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Relativism and Scepticism

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.