Mathematical concepts play at least three roles in the application of mathematics: an inferential role, a representational role, and an expressive role. In this paper, I argue that, despite what has often been alleged, platonists do not fully accommodate these features of the application of mathematics. At best, platonism provides partial ways of handling the issues. I then sketch an alternative, anti-realist account of the application of mathematics, and argue that this account manages to accommodate these features of the application (...) process. In this way, a better account of mathematical applications is, in principle, available. (shrink)

Pyrrhonism involves the inability to defend claims about the unobservable world, or, more generally, about what is really going on beyond the phenomena. As a result, the Pyrrhonist is not engaged in developing a philosophical doctrine, at least in the sense of defending a view about the underlying features of reality. The issue then arises as to whether the Pyrrhonist also has something positive to say about our knowledge of the world, while still keeping Pyrrhonism. In this paper, I develop (...) a positive neo-Pyrrhonist attitude, indicating that we can use this attitude to make sense of important aspects of science and empirical knowledge. To do that, I explore the connection between this revived form of Pyrrhonism and contemporary versions of empiricism, in particular constructive empiricism. Although constructive empiricism is not a form of skepticism, there are important elements in common between constructive empiricism and Pyrrhonism. The resulting form of Pyrrhonism suggests that there is something right about the original stance articulated by Sextus Empiricus, and that suitably formulated it provides an insightful approach to think about empirical knowledge. (shrink)

While ante rem structuralism offers a promising account of mathematical truth and mathematical ontology, several of the most prominent formulations of the view seem to be subject to significant difficulties involving the identity conditions of the objects they posit. In this paper I argue that those difficulties can be overcome by adopting encoding structuralism, a version of realism about mathematical objects developed by Bernard Linsky, Uri Nodelman and Edward Zalta.

Tim Crane (2011) characterizes the cognitive role of singular thought via singular mental files: the application of such files to more than one object is senseless. As many do, he thus stresses the contrast between ‘singular’ and ‘general’. I give a counterexample, plurally-directed singular thought, and I offer alternative characterizations of singular thought—better described as ‘objects-directed thought’—initially in terms of the defeasibility of the descriptions associated with one's thinking of an object, and then more broadly in terms of whether descriptions (...) of the object or description-independent epistemic routes to the object are primarily operative in an agent's thinking. (shrink)