Category: logic
Type: argument
Associated thinker(s): Saul Kripke, Ludwig Wittgenstein
Original publication or approximate period: Kripke, Wittgenstein on Rules and Private Language (1982), an interpretation of remarks in Wittgenstein’s Philosophical Investigations
Difficulty: Advanced
Themes: rule-following, meaning, skepticism
Related experiments: Goodman’s New Riddle of Induction (Grue); Beetle in a Box
Suppose every pair of numbers you had previously added had both operands below 57. You are now asked, “What is 68 plus 57?” You answer 125 and are confident this is correct.
A skeptic asks what fact about your past use establishes that you meant addition by “plus.” Perhaps, the skeptic suggests, you meant a different function, “quus” (⊕), defined as follows: x ⊕ y = x + y when both x and y are less than 57, and 5 otherwise. On that interpretation, 68 ⊕ 57 is 5. The ordinary sum is still 125; the challenge concerns what your earlier use of “plus” fixed about how to continue in a new case. This is Kripke’s constructed skeptical example, not a claim that Wittgenstein used this particular arithmetic example. (Kripke, 1982, ch. 2; Miller, “Rule-Following and Intentionality,” §2)
What fact about you, past or present, makes it the case that you meant plus and not quus?
Kripke’s skeptic tests candidate meaning-fixing facts—including past uses, mental states, instructions, and dispositions—and argues that they do not uniquely determine the intended function while also explaining why a speaker ought to apply it in new cases. The basic skeptical conclusion in Kripke’s presentation is that no fact of the sought-after kind constitutes meaning addition rather than quaddition. The stronger conclusion that nobody means anything is a further, radical consequence; Kripke rejects it as intolerable rather than endorsing it. (Kripke, selected excerpt; Miller, §§2–3.3)
Kripke’s “skeptical solution” attempts to preserve ordinary meaning-ascriptions after conceding the failure of the demanded kind of meaning-fixing fact. It shifts attention to the circumstances in which such claims are appropriately asserted and to their role in shared practice. Community response patterns matter to those assertibility conditions; Kripke does not present simple agreement as a new truth-making fact that uniquely determines meaning. How best to understand this solution remains disputed. (Kripke, selected excerpt; Miller, §§3.1–3.3)
Kripke presents this as his interpretation of Wittgenstein, not as an uncontested statement of Wittgenstein’s own position. Philosophical Investigations §201 calls the rule-following paradox a misunderstanding and says rule-grasping is exhibited in actual cases of following and going against a rule; §202 says following a rule is a practice. John McDowell argues that these remarks tell against Kripke’s claim that Wittgenstein accepts the skeptical paradox. Other interpretations defend or revise Kripke’s reading. (Wittgenstein, §§201–202; McDowell, pp. 331–333; Miller, §§3–5)
Kripke’s skeptical solution. Meaning-ascriptions are treated through conditions for their warranted or appropriate use and the practical role they play. In Kripke’s account, we may attribute a rule to a speaker when her responses agree sufficiently with community responses in relevant cases. This is an account of the practice of attribution, not a proof that consensus supplies truth-conditions for meaning. (Kripke, selected excerpt; Miller, §§3.1–3.3)
Dispositionalist responses. Reductive dispositionalism tries to explain meaning through what a speaker is disposed to do. Kripke argues that an individual’s dispositions are finite, may diverge from the relevant mathematical function, and describe what the person would do rather than by themselves explaining what she ought to do. Responses differ: Paul Horwich develops a community-use/dispositional account, while other approaches, such as Hannah Ginsborg’s, treat the relevant dispositions as involving a primitive notion of appropriateness. These are distinct proposals, not one settled “dispositionalist” answer. (Miller, §4)
Non-reductionism and primitivism. Some non-reductionist views deny that meaning can be explained in wholly non-semantic terms. A more specific primitivist proposal treats meaning as a sui generis state. Kripke considers and criticizes a primitive-state response, but the broader non-reductionist family is not identical to that single proposal, and the adequacy of these responses remains contested. (Miller, §5)
Criticism of Kripke’s interpretation. McDowell argues that Wittgenstein treats the paradox in §201 as arising from a misunderstanding to be corrected, rather than as a skeptical result to accept and solve. Scholars continue to disagree about the relation between Kripke’s reconstruction and Wittgenstein’s text; this entry does not present either reading as a consensus. (McDowell, pp. 331–333, 356–357; Miller, §§3–5)
The puzzle is not an ordinary disagreement about arithmetic: 68 + 57 = 125. The value 5 is produced only by the stipulated quus function. The skeptical question is what, if anything, fixes which function was meant and what counts as following it in an unfamiliar case.
Do not conflate the basic skeptical conclusion—that no fact of the demanded kind constitutes a particular meaning—with the radical conclusion that nobody means anything. Kripke’s skeptical solution rejects that radical consequence and proposes a different account of meaning-ascription.
The plus/quus construction and the skeptical-solution framework are Kripke’s reconstruction. Wittgenstein’s Philosophical Investigations §§201–202 discusses rule-following and practice but does not present this exact quus case or Kripke’s chapter-three solution. Whether Kripke’s account captures Wittgenstein’s own position is disputed.
Kripke generalizes the skeptical challenge beyond arithmetic to meaningful language more broadly. Comparing it with Goodman’s grue and Quine’s indeterminacy is a teaching prompt about structural similarities, not a claim that these are the same problem or that Wittgenstein presented them as variants.
Kripke’s 1982 book was not accessed in full. A selected reprint excerpt of “On Rules and Private Language” was read directly for the plus/quus construction and the skeptical-solution summary; the Internet Archive record was consulted for book metadata only. The relevant passages and page references in the book were also checked against the Stanford Encyclopedia discussion. Wittgenstein’s Philosophical Investigations fourth-edition text was accessed, and §§185, 201–202, and 241–242 were read. McDowell’s article was read at the cited passages. The SEP sections on the skeptical argument, solution, dispositionalism, and non-reductionism were read. This is an educational explanation, not a substitute for the primary texts; interpretations remain disputed, and no expert review is claimed. The comparisons in §7 are teaching prompts, not established historical variations.
Research check: 2026-11-01. This entry has been source-checked for traceability; that status does not mean the skeptical argument is sound, that the literature has reached consensus, or that the entry has received expert review.