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  • Print publication year: 2014
  • Online publication date: June 2014

19 - God, Ants, and Thomas Bayes

Summary

The editors of this volume have invited me to present here my personal philosophy. But I cannot distinguish between my personal philosophy and my theoretical philosophy. As I explained in my autobiography (Markowitz 1990), when I was in high school I read science at a nontechnical level, like the ABC of Relativity, and the original writings of great philosophers. In particular, I was struck by David Hume’s (1776) argument that even though I release a ball a thousand times and, in every instant, it falls to the floor, that does not prove that it will necessarily fall to the floor the thousand-and-first time. In other words, even though Newton’s law of gravity worked in thousands of instances, that did not prove that it would never fail – such as in explaining the orbit of Mercury! Essentially, my philosophical interest in high school lay in the question “What do we know and how do we know it?”

When I entered the Economics Department at the University of Chicago I was naturally drawn to the economics of uncertainty. In particular, the work of Leonard J. Savage (1954) – building on that of von Neumann and Morgenstern (1944) – presented, to me among many others, a convincing axiomatic argument that, in acting under uncertainty, one should maximize expected utility using probability beliefs where objective probabilities are not known. It is a corollary of the latter conclusion that, as information accumulates, one should shift one’s beliefs according to Bayes’s rule, reviewed later in this essay. (Hume, too, said that one should attach probabilities to beliefs but did not specify that Bayes’s rule should be used in response to growing evidence for or against various hypotheses.)

References
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