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AMONG fallacious arguments the one which the Greeks call ἀντιστρέφον seems to be by far the most fallacious. Such arguments some of our own philosophers have rather appropriately termed reciproca, or “convertible.” The fallacy arises from the fact that the argument that is presented may be turned in the opposite direction and used against the one who has offered it, and is equally strong for both sides of the question. An example is the well-known argument which Protagoras, the keenest of all sophists, is said to have used against his pupil Euathlus. [p. 407] For a dispute arose between them and an altercation as to the fee which had been agreed upon, as follows: Euathlus, a wealthy young man, was desirous of instruction in oratory and the pleading of causes. He became a pupil of Protagoras and promised to pay him a large sum of money, as much as Protagoras had demanded. He paid half of the amount at once, before beginning his lessons, and agreed to pay the remaining half on the day when he first pleaded before jurors and won his case. Afterwards, when he had been for some little time a pupil and follower of Protagoras, and had in fact made considerable progress in the study of oratory, he nevertheless did not undertake any cases. And when the time was already getting long, and he seemed to be acting thus in order not to pay the rest of the fee, Protagoras formed what seemed to him at the time a wily scheme; he determined to demand his pay according to the contract, and brought suit against Euathlus. And when they had appeared before the jurors to bring forward and to contest the case, Protagoras began as follows: “Let me tell you, most foolish of youths, that in either event you will have to pay what I am demanding, whether judgment be pronounced for or against you. For if the case goes against you, the money will be due me in accordance with the verdict, because I have won; but if the decision be in your favour, the money will be due me according to our contract, since you will have won a case.” To this Euatlllus replied: “I might have met this sophism of yours, tricky as it is, by not pleading my own cause but employing another as my advocate. But I take greater satisfaction in a victory in which [p. 409] I defeat you, not only in the suit, but also in this argument of yours. So let me tell you in turn, wisest of masters, that in either event I shall not have to pay what you demand, whether judgment be pronounced for or against me. For if the jurors decide in my favour, according to their verdict nothing will be due you, because I have won; but if they give judgment against me, by the terms of our contract I shall owe you nothing, because I have not won a case.” Then the jurors, thinking that the plea on both sides was uncertain and insoluble, for fear that their decision, for whichever side it was rendered, might annul itself, left the matter undecided and postponed the case to a distant day. Thus a celebrated master of oratory was refuted by his youthful pupil with his own argument, and his cleverly devised sophism failed.
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