Kerry McKenzie (University of California, San Diego) - Mathematical structuralism and scientific structuralism both aspire to provide a metaphysics of objects based on the structure of theories. But separating them is the fact that only the latter must accommodate the historical fact of radical theory change. Epistemic structuralism was introduced in an attempt to secure scientific knowledge in a period when further such change is anticipated. But its metaphysical counterpart, ontic structural realism, consists of the thesis that ‘structure is ontologically fundamental,’ and thus fashions itself as though we already know about the fundamental. Since we can only make such assertions when we are confident that there will be no further significant theory change in science, it seems that structuralism as a general philosophy of science is guilty of a form of incoherence. In the face of this, I suggest that structuralist metaphysics should proceed with a different agenda: that of articulating what the value of metaphysics is while we still want for a theory of the fundamental. By analogy with science, such a project would seem to demand that we state what progress in metaphysics consists of and whether we can hope to achieve it. In this paper I will argue that there is no obvious answer to either question, and certainly no easy inference from progress in science to progress in metaphysics. For what makes it possible to say that science makes progress is the availability of a meaningful notion of approximation – something facilitated by the fine-grained nature of the mathematical language in which scientific theories are couched and the clear purposes of scientific enquiry. But I will argue both of these features seem inapplicable to metaphysics, construed as an activity aspiring to the highest generality and lacking in independent purpose. In the face of this criticism, two options are open to the contemporary structuralist who insists on engaging in metaphysics. Either they develop a notion of metaphysical progress highly distinct from that applicable in science – something that seems of questionable coherence given structuralism’s avowed naturalism. Alternatively, they confine its purpose to a project more normally viewed as belonging to the philosophy of mathematics: that of describing the conditions that make possible the applicability of mathematics, and hence that make possible the only body of theory to which progress can unambiguously be ascribed.
