Paradox

BURIDAN’S SOPHISMS 207BURIDAN’S BRIDGEBuridan repackages “Your reply will be negative” as astepping stone to a more famous sophism: Suppose Plato is abridge keeper. Plato is enraged and tells Socrates, “If whatyou say is true, then I will let you cross the bridge; and if whatyou say is false, then I will throw you into the water.” Socratesreplies, “You will throw me into the water.” What Socratessaid is true if and only if it is false.Although Buridan is sometimes credited with being theinventor of the bridge paradox (Jacquette 1991), the puzzleprobably goes back to Chrysippus. In “The Auction of Philosophers,”Lucian (ca. 115–ca. 200) depicts a slave market withZeus in charge and Hermes as auctioneer. The offeringsinclude Pythagoras, Diogenes, Aristippus, Democritus, Heraclitus,Socrates, Epicurus, Chrysippus, Aristotle, and Pyrrhon.The philosophers are put through their paces. As afatalist, Chrysippus is resigned to being sold as a slave. Heillustrates his value as a logician with an exhibition ofparadoxes: the Reaper, the Electra, and the Sorites. Finally,he rescues a customer’s child from a hypothetical dilemma:Chrysippus: Now, suppose a crocodile, finding the childroaming about the river’s side, should perchanceseize it and then promise to restore it toyou, provided you state correctly what he hasmade up his mind to do about giving up thebrat—what would you say was his intention inthe matter?Customer: Your question is a poser. For I’m at a loss whatto say first, so as insure the recovery of the child.But, for Heaven’s sake, do you make answer