To exorcise the demons of irrationality, turn to this rigorous--if overzealous--study of everyday logic. Cognitive illusions--like optical illusions--hold us in their thrall, says Piattelli-Palmarini (Cognitive Science/Institute San Raffaele, Milan). But theoretical breakthroughs in cognitive science provide revolutionary new avenues for thought. Addressing everyone who wants to make more rational decisions, Piattelli- Palmarini unveils the ``discovery'' of the ``cognitive unconscious.'' This term, with its nod to Freud, refers to the reflexive patterns of reasoning in which we engage unreflectively, even though counterintuitive but logically correct thinking would serve us better. Asked, for instance, which outcome is more likely in a coin flip, ``heads-heads-heads'' or ``heads-tails-heads- tails,'' most people use incorrect logic to conclude that the latter is more likely (in fact, ``the longer the sequence, the less probable it is''). Piattelli-Palmarini explores the ``tunnels'' of cognitive illusion, showing how familiar problems, (drawn from the realms of medicine, demography, economics, and gambling) flummox most people. Then he corrects common misapprehensions, mapping the rational terrain that lies outside these tunnels, even making an arcane but crucial fact about statistics clear to the general reader. By revealing how most respondents err in, for instance, guessing someone's profession based on a personality profile, Piattelli-Palmarini rigorously defines the rules of probability and deduction. Some will object that what he calls ``irrationality'' is itself a function of the abstraction of such problems, but he vigorously defends cognitive science against such arguments. Perhaps less defensible is his pretense that its ideas represent a revolutionary breakthrough; the issues he raises are, after all, part of a 2,000-year-old philosophical debate. Whether or not his grand claims are justified, as a primer for problem-solvers, this book has great merit.