Kripke's "Plus" vs "Quus"
The rule-following paradox
First published: S. Kripke, *Wittgenstein on Rules and Private Language* (1982).
How do you know you have always meant plus, rather than "quus" (= plus except returning 5 for arguments above some bound)? No fact about your past use settles it.
Kripke's reading of Wittgenstein: when you add 68 + 57, what makes it the case that you mean *plus* rather than some bizarre function "quus" that agrees with plus on all your past computations but returns 5 for arguments above some bound? Nothing in your past behaviour, dispositions, or introspective states (all finite) settles which function you mean. The "skeptical paradox" suggests there is no fact of the matter about what one means; the "skeptical solution" is communal — meaning is constituted by participation in a linguistic community.
Formulation
Define quus: x ⊕ y = x + y if x, y < N; else 5. Your finite past computations are consistent with both plus and quus. No internal state distinguishes. Therefore no fact of the matter about which function you meant.
Dimensions Engaged
Observer
Observer · Knowledge Extent: can self-knowledge about meaning ever be secured?
Information
A challenge to the determinacy of informational content.
Responses — How Schools Engage
Affirms / takes the bait 2
Meaning is constituted by participation in linguistic practice; Kripke's skeptical solution is essentially pragmatist.
Meaning is structural — fixed by inferential and communal role rather than by interior episode.
Denies / rejects the premise 2
Functions are abstract objects; we grasp them by acquaintance with mathematical structure, not by surveying finite past use. Quus is a coherent function we simply don't grasp.
The first-person givenness of meaning grasps the rule itself, not a behavioural sample of its application. The paradox misdescribes meaning.
Reframes the question 1
Dispositionalist naturalism (Fodor): facts about brain states fix meaning, given enough detail. The paradox is about our access to such facts, not their existence.
Holds it inconclusive 1
A canonical pressure-test for theories of meaning; dispositionalist, communitarian, and platonist responses all have defenders.
Related Experiments
Experiments engaged by an overlapping set of schools — likely to surface the same fault lines.
Further reading
- Kripke (1982), op. cit.
- Boghossian, "The Rule-Following Considerations", *Mind* 98 (1989)
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