CONCEPT
The Rule-Following Paradox
Kripke’s reconstruction of the most radical skeptical problem in modern philosophy: for any finite sequence of behavior, infinitely many rules are consistent with it, so no fact about an individual can establish which rule they meant—a theorem that proves, in advance, why evaluating whether a machine has learned a rule from any finite test is structurally impossible.
The rule-following paradox, developed by Saul Kripke in Wittgenstein on Rules and Private Language (1982) and now sometimes called “Kripkenstein,” begins with an arithmetic problem and ends at the foundations of meaning. The setup is deceptively small: you have always meant addition by “plus.” Prove it. Not that you will keep adding correctly, but that some fact in your history or your mind makes addition rather than a deviant function the thing you actually meant. Kripke shows that no such fact can be produced. The machinery is the function “quus,” which agrees with addition on all inputs you have ever tried and returns five for anything larger—so your entire track record is consistent with both. The mental rule you appeal to was also finite; the disposition you appeal to is also consistent with the deviant function and says
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