Abstract

The thesis defends the legitimacy of a 'platonistic' metaphysic, according to which there exist non-spatiotemporal 'abstract' objects, against a series of recent nominalist challenges. After distinguishing the nominalism I intend to discuss from a range of distinct views with which it has been historically confused, I take up the core of the nominalist's challenge: the suggestion that abstract objects, if there were such things, would be incapable of causal interaction with us and our surroundings, and hence unknowable. I suggest that every attempt to make this line of thought precise is either internally incoherent or depends upon an implausible conception of rational opinion. There is no a priori case for nominalism grounded in the theory of knowledge. I then take up Hartry Field's case for nominalism, which I take to be grounded in a broadly Quinean conception of philosophical and scientific methodology. And once again it is suggested that there is no way to develop the case in detail against the background of an independently plausible normative epistemology. Finally I take up one strand in the positive case for platonism: the 'Fregean' view that the existence of abstract objects is an analytic consequence of certain independently unproblematic states of affairs. I offer a reconstruction of certain arguments due to Crispin Wright, and tentatively endorse one development of this line of thought. If this is right, nominalism is not simply undermotivated: it is an essentially unstable account of what there is