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 rulefollowing 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. The rule-following paradox and the impossibility of private rule-following 2 1. BACKGROUND AND STAGE-SETTING “Understanding,” as in the “understanding of a concept,” is a word for a complex human capacity that bewilderingly involves subpersonal, conscious/phenomenological, sociological, and normative elements. It’s a notion—therefore—that’s too dangerously complex to be presupposed in philosophical analyses: it should only be the target of such analyses. Common to several philosophical traditions is the assumption that someone’s understanding of a set of concepts is to be grounded in her grasping of the rules that govern those concepts. This captures, according to some philosophers, how we understand the meanings of words, as well as how we understand the concepts involved in simple mathematical practices—such as counting. Some of those philosophers describe us as having “dispositions” to grasp those rules, or even as having such rules embodied in our dispositions (or as having such rules “embodied as dispositions”) so that we behave appropriately when in situations where we are to exhibit that understanding (e.g., when counting the number of oranges in a basket). A huge literature has focused on “the rule-following” paradox that seems to arise from this picture—that aspects of our rulefollowing practices seem at odds with the natural picture of our grasping rules, and as a result acquiring dispositions to exhibit those rules in future situations where their application is appropriate. In particular, Kripke’s 1982 has generated a large philosophical industry focused on the problems he presented Wittgenstein as raising for any approach that grounds the understanding of simple mathematical rules in the exercise of a set of dispositions. In the first part of this paper (sections 2-4) I’ll describe these problems for dispositional approaches to numerical competence; to a very large extent, the considerations I raise are Kripke’s. In so doing, I won’t worry about questions of exegesis—of how true to Wittgenstein’s concerns Kripke’s are. Kripke’s formulation of the challenges to the dispositionalist is significant regardless of how true it is to Wittgenstein’s own thinking on the matter. However, the reader familiar with Kripke’s exposition will notice two changes in my presentation of it, one that’s very important, and the other less so. First, Kripke’s discussion focuses on the central example of a subject adding, and the sceptical challenge that everything she has learnt and previously experienced is consistent Vol. 5: Meaning, Understanding and Knowledge