July/Aug 1999

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If mathematics is about finding solutions to well-defined problems, then philosophy is about finding problems in what previously we thought were well-settled solutions. Mark Steiner's The Applicability of Mathematics As a Philosophical Problem mirrors both sides of this statement, admitting that mathematics is the key to solving problems in the physical sciences, but also asserting that this very applicability of mathematics to physics constitutes a problem.

What sort of problem? According to Steiner, the reigning "ideology" or "background belief" for the natural sciences is naturalism. Typically naturalism is identified with the view that nature constitutes a closed system of causes that is devoid of miracle, teleology, or any mindlike superintendence. An immediate consequence of naturalism is that it leaves humanity with no privileged place in the scheme of things. It's this aspect of naturalism that Steiner stresses. Naturalism gives us no reason to think that investigations into nature should be, as Steiner puts it, "user-friendly" to human idiosyncrasies. And yet they are.

Steiner's point of departure is Eugene Wigner's often reprinted article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Wigner concludes that article with a striking aphorism: "The appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Throughout the article Wigner refers to the "miracle" and "mystery" of mathematics in solving the problems of physics. Yet although Wigner leaves the reader with a sense of wonder, he does not indicate how this sense of wonder translates into a problem that demands resolution. Enter the philosopher ...