Wittgenstein on Rules and Private Language: An Elementary Exposition

The central argument is a skeptical paradox about rule-following: no fact about a speaker's past behavior, mental states, or dispositions can determine whether they are following the rule of addition or a deviant rule ('quaddition') that diverges only for numbers never previously computed. Kripke rejects the classical realist view that there is a fact of the matter constituting what a speaker means by a symbol. He then offers a 'skeptical solution' that accepts the impossibility of such facts while explaining why our practice of ascribing meaning remains legitimate: it rests on communal agreement in assertability conditions, not on correspondence to meaning-facts.

Kripke himself acknowledged that his book is not strict exegesis, and the scholarly consensus is that it misrepresents Wittgenstein's position. Crispin Wright notes that 'Wittgenstein does not accept the paradox' that Kripke attributes to him, and that Kripke's reading fails as interpretation . Colin McGinn's book-length critique argues that Wittgenstein's concerns were predominantly negative—dissolving the paradox as a misunderstanding—rather than endorsing skepticism about meaning . Baker and Hacker, David Pears, and others hold that Wittgenstein's later work is fundamentally anti-skeptical . Kripke's book is thus best read as a philosophical provocation inspired by Wittgenstein, not as a reliable guide to his thought.

The quus function is Kripke's deviant alternative to addition: it yields the same results as addition for all numbers the speaker has actually computed, but diverges beyond that range (for example, returning 5 for sums above 57). The skeptic's point is that the speaker's entire finite history of calculations is equally compatible with meaning addition and meaning quus. Since no past fact distinguishes the two, and no present fact (dispositions, images, intentions) does either, there is no fact constituting what the speaker means. The quus example is a dramatic illustration of the underdetermination of meaning by all available evidence.

A straight solution would rebut the skeptic by identifying the fact that constitutes meaning—a disposition, a mental state, or a Platonic entity. Kripke argues no such fact exists. The skeptical solution instead accepts the skeptic's conclusion and shows that our practice of meaning ascription does not require such facts. Meaning claims are justified by their role in communal life: we call someone a 'plus-meaner' if they are disposed to assent to the same arithmetical statements as the rest of the community under normal conditions. The solution preserves the practice while abandoning the metaphysics. This distinction between straight and skeptical solutions is one of the book's most influential contributions to philosophy of language .

The book is widely credited with putting the normativity of meaning at the center of philosophy of language. Kripke's skeptic argues that meaning is normative—it tells us what we ought to say—and that no naturalistic fact can account for this normativity. This claim generated an avalanche of responses from philosophers including Paul Boghossian, Crispin Wright, and Anandi Hattiangadi, who have debated whether meaning really is normative and, if so, whether the normativity can be naturalized. A 2022 volume reassessing the book at forty years calls it 'one of the most celebrated and important books in philosophy of language and mind of the past forty years,' noting that it 'introduced a series of questions that had never been raised before' . The book's influence thus extends far beyond Wittgenstein exegesis.

The most persistent misreading treats Kripke's book as a straightforward exposition of Wittgenstein's Philosophical Investigations. Kripke himself called it an 'elementary exposition,' but the title is misleading: his Wittgenstein is a construction, and the skeptical paradox is Kripke's own invention, not Wittgenstein's. Another misreading assumes Kripke endorses the skeptic's conclusion and is therefore a meaning nihilist. On the contrary, the skeptical solution is offered as a way of preserving meaning-talk while abandoning the search for meaning-facts. Kripke is not claiming that meaning is an illusion; he is claiming that its reality is practical and communal rather than factual and individual.