Paul Halmos (he who coined ‘iff’ for ‘if and only if’, among a few other things), wrote in his ‘automathography’ that a good way to learn a lot of mathematics is by reading the first chapters of many mathematics books. Wouldn’t it be great if someone wrote a single book in the spirit of this advice, but put the material order, cross-referenced it, showed connections between different areas, and included exercises? That’s what Eric Schechter’s Handbook of Analysis and Its Foundations does. I simply love this book.

If you see a technique in a paper that stumps you–assuming it is not written in the annoying “analytic” style, which dusts out the formal tracks for the sake of “clarity”–a book like Schechter’s can help you to get under the puzzling construction to (hopefully) allow you to build up to understanding it or, sometimes nearly as valuable, understanding more about what it is that you do not understand in that case.

Choices: An Introduction to Decision Theory by Michael D. Resnik.

A new book that seems interesting (although I have not read it in its entirety) is:

An Introduction to Decision Theory (Cambridge Introductions to Philosophy) by Martin Peterson

This book is also philosophically oriented and not very difficult under a mathematical point of view.

A new book that seems very interesting is:

Theory of Decision under Uncertainty (Econometric Society Monographs) by Itzhak Gilboa

It has a philosophical introduction and then it offers a mathematically more involved presentation of Savage, De Finetti, etc. Perhaps this is one of the best existing introductions.

In the past I usually used:

Notes On The Theory Of Choice (Underground Classics in Economics) by David Kreps

This is an excellent book, perhaps the most technically oriented of the previous books. But it is very well written and the selection of topics is excellent.

Perhaps the most complete books in this area are the books written by Peter Fishburn. But most of them are out of print. They are mathematically more involved but they are almost self contained.

If you have some previous knowledge of decision theory and some mathematical background perhaps Kreps is the best option. Otherwise the combination of Peterson (Resnik) and Gilboa might be optimal. Hope that this helps.

A similar book would be, for example, Decision, Probability and Utility: Selected Readings by Peter Gärdenfors and Nils-Eric Sahlin. The introductions in this book are brief but focusing on the topics. Nevertheless, the book cannot replace a textbook in decision theory. But it could be used to complement a textbook of this sort. At least I tend to use the book in this way in my classes on rational choice.

Kyburg and Teng’s book has basic introductions to first order logic, logics for AI and probability theory, for example. Some of this will be taken for granted in our book, I think. K&T’s book has also chapters on belief revision and non-monotonic logic. In this respect we will offer something similar. The section on belief change, for example, contains articles by Hansson. Rott, Levi, Spohn, Pearl and the original AGM article, plus a general introduction. This offers a variety of semantics for belief change (possible worlds semantics, decision theoretic semantics of two types, ranking functions, etc). So, reading the basic sections of K&T could motivate the reader to go deeper.

But K&T’s book has chapters on evidential probability and scientific and statistical inference which reflect Kyburg’s own views. We will cover only a subset of these topics. For example, we will not include papers on statistical inference, and about evidential probability we will only include a paper by Kyburg.

The book has to have a reasonable size, so one faces tough choices when it comes to select material. But I think that the book as it is conceived right now can be used at a slightly more advanced level than K&T’s book, which requires a minimum of mathematical and philosophical maturity on the part of the reader. I think that a reader that has some knowledge of logic (say, the completeness results for first order and modal logic) and decision theory (a basic course in rational choice) would be an ideal reader for the entire book. But a reader with exposure to at least some of the basic chapters of K&T’s book might be able to read most of the material in the book. So, under this point of view the two books could complement each other.

Even if the answer is the latter, this comes as a very useful publication; perhaps the best option for texts for the sort of course that I have in mind would be a combination of an introductory text (of the sort that I was talking about) as well as your forthcoming anthology. On that topic, how well do you think that your text would cohere with Kyburg and Teng’s?