the book. But it seems to me that — in fact, as you’d expect from these authors — the expositions of the techie stuff is quite exemplary (they have a good policy of shuffling some extended proofs into chapter appendices), and the philosophical discussion is done with vigour and a rather engaging style. The breadth and depth of knowledge brought to the enterprise seems to be remarkable.

So first impressions: this book looks as if it is an outstanding achievement. Logic-minded philosophers should find it fascinating; and — with judicious skimming/skimming (the signposting in the book is excellent) — so should mathematicians with an interest in some foundational questions. Make sure it is in your university library (and at that price, in *your* library!).

Daniel NagaseHaving just read a few chapters from this book, I wanted to share your enthusiastic endorsement of this book. It is indeed quite an outstanding achievement! It is exceptionally clear, organized, and lucid. It includes many thoughtful discussions of the relevant literature, and it manages to blend in philosophical questions with technical ones with ease. It is a model for us to follow!

Daniel NagaseI’m looking forward to reading this. Did you see that John Baldwin has also published a book on philosophy and model theory, also by OUP? It’s called

Model Theory and the Philosophy of Mathematical Practice. To be honest, I found Baldwin’s book a bit confusing and even rambling at places (and I don’t think he did a good job in making stability theory very palatable), so I was wondering if that was a general perception or just me… I do hope Button and Walsh’s book is better organized!Peter SmithBaldwin’s book is CUP, not OUP. I must take a look at it in the Press bookshop (odd that I missed it on the new books shelves). Comparing contents lists, I think the books are rather different enterprises though.

Daniel NagaseOh yes, that’s right. For some reason I just assumed it was OUP.

Yes, they are different enterprises, maybe even complimentary: from what I saw, B & W are showing how to use certain model-theoretic techniques to discuss certain classical philosophical ideas, whereas Baldwin is trying to uncover philosophical ideas from model theory as it is practiced today (B & W also seems more introductory). Regardless, I’d be very interested in hearing your opinion of the latter book as well.

Martin CookeTim Button spoke exceptionally well at a graduate conference in St Andrews ten years ago, where I remember him jogging along the beach in the early morning; he seemed like he was going somewhere good. And I must read this book, as I think of myself as a logician but I have no understanding of model theory; so thanks for bringing it to my attention.