One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should not be thought of as describing, in any substantive sense, (...) an abstract realm of eternal mathematical objects, as traditional platonists have thought. In Rules to Infinity, this view, which I call mathematical normativism, is updated with contemporary philosophical tools, and it is argued that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the platonistic idea that there exist abstract mathematical objects that explain such truths. Furthermore, Rules to Infinity defends a particular account of the distinction between scientific explanations that are in some sense distinctively mathematical – those that explain natural phenomena in some uniquely mathematical way – and those that are only standardly mathematical, and it lays out desiderata for any account of this distinction. Normativism is compared with other prominent views in the philosophy of mathematics such as neo-Fregeanism, fictionalism, conventionalism, and structuralism. Rules to Infinity serves as an entry point into debates at the forefront of philosophy of science and mathematics, and it defends novel positions in these debates. (shrink)

Moral expressivists think that moral thoughts and sentences don’t represent or describe the world, at least not in any interesting sense. Global expressivists think that _no_ thoughts or sentences represent the world; local expressivists think that some do and others don’t. Huw Price has influentially argued that local expressivism collapses into global expressivism, due both to the effects of minimalist theories of representation and similar concepts, and to an unappreciated consequence of the success of specific expressivist theories like moral expressivism. (...) In this paper I argue that Price’s arguments don’t succeed. While they can be fixed, doing so makes them miss their intended target. Local expressivists should therefore not be worried by Price’s arguments. (shrink)

The problem of creeping minimalism is the problem of drawing a principled distinction between expressivists and non-expressivists. Explanationism is a popular strategy for solving the problem, but two of its forms—ontological explanationism and representational explanationism—have fatal problems. Christine Tiefensee and Matthew Simpson have recently, and independently, endorsed a third form: subject matter explanationism. But this form also fails. At bottom, the problem is that it does not note the existence of non-reductive expressivist views, just as earlier forms of explanationism did (...) not note the existence of error theories, or non-naturalist realists, or realists who wanted to endorse deflationary views of truth and representation. The failure of this latest version of explanationism—one that does indeed avoid problems with earlier versions—strengthens the case that we may not actually want a solution to the problem of creeping minimalism after all. Rather, a form of global expressivism—neopragmatism—might be regarded as yielding a version of non-naturalist normative realism. (shrink)