The Rule-Following Paradox and the Impossibility of Private Rule-Following

Kripke’s version of Wittgenstein’s rule-following paradox has been influential. My concern is with how it—and Wittgenstein’s views more generally—have been perceived as undercutting the individualistic picture of mathematical practice: the view that individuals—Robinson Crusoes—can, entirely independently of a community, engage in cogent mathematics, and indeed (more generally) have “private languages.” What has been denied is that phrases like “correctly counting” can be applied to such individuals because these normative notions (so the Wittgensteinian analysis is taken to show) can only be applied cogently in a context involving community standards. I attempt to show that this shocking corollary doesn’t follow even if Kripke’s Wittgensteinian objections to dispositional approaches to rule-following are largely right. My reason for claiming this is that there is another (“sceptical”) solution to the rule-following paradox, one that doesn’t favor community standards over individual ones. Furthermore, it doesn’t replace truth conditions with assertability conditions; and this latter maneuver is essential to Kripke’s sceptical solution favoring the community over the individual.