Labyrinths of Reason: Paradox, Puzzles, and the Frailty of Knowledge [Paperback]

Paradoxes are fascinating. You may not agree with Jorge Luis Borges when he speculates that paradoxes and antinomies are evidence that the "undivided divinity within us" has "dreamt the world" (although there is actually a pretty good case that something like this is so). But at any rate, a good paradox is -- to borrow a phrase that was not available when Poundstone wrote this book -- an "incongruity in the structure of the Matrix," an indication that there's _something_ subtly wrong with our intellectual take on reality, whether or not we can agree on _what's_ wrong. (In general but with rare exceptions, there isn't any widespread agreement about exactly how to resolve any of the famous paradoxes, even the ancient ones credited to Zeno of Elea.)

William Poundstone's _Labyrinths of Reason_ is as good an introduction as I know to this entire area of philosophical thought. His exposition is clear and intelligible without sacrificing either accuracy or depth, and he tackles a very broad range of philosophical puzzles, from the problems of inductive logic to NP-completeness. Moreover, he's clearly fascinated by these puzzles and he infects the reader with that fascination. If you don't like Poundstone's book, then this entire subject probably isn't your cup of tea.

If you _do_ like Poundstone's book, you'll find it a window onto what may be a whole new world (if you haven't read other books on this subject before). It's a great way to introduce yourself to mind-bending problems at the foundations of several fields: philosophy, of course (especially epistemology), but also the theory of complexity and computability, artificial intelligence, and even some aspects of theology.

Depending which features interest you most, you might go on to Douglas Hofstadter's Pulitzer Prize-winning tour-de-force _Godel, Escher, Bach: An Eternal Golden Braid_, a magical mystery tour that is primarily intended as a defense of artificial intelligence. (Can machines be conscious? Yes, Hofstadter argues, because we are such machines ourselves.) Or you may prefer to start with his _Metamagical Themas_, part of which deals with the Prisoner's Dilemma. (Robert Axelrod's _The Evolution of Cooperation_ will be a good follow-up too.)

Or you might want to read another good introductory discussion with a somewhat different "take"; in that case you'll want to consider R.M. Sainsbury's _Paradoxes_, which is aimed at arousing philosophical interest in these problems. If you want to see an attempt at a general solution of the full spectrum of paradoxes, check out Nicholas Rescher's _Paradoxes: Their Roots, Range, and Resolution_.

Or you may want to move on to logic and logic puzzles. In that case Raymond Smullyan is your man. Find used copies of _What Is the Name of This Book?, _This Book Needs No Title_, and _5000 B.C._, and/or get a new copy of _The Tao Is Silent_. Or, if you want to dive into rigorous formal logic, try his _First-Order Logic_ and then _Godel's Incompleteness Theorems_. (You may want to read Graham Priest's _Logic: A Very Short Introduction_ first.)

Or if it's the philosophical-theological aspects of infinity that got your attention, try Rudy Rucker's _Infinity and the Mind_. Rucker also deals with, and tries to resolve, some of the paradoxes discussed by Poundstone (e.g. the Berry paradox, involving "the smallest number not nameable in fewer than nineteen syllables," which is apparently an eighteen-syllable name for that very number).

Wherever you go next, if you're not already familiar with these subjects, you won't find a better introduction than Poundstone's book. If any of the above sounds interesting to you, start here.