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I would like to thank Sidney Morgenbesser for many hours of discussion. Isaac Levi, Jim Higginbotham, Charles Parsons, Richard Friedberg, and Howard Stein also provided helpful critique. A version of this paper was read at the University of WisconsinMilwaukee, and at a philosophical conference organized by Parviz Morwedge.
I am grateful to the following mathematicians who showed me examples of mathematical explanation, and their attitudes toward it: Sylvain Cappell, Paul Rosenbloom, Leon Ehrenpreis, Leslie Tharp, Harold Shapiro, Martin Davis, Georg Kreisel, Solomon Feferman, and Ellis Kolchin. Some of what I learned from them will appear in subsequent work. I acknowledge a general debt to the writings of Hao Wang.
After completing this paper (in an earlier version), I received helpful comments from Feferman, Tharp, Mike Resnik, Dale Gottlieb, Philip Kitcher, and Mic Detlefsen. I have responded to some of their detailed criticism; objections of a methodological nature I have left to the future.
Finally, thanks to the National Endowment for the Humanities, the Columbia Council for Research in the Humanities, and the National Science Foundation, for grants which enabled me to devote time to mathematics and philosophy.
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Steiner, M. Mathematical explanation. Philosophical Studies 34, 135–151 (1978). https://doi.org/10.1007/BF00354494
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DOI: https://doi.org/10.1007/BF00354494