Some Naturalistic Reflections on Set Theoretic Method

and impressive applicability of mathematics in the natural sciences. Quineans hold that mathematics is conIlrDled by these applications, that only that part of mathematics with application is justified. Defenders of pure mathematics naturally disagree, finding justification for unapplied mathematics in various places, perhaps in some largely unspecified aesthetic virtues or in some philosophy of mathematics. My ultimate goal in this paper is to illuminate, from a naturalistic point of view, the significance of the application of mathematics in the natural sciences for the practice of contemporary set theory. But it will take me a while to get there. In section I, I give a sketch of the naturalistic approach by outlining an assessment of the role and rationality of two methodological maxims; in section II, I suggest that this way of seeing things undermines some misguided analogies familiar from discussions of set theoretic method. This leads back, in section III, to the issue at hand: the significance of applied mathematics for mathematics in general, and for the practice of set theory in particular.