Robyn Dawes, "Rational Choice in an Uncertain World", great intro for a popular educated audience.

The edited volumes "Judgment Under Uncertainty", "Heuristics and Biases", and optionally "Choices, Values, and Frames", in that order, for a survey of the research in heuristics and biases.

Probability theory for complicated problems that can be solved by calculus: E.T. Jaynes, "Probability Theory: The Logic of Science"

Probability theory and the structure of the real world exploited by tractable cognitive algorithms: Judea Pearl, "Probabilistic Reasoning in Intelligent Systems"

Some other books I found important on my journey:

"The Moral Animal" by Robert Wright, popular intro to ev-psych

"The Adapted Mind", especially "The Psychological Foundations of Culture", by Tooby and Cosmides (less popular ev-psych)

"Adaptation and Natural Selection" by George Williams (how to stop anthropomorphizing evolution)

"The Tao is Silent" by Raymond Smullyan (correct action does not have to be effortful or rigidly controlled)

Robin Hanson runs a blog called "Overcoming Bias" at http://www.overcomingbias.com/ . It's heavily Bayesian. Hanson's the George Mason economist who invented prediction markets.

Damn it, perils of reading too many blogs at once on RSS; thought I was looking at another blog asking for cites on bayesianism. Elizer: feel free to delete both posts.

Nassim Nicholas Taleb is a really good writer on this subject, especially with regards to the financial markets. You can either read the Black Swan or Fooled by Randomness (or both, but there is a lot of overlap, personally I think Fooled by Randomness is a better read, although the ideas in the Black Swan are a little more developed).

If you want to get technical, my textbook: Jay Devore, Probability and Statistics for the Engineering and Sciences is an excellent treatment of the subject and begins at the most basic level and covers many advance subjects. I think any econometrics textbook is good too, as the skills you learn apply not just to economic time series but in general when thinking about how to synthesize observed data into a descriptive model.

Eric: Can't I keep them, please? (If not, I'll delete all four comments, I guess.)

"Causality" by Judea Pearl is an excellent formal treatment of the subject central to empirical science.

W. W. Bartley's "The Retreat to Commitment" is the best book on epistemology, bar none, in my opinion. He fixes a small bug in Popper's Critical Rationalism, to suggest that even the epistemic approach should be subject to criticism, and produces Pan-Critical Rationalism (hence my blog's title: pancrit.org). He then proceeds to attack PCR from every direction he can think of.

Extreme Bayesianism may be a more modern incarnation of the approach, but the history of rationalism and the description of how to evaluate your rationality is truly valuable, and hasn't been replicated in the current context.

My general advice for undervalued reading: textbooks. Go to your nearest college bookstore, sit in the aisles, and browse and read textbooks on your main subjects of interest. Until you've read and understood textbooks, why bother with anything else?

Got any specific textbooks to recommend?

(Seconding the general principle, but it can be hard to find the good textbooks.)

The best textbooks ever are "The Feynman Lectures On Physics"

I constantly buy textbooks and use them as bedtime reading. A wonderful way to pick up the fundamentals (or at least a superficial familiarity) with many subjects. However, just reading any textbook is unlikely to actually give a great insight into any field. Doing exercises, and in particular having a teacher or mentor point out what is important, is necessary for actually getting anywhere.

To add at least some thread-relevant material, I'd like to recommend Eliezer's web page "An Intuitive Explanation of Bayesian Reasoning" at http://yudkowsky.net/bayes/bayes.html

I'm reading Piattelli Palmarini's "Inevitable Illusions" right now, but I'm not that impressed so far. Most of the contents seem to be familiar from this list.

Eliezer:'Probability theory and the structure of the real world exploited by tractable cognitive algorithms: Judea Pearl, "Probabilistic Reasoning in Intelligent Systems"'

Is the use of the phrase "cognitive algorithms" intended to mean that these algorithms are plausibly implemented in our own brains?

I have been looking for 2 texts on the design of experiments. One that can be used by non-statisticians like graduate students in physics, chemistry, economics and the like. Another to introduce the non-mathematical to the field. One group who I think could benefit from the design and analysis of experiments are some people I know who run microcredit operations. Any suggestions? John

I thought "Inevitable Illusions" was terrible. Full of smugness of the "ha ha, look how stupid you are" variety, and (appropriately, I guess) vitiated by reasoning errors of its own. (See a brief analysis of one glaring example; those who are fluent with probability calculations will find it a bit laborious.)

"Perception and Misperception in International Politics" by Robert Jervis.

I have to recommend Eliezer's essay on his web site An Intuitive Explanation of Bayesian Reasoning. I am sure that everything on there (yudkowsky.net) is well worth reading, but I haven't gotten to anything else yet.

For a lay reader looking for an introduction to ev-psych, I advise against Wright's "The Moral Animal", suggested in Eliezer's first comment. It's been several years since I read it, but I remember it being boring, unenlightening, and bogged down with biographical vignettes of Charles Darwin. It might be a good intro for people who enjoy history and literature more than science texts, but this is pure speculation--I know few of these people and rarely give them books. If you want a light intro without the fluff, I'd suggest "Evolutionary Psychology: An Introduction" by Workman and Reader, a completely nontechnical textbook that actually spends more time explaining ev-psych than trying to convince the reader it's not an evil, misogynistic pseudoscience. It's the sort of text high-school (or even middle-school) teachers would use in a parallel universe where "evolutionary psychology" has a redundant adjective.

Ev-psych seems to get advertised a lot around here, so it might be good to add David Buller's Adapting Minds: Evolutionary Psychology and the Persistent Quest for Human Nature, a criticism of evolutionary psychology, to the reading list. (After that, of course, do also read Debunking Adapting Minds, the criticism of the criticism.)

An oldie but goodie that I forgot to add: Language in Thought and Action by S. I. Hayakawa.

E.T. Jaynes, Probability Theory: The Logic of Science

and make sure you get the "unofficial errata"