It's sometimes useful to start with a quiz, even if it seems irrelevant to the issues at hand. Suppose you have to organize a tennis tournament with, say, 1025 players. Match winners will go on to the next round while losers bow out until all have been eliminated except, of course, the final champion. Your problem is this: How many matches must you book for this tournament?
James Robert Brown is Professor of Philosophy at the University of Toronto. His research interests include philosophy of science, philosophy of mathematics, foundations of physics, and the social relations of science. His publications include Who Rules in Science? An Opinionated Guide to the Wars (2001); Philosophy of Mathematics: An Introduction to the World of Proofs and Pictures (1999); Smoke and Mirrors: How Science Reflects Reality (1994); The Laboratory of the Mind: Thought Experiments in the Natural Sciences (1991); and The Rational and the Social (1989).