David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Relativism and scepticism are often taken to be incompatible doctrines. After all, the relativist typically attempts to argue that there are no universal standards of assessment between different conceptual schemes – hence the slogan: everything is relative. The sceptic, in turn, is often portrayed as defending the view according to which knowledge is impossible – and thus we cannot even know that the relativist’s claim is true. Despite their incompatibility, both views are taken to be wrong, and for similar self-refuting reasons: they undermine themselves. In his recent book, Relativism and the Foundations of Philosophy, Steven Hales argues that relativism can be defended – as long as it is suitably formulated and restricted to philosophical propositions (Hales, 2006). These propositions are relatively true: true in some contexts (or perspectives) and false in others. In this paper, I defend two main claims. First, Hales’ proposal is not restricted to philosophical propositions, but applies equally well to mathematical ones. Second, with a proper understanding of scepticism, Hales’ proposal would actually be welcomed by the sceptic. Some may take these two claims to amount to a sort of reductio of Hales’ project. Since mathematical claims are typically not taken to be relatively true, and given that scepticism is typically taken to be false, a proposal that leads to these results would be unacceptable. Rather than drawing this conclusion, I think these results show that we need to rethink deeply held assumptions about the nature of mathematics and of scepticism. Hales’ book is an excellent contribution to that
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