We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

If Australasian philosophers constitute the kind of group to which a collective identity or broadly shared self-image can plausibly be ascribed, the celebrated history of Australian materialism rightly lies close to its heart. Jack Smart’s chapter in this volume, along with an outstanding series of briefer essays in A Companion to Philosophy in Australia and New Zealand (Forrest 2010; Gold 2010; Koksvik 2010; Lycan 2010; Matthews 2010; Nagasawa 2010; Opie 2010; Stoljar 2010a), effectively describe the naturalistic realism of Australian philosophy (...) of mind. In occasional semi-serious psychogeographic speculation, this long-standing and strongly-felt intellectual attitude has been traced back to the influences of our light, land, or lifestyle (Devitt 1996, x; compare comments by Chalmers and O’Brien in Mitchell, 2006). Australasian work in philosophy of mind and cognition has become more diverse in the last 40 years, but is almost all still marked, in one way or another, by the history of these debates on materialism. (shrink)