In 1982 Saul Kripke published Wittgenstein on Rules and Private Language and ushered in a new era of Ludwig Wittgenstein interpretation. Although elements of Kripke's view of Wittgenstein could be found in the preceding literature (notably in Robert Fogelin's Wittgenstein ), nothing had captured attention like his presentation of the "rule-following considerations."
Kripke presented his essay as a reconstruction of the problems Wittgenstein is addressing between around §140 and §203 of the Philosophical Investigations. These issue in the form of a paradox—that there can be no such thing as the meaning of a word; no fact of the matter that entails that a word is used according to a rule, whereby some applications of it are determined to be correct and other applications incorrect. In §201 Wittgenstein wrote "This [is] our paradox: no course of action could be determined by a rule, because every course of action can be made out to accord with the rule. The answer [is] if everything can be made out to accord with the rule, then it can also be made out to conflict with it. And so there would be neither accord nor conflict here."
The paradox is developed by Kripke through the figure of a "bizarre skeptic." The defender of common sense, here the view that words do indeed have meanings and obey rules, is challenged to show what this meaning consists in. The facts he or she can adduce typically include past applications and present dispositions to apply words in new cases. They may also include flashes of consciousness—for instance, if we associate a particular image with a term. But, Kripke's skeptic argues, these are not the kinds of facts that can determine the actual rule that governs the meaning of a word. The skeptic adduces three kinds of problems. First, our dispositions are finite, whereas a rule can cover a potential infinity of new cases. Second, our dispositions sometimes fail to match the relevant rules: This is precisely what happens when we mistakenly apply words to things to which they do not in fact apply. Third, the existence of a rule has normative implications. It determines correctness and incorrectness of application of the term it governs. Our dispositions, by contrast, have no such implication. There is nothing intrinsically wrong about bending our dispositions from moment to moment, in the way that there is about applying a term in a way that fails to accord with its meaning. Finally, the addition of flashes of consciousness is unlikely to help, for, as Wittgenstein himself said, any such fact itself stands in need of interpretation. A flash of consciousness cannot comprehend all the possible applications of a term and sort them into those that are correct and those that are not.
Kripke illustrates these points with the case of a strange arithmetical operator, "quus." For two numbers n and m, n quus m is identical with n plus m for sufficiently small or common numbers, but the two results (or calculations) diverge when n and m are greater than a certain value (the function is therefore reminiscent of Nelson Goodman's predicate, "grue"). We do not mean n quus m when we talk of n plus m. But our dispositions with "plus" might match those of people who in fact use the term to mean quus; we might give the answer n quus m when we attempt to add n and m, since we make mistakes; and finally there is nothing right or wrong about having one disposition or another.
The conclusion is paradoxical, since nothing seems more certain than that we do succeed in attaching reasonably determinate meanings to terms. It may be true that the "open texture" of terms suggests that meanings are never fully precise, capable of determining their application in any circumstances, however outlandish. Nevertheless, over an indefinite normal range of cases, there is no doubt that some applications are correct and others not, and any interpretation of us according to which we mean something along the lines of the "quus" function is incorrect. Yet so long as the skeptic wins, we have no conception of our right to say such things. Kripke's own solution to the paradox is that the skeptic wins on his chosen ground. There is indeed no fact of the matter whether one rule rather than another governs the use of a term. But we can advance a "skeptical solution" (David Hume's phrase from a different context) to the doubts. What there is instead is a practice of regarding ourselves and others in certain lights. We dignify each other as meaning one thing or another by our terms, and this ongoing practice is all that there is.
Kripke's work generated enormous interest and a variety of responses in the literature. Some outraged students of Wittgenstein argued that it was not at all his intention to produce a paradox but to lay bare the oversimplifications, or desire for a simple theory, that trap people into finding rule following problematic (Baker and Hacker 1984). Many writers queried whether Wittgenstein could consistently have been content with a "non-truth-conditional" account of rule following, which is what Kripke offers him, since Wittgenstein's abhorrence of theory and his belief that philosophy leaves everything as it is would make it impossible for him to say that it is not strictly speaking true that the application of words is correct or incorrect. Some (McDowell 1981) detected a mischievous dislike of soft, humanly oriented facts in the setting up of the paradox and argued that a proper appreciation of the human constitution of rule following had wide implications for the notion of objectivity, as it occurs in domains such as aesthetics or ethics. Some (McGinn 1984) found that Kripke had not looked hard enough for natural facts with which to identify the obtaining of a rule; others (Blackburn 1985) embraced the thought that since the loss of a normative element in meaning was the main problem underlying the paradox, and since naturalistic theories of normativity have been proposed in many guises, a more generous sense of how to talk about facts solves the paradox. Paul Boghossian (1989) provided a summary of the state of the debate and a controversial contribution to it.
Baker, G. P., and P. M. S. Hacker. Scepticism, Rules, and Language. Oxford: Blackwell, 1984.
Blackburn, S. "The Individual Strikes Back." Synthese 20 (1985).
Boghossian, P. "The Rule-Following Considerations." Mind 98 (1989).
McDowell, J. "Non-Cognitivism and Rule-Following." In Wittgenstein: To Follow a Rule, edited by S. Holtzman and C. Leich. London: Routledge and Kegan Paul, 1981.
McGinn, C. Wittgenstein on Meaning. Oxford: Blackwell, 1984.
Wittgenstein, L. Philosophical Investigations. Oxford: Blackwell, 1953.
Simon Blackburn (1996)