Can a scientific naturalist be a mathematical realist? I review some arguments, derived largely from the writings of Penelope Maddy, for a negative answer. The rejoinder from the realist side is that the irrealist cannot explain, as well as the realist can, why a naturalist should grant the mathematician the degree of methodological autonomy that the irrealist's own arguments require. Thus a naturalist, as such, has at least as much reason to embrace mathematical realism as to embrace irrealism.

In this paper I return to the mid-20th-century debate between Quine and Carnap on the status of metaphysics questions with an eye toward advancing contemporary debates about whether naturalists can coherently undertake substantive metaphysical inquiry. Following Huw Price, I take the debate between Quine and Carnap to hinge, in part, on whether human inquiry is functionally unified. However, unlike Price, I suggest that this question is not best understood as a question about the function(s) of descriptive discourse. This goes along (...) with rejecting a “linguistic conception” of the starting point of metaphysical inquiry, which, although shared by Quine and Carnap, Price gives us no good reason to think is mandatory for naturalists. I sketch two reasons naturalists have to reject a particular manifestation of this linguistic conception in Quine’s work—his criterion of ontological commitment. Finally, I show how these reasons can help us identify the grains of truth in some recent critiques of “mainstream metaphysics of mind.”. (shrink)

In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...) notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: mathematics is not independent of idealizations in modelling and idealizations help mathematics to carry the explanatory load of a model in different degrees. (shrink)

Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of (...) the indispensability argument. (shrink)