BOOK III.

Plato then explains the opinions which he entertains himself, and refutes false ones; and about doubtful matters he suspends his judgment. His opinions of matters as they appear to him he puts into the mouth of four persons, Socrates, Timæus, an Athenian poet, and an Eleatic stranger. But the strangers are not, as some people have supposed, Plato and Parmenides, but certain nameless imaginary characters. Since Plato asserts as undeniable axioms all the opinions which he puts into the mouth of Socrates or Timæus. But when he is refuting false propositions, he introduces such characters as Thrasymachus, and Callicles, and Polus, and Gorgias, and Protagoras, Hippias too, and Euthydemus, and men of that stamp. But when he is demonstrating anything, then he chiefly uses the inductive form of argument, and that too not of one kind only, but of two. For induction is an argument, which by means of some admitted truths establishes naturally other truths which resemble them. But there are two kinds of induction; the one proceeding from contraries, the other from consequents. Now, the one which proceeds from contraries, is one in which from the answer given, whatever that answer may be, the contrary of the principle indicated in the question must follow. As for instance. My father is either a different person from your father, or he is the same person. If now your father is a different person from my father, then as he is a different person from a father, he cannot be a father. If, on the other hand, he is the same person as my father, then, since he is the same person as my father, he must be my father. And again, if man be not an animal, he must be either a stone or a piece of wood; but he is not a stone or a piece of wood, for he is a living animal, and capable of independent motion. Therefore, he is an animal. But, if he is an animal, and a dog or an ox is likewise an animal, then man