Tuesday, January 10, 2006

Aumann's Dangerous Idea

This year's Edge question was "What's Your Dangerous Idea?"
Here's mine.
From the beginning of the Western Philosophical tradition, there has been a fuzzy but important divide between Idealists, or Platonists, and Realists, or Aristotilians. The former see abstractions, especially mathematical truths as more fundamental than the specific truths they are abstracted from, while the latter see abstractions as mere human constructs to simplify the universe and make it managable. The divide between the two traditions was greatly increased when David Hume questioned the validity of inductive reasoning, calling its justification circular, and philosophers have struggled to mend it ever since. Finally, in the latter half of the 20th century, a bridge was built, when it was discovered that Bayesian Probability Theory is both the generalization of Boolean Algebra from the special case of total certainty AND (in combination with a consistant set of priors, almost necessarily Kolmogorov complexity) normative epistemology. Induction is justified in terms of Bayesian probability, and empiricism becomes, in principle if not in practice, a part of pure mathematics.
Unfortunately, Western Civilization was also rent by another deeper, or at least less friendly philosophical divide. There is much hostility between philosophers, broadly construed as people who believe that one should only believe a proposition in the face of evidence or sound argument for its truth, and traditionalists, who believe that assertions should be accepted on the authority of the person or institution making the assertion. Surprisingly, recent arugmente from the philosophers seems to provide confirming evidence for the authoritarian proposition. With the spread of Bayesian Updating and Decision Theory, and their expansion as analytical tools for human life, it has been noted that any pair of rational truth seekers should always agree. An unfortunate appearent consequence of this observation is the formalization of what had previously been an implicit criticism in most debate, the accusation of anyone who disagrees with you of not rationally attempting to reach valid conclusions.
This is not actually to say that we should all give up and accept papal infallibility. Rather, the correct solution is to note that most objects in the universe do not rationally attempt to reach valid conclusions, take this as our point of default, and respond to evidence of rationality with praise and due deferrance rather than uselessly attacking the behavior of almost all humans everywhere. Bayesian updating eliminates the appearent impossibility of the attempt to agree with everyone, as it only requires you to agree with people who always agree with one another. Furthermore, it only requires you to agree with others in so far as they agree with you. For aspiring Bayesians, all evidentiary standards are mutual, so if you are asked to accept the immortality of the soul on the basis of your faith in the pope's informed and calibrated judgement, you are only obligated to do so if he likewise accepts your 99.999999% confidence assertion that Antarctica is covered with lush tropical forest by adopting a pretty high confidence for that statement or if he fails to do so by (explicitly under the light of Decision Theory) calling you a liar, at which point you can call him one without violating etiquette.
Although it doesn't support Papal infallibility, Agreement theory does support a more limited infallibility on the point of those who have extremely good track records. In conjunction with economic and psychological analyses of motivation, it gives a very good justification for discarding the cliche about even the best scientists being unreliable when they go outside of their fields, and for instance for seeing Linus Pauling as the likely source of accurate insight in any argument between him and the AMA.

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