[Footnote 18: Aristot. Analyt. Prior. I. ii. p. 25, a. 17-22.] [Footnote 19: Ibid. p. 25, a. 22-26.] [Footnote 20: Though some may fancy that the rule for converting the Universal Negative is intuitively known, yet every one must see that the rule for converting the Universal Affirmative is not thus self-evident, or derived from natural intuition. In fact, I believe that every learner at first hears it with great surprise. Some are apt to fancy that the Universal Affirmative (like the Particular Affirmative) may be converted _simply_. Indeed this error is not unfrequently committed in actual reasoning; all the more easily, because there is a class of cases (with subject and predicate co-extensive) where the converse of the Universal Affirmative _is_ really true. Also, in the case of the Particular Negative, there are many true propositions in which the simple converse is true. A novice might incautiously generalize upon those instances, and conclude that both were convertible simply. Nor could you convince him of his error except by producing examples in which, when a true proposition of this kind is converted simply, the resulting converse is notoriously false. The appeal to various separate cases is the only basis on which we can rest for testing the correctness or incorrectness of all these maxims proclaimed as universal.] From one proposition taken singly, no new proposition can be inferred; for purposes of inference, two propositions at least are required.[21] This brings us to the rules of the Syllogism, where two propositions as premisses conduct us to a third which necessarily follows from them; and we are introduced to the well-known three Figures with their various Modes.[22] To form a valid Syllogism, there must be three terms and no more; the two, which appear as Subject and Predicate of the conclusion, are called the _minor_ term (or minor extreme) and the _major_ term (or major extreme) respectively; while the third or _middle_ term must appear in each of the premisses, but not in the conclusion. These terms are called _extremes_ and _middle_, from the position which they occupy in every perfect Syllogism--that is in what Aristotle ranks as the First among the three figures. In _his_ way of enunciating the Syllogism, this middle position formed a conspicuous feature; whereas the modern arrangement disguises it, though the denomination _middle_ term is still retained. Aristotle usually employs letters of the alphabet, which he was the first to select as abbreviations for exposition;[23] and he has two ways (conforming to what he had said in the first chapter of the present treatise) of enunciating the modes of the First figure. In one way, he begins with the major extreme (Predicate of the conclusion): A may be predicated of all B, B may be predicated of all C; therefore, A may be predicated of all C (Universal Affirmative). Again, A cannot be predicated of any B, B can be