Paradox

346 A BRIEF HISTORY OF THE PARADOXcredits Wittgenstein with the discovery of a skeptical paradoxabout rule following. Suppose you have never computed 68+ 57 before. You answer 125, confident that this correspondsto your past usage of “plus.” A skeptic questions your certainty:perhaps your past usage requires that the answer be 5.After all, there are indefinitely many rules that could haveyielded your past results. How do you know which rule youintended?This was our paradox: no course of action could bedetermined by a rule, because every course of action canbe made out to accord with the rule. The answer was: ifeverything can be made out to accord with the rule, thenit can also be made out to conflict with it. And so therewould be neither accord nor conflict here.(1958, 201)Kripke says Wittgenstein solves the paradox by denying thatrule following involves self-interpretation. Instead, we arejust trained to use words. Our mastery of a rule is a matter ofbeing inducted into a linguistic practice.Many philosophers think Kripke is perverting the aim ofWittgenstein’s therapy. Wittgenstein had no interest in discoveringnew paradoxes. He only wanted to eliminate oldones. If Wittgenstein were right about paradoxes beingpseudoproblems, then it should not be possible to solve them.However, Wittgenstein regularly relapses into the kindof philosophizing he renounces. He is not immune to thecharm exerted by an answer “which sets the whole mind ina whirl, and gives the pleasant feeling of paradox.” (1976, 16)Like a fellow alcoholic, Wittgenstein identifies with Cantorwhen he giddily concludes that there are infinitely many