book: “Labyrinths of Reason”

book cover: Labyrinths of ReasonThis 1988 book addresses Reason’s power and limitations and raises a lot of questions, but answers only a few. But it could have given more useful answers-or at least it could have cited more well-known, well-tested approaches–had it not overly focused on all-or-nothing, hard-logic approaches. Most tellingly: I cannot imagine how a prestigious thinker could drone on for 263 pages about reasonable choices, without once mentioning Bayes’ Law.

If you need an approximate litmus test for whether a person really understands reasonable behavior–as opposed to superstitious, random, or groupthink behavior–you could do a lot worse than simply getting his reactions to two ideas: Bayes’ Law and Newcomb’s Paradox.

  • Bayes’ Law diagnoses “What should I believe?”
  • Newcomb’s Paradox probes his answer to “Am I a rational free agent?”

Now, Poundstone’s book very nicely covers Newcomb’s Paradox. And it does cite the real conflict embedded in it, but, look, the choice presented in the paradox is really not as hard as all that: either you take both boxes because by doing so you simply get more money, or you take only one box. But you would only take one box if you believed that either (1) someone you don’t know can read your mind, or (2) your choice actually directs the predictor’s earlier choice. Well, in the universe I inhabit, and that I assume you inhabit too, the first choice is obviously the rational one. Either you believe that what’s in a box is actually in it, or you actually believe in superstition, wishful thinking, mind control, etc–whether or not you think you do. The secret to choosing to open the second box with confidence is the principle of dominance, which Poundstone cites as though it is just one choice in a series of valid choices. It is not. Too bad the cases where dominance applies are so infrequent, but they are not forbidden, and Newcomb’s Paradox is a perfect case for it: the two boxes are right in front of you, and taking the sure money in one box makes you exactly that much richer, no matter what’s in the other box. That box contains what that box contains. It is what it is.

This last sentence is not just a movie line or a cute truism. It is more important for what it warns against–superstition, wishful thinking, etc–as for what it directly recommends–confidence in relying on reality. No being in the physical universe can read my mind and its own, in their entireties, at the same time. Gödel’s Theorem, proven in 1931, perfectly rules that out. Whatever all that peripheral,  unknowable, metaphysical, mumble-jumble, if an action is better in each case of all possible cases–that is, if it dominates–it’s just a better choice. Look, once in a while things are that easy. So calm down. Save your energy for something hard. A dominant strategy, in the few cases where it exists, is a sort of gift. So take it and move on. Somewhere, Bertrand Russell is smiling.

Poundstone’s book fails badly, however, in ignoring Bayes’ Law, instead opting to fool around with dozens of Quixotic paradoxes. Paradoxes are a fine subject, and Newcomb’s is still the deepest of the lot. But this book professes to be about Reason, and paradoxes are not the whole story. Here’s why.

In evaluating your strategies, you usually have to decide what you know or believe, plus how sure you are of those beliefs. You. You have to decide what you believe. Not your parents 10, 20, or 40 years ago, and not your church or synagogue or mosque, however beautiful. Not the National Front, nor La Raza, not your favorite Deity, not South Park. Not even coin flips unless that’s the best you have. Those may be valuable starting points especially early in life. But to be an adult, you are responsible for what you believe. Fortunately, there’s help: Bayes’ Law can (and should) help you sort this out. You start with some Prior beliefs, which are what you might best expect before you have any real evidence. Perhaps this is what you were taught as a child, or perhaps it is an sober admission that without knowing anything about a problem, a coin flip would do. The idea is to keep your Priors as weak and naive as possible, which means simply: don’t pretend you know something you don’t. Then, you add the influence of relevant Evidence, as much you can get. This is what Bayes’ Law covers: Evidence modifies Prior beliefs to yield Posterior beliefs, which are the beliefs you would most sanely adopt right now given all the Evidence and your (weakest possible) Priors. The goal is to get enough Evidence to make whichever Priors you started with…totally irrelevant. That is: with mounting relevant Evidence, two honest people with opposing Prior beliefs will eventually come to similar Posterior beliefs…which is pretty much the history of Science. Whether you call it Bayes’ Law or just sanity, this is the basis of real-world reason–but Poundstone never mentions it.

And this is the problem with a lot of thinking out there. All-or-nothing thinking is too inflexible for this universe, the actual one we’re in. It gets you up too many blind alleys with no way to escape, or change your mind, or reinvent your life. If you find this hard to believe, just read the news. In the aggregate, life rewards neither perfect clarity nor perfect paradox. The universe is closer to backgammon than to chess. You cannot know with clarity how the dice fall next, but so what?–you work the odds, deal with the last move, and prepare yourself for the next ones. Whatever people have told you, there is no Book of Perfect Moves. Sorry. You weren’t born into that universe.

Bayes’ Law will set you free. Free to change your mind without embarrassment–indeed, with glee!–when new Evidence surprises you. Free to operate cautiously on reasonable Priors until you get the Evidence you want.  But not free, never free, to ignore the Evidence and cling to your old Priors, however comfortable, socially accepted, or spiritually urged. Free to refuse to rip each other’s throats out over different Priors, because you are modest enough to know that later Evidence might someday prove one side wrong…and it might be yours. It doesn’t tell you what to believe–indeed the opposite. It gives the most reasonable method for deciding for yourself. And it’s hard to understand a book on Reason that doesn’t give the basis for Reason, in Bayes’ form or any other, rather fooling around with paradoxes in a Quixotic insistence that if we were just smart enough, we could have certainty.

But there is no such beast as absolute certainty. There is only the hunt for it, the struggle to better focus the blurry maps of reality that we carry in our heads.

Oh yes, the book. Four stars.

“Labyrinths of Reason”, William Poundstone, 1988, Anchor Books.

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