[54] Plat. Euthyd. p. 298.
Those animals, and those alone are yours (sheep, oxen, &c.), which you can give away, or sell, or sacrifice at pleasure. But Zeus, Apollo, and Athênê are your Gods. The Gods have a soul and are animals. Therefore your Gods are your animals. Now you told us that those alone were your animals, which you could give away, or sell, or sacrifice at pleasure. Therefore you can give away, or sell, or sacrifice at pleasure, Zeus, Apollo, and Athênê.[55]
[55] Plat. Euthydêm. p. 302. This same fallacy, in substance, is given by Aristotle, De Sophist. El. 17, 176 a. 3, 179, a. 5, but with different exemplifying names and persons.
This fallacy depends upon the double and equivocal meaning of yours — one of its different explanations being treated as if it were the only one.
Fallacies involving deeper logical principles — contradiction is impossible. — To speak falsely is impossible.
Other puzzles cited in this dialogue go deeper:— Contradiction is impossible — To speak falsely is impossible.[56] These paradoxes were maintained by Antisthenes and others, and appear to have been matters of dialectic debate throughout the fourth and third centuries. I shall say more of them when I speak about the Megarics and Antisthenes. Here I only note, that in this dialogue, Ktesippus is represented as put to silence by them, and Sokrates as making an answer which is no answer at all.[57] We see how much trouble these paradoxes gave to Plato, when we read the Sophistês, in which he handles the last of the two in a manner elaborate, but (to my judgment) unsatisfactory.
[56] Plato, Euthydêm. pp. 285-286.
[57] Plato, Euthydêm. pp. 286 B — 287 A.
Plato’s Euthydêmus is the earliest known attempt to set out and expose fallacies — the only way of exposing fallacies is to exemplify the fallacy by particular cases, in which the conclusion proved is known aliunde to be false and absurd.
The Euthydêmus of Plato is memorable in the history of philosophy as the earliest known attempt to set out, and exhibit to attention, a string of fallacious modes of reasoning. Plato makes them all absurd and ridiculous. He gives a caricature of a dialectic debate, not unworthy of his namesake Plato Comicus — or of Aristophanes, Swift, or Voltaire. The sophisms appear for the most part so silly, as he puts them, that the reader asks himself how any one could have been ever imposed upon by such a palpable delusion? Yet such confidence is by no means justified. A sophism, perfectly analogous in character to those which Plato here exposes to ridicule, may, in another case, easily escape detection from the hearer, and even from the reasoner himself. People are constantly misled by fallacies arising from the same word bearing two senses, from double construction of the same phrase, from unconscious application of a dictum secundum quid, as if it were a dictum simpliciter; from Petitio Principii, &c., Ignoratio Elenchi, &c. Neither Plato himself, nor Aristotle, can boast of escaping them.[58] If these fallacies appear, in the examples chosen by Plato for the Euthydêmus, so obviously inconclusive that they can deceive no one — the reason lies not in the premisses themselves, but in the particular conclusions to which they lead: which conclusions are known on other grounds to be false, and never to be seriously maintainable by any person. Such conclusions as — “Sokrates had no father: Sophroniskus, if father of Sokrates, was father of all men and all animals: In beating your dog, you beat your father: If you know one thing, you know everything,” &c., being known aliunde to be false, prove that there has been some fallacy in the premisses whereby they have been established. Such cases serve as a reductio ad absurdum of the antecedent process. They make us aware of one mode of liability to error, and put us on our guard against it in analogous cases. This is a valuable service, and all the more valuable, because the liability to error is real and widespread, even from fallacies perfectly analogous to those which seem so silly under the particular exemplifications which Plato selects and exposes. Many of the illustrations of the Platonic Euthydêmus are reproduced by Aristotle in the Treatise de Sophisticis Elenchis, together with other fallacies, discriminated with a certain method and system.[59]