Even the friends and companions of Aristotle were not satisfied with his manner of establishing this fundamental rule as to the conversion of propositions. Eudêmus is said to have given a different proof; and Theophrastus assumed as self-evident, without any proof, that the Universal Negative might always be converted simply.[15] It appears to me that no other or better evidence of it can be offered, than the trial upon particular cases, that is to say, Induction.[16] Nothing is gained by dividing (as Aristotle does) the whole A into parts, one of which is C; nor can I agree with Theophrastus in thinking that every learner would assent to it at first hearing, especially at a time when no universal maxims respecting the logical value of propositions had ever been proclaimed. Still less would a Megaric dialectician, if he had never heard the maxim before, be satisfied to stand upon an alleged _à priori_ necessity without asking for evidence. Now there is no other evidence except by exemplifying the formula, No A is B, in separate propositions already known to the learner as true or false, and by challenging him to produce any one case, in which, when it is true to say No A is B, it is not equally true to say, No B is A; the universality of the maxim being liable to be overthrown by any one contradictory instance.[17] If this proof does not convince him, no better can be produced. In a short time, doubtless, he will acquiesce in the general formula at first hearing, and he may even come to regard it as self-evident. It will recall to his memory an aggregate of separate cases each individually forgotten, summing up their united effect under the same aspect, and thus impressing upon him the general truth as if it were not only authoritative but self-authorized. [Footnote 15: See the Scholia of Alexander on this passage, p. 148, a. 30-45, Brandis; Eudemi Fragm. ci.-cv. pp. 145-149, ed. Spengel.] [Footnote 16: We find Aristotle declaring in Topica, II. viii. p. 113, b. 15, that in converting a true Universal Affirmative proposition, the negative of the Subject of the convertend is always true of the negative of the Predicate of the convertend; _e.g._ If every man is an animal, every thing which is not an animal is not a man. This is to be assumed (he says) upon the evidence of Induction--uncontradicted iteration of particular cases, extended to all cases universally--[Greek: lamba/nein d' e)x e)pagôgê=s, oi(=on ei) o( a)/nthrôpos zô=|on, to\ mê\ zô=|on ou)k a)/nthrôpos; o(moi/ôs de\ kai\ e)pi\ tô=n a)/llôn. . . . . e)pi\ pa/ntôn ou)=n to\ toiou=ton a)xiôte/on.] The rule for the simple conversion of the Universal Negative rests upon the same evidence of Induction, never contradicted.]