To an unappreciated degree, the history of Western philosophy is the history of attempts to understand why mathematics is applicable to Nature, despite apparently good reasons to believe that it should not be. A cursory look at the great books of philosophy bears this out. Plato's Republic invokes the theory of “participation” to explain why, for instance, geometry is applicable to ballistics and the practice of war, despite the Theory of Forms, which places mathematical entities in a different (higher) realm of being than that of empirical Nature. This argument is part of Plato's general claim that theoretical learning, in the end, is more useful than “practical” pursuits. John Stuart Mill's account of the applicability of mathematics to nature is unique: it is the only one of the major Western philosophies which denies the major premise upon which all other accounts are based. Mill simply asserts that mathematics itself is empirical, so there is no problem to begin with.
