[Footnote 34: Analyt. Prior. I. vii. p. 29, a. 30-b. 25.] [Footnote 35: Ibid. I. iv. p. 26, b. 30, p. 27, a. 1, p. 28, a. 9, p. 29, a. 15. An admissible syllogism in the Second or Third figure is sometimes called [Greek: dunato\s] as opposed to [Greek: te/leios], p. 41, b. 33. Compare Kampe, Die Erkenntniss-Theorie des Aristoteles, p. 245, Leipzig, 1870.] Such are the main principles of syllogistic inference and rules for syllogistic reasoning, as laid down by Aristotle. During the mediæval period, they were allowed to ramify into endless subtle technicalities, and to absorb the attention of teachers and studious men, long after the time when other useful branches of science and literature were pressing for attention. Through such prolonged monopoly--which Aristotle, among the most encyclopedical of all writers, never thought of claiming for them--they have become so discredited, that it is difficult to call back attention to them as they stood in the Aristotelian age. We have to remind the reader, again, that though language was then used with great ability for rhetorical and dialectical purposes, there existed as yet hardly any systematic or scientific study of it in either of these branches. The scheme and the terminology of any such science were alike unknown, and Aristotle was obliged to construct it himself from the foundation. The rhetorical and dialectical teaching as then given (he tells us) was mere unscientific routine, prescribing specimens of art to be committed to memory: respecting syllogism (or the conditions of legitimate deductive inference) absolutely nothing had been said.[36] Under these circumstances, his theory of names, notions, and propositions as employed for purposes of exposition and ratiocination, is a remarkable example of original inventive power. He had to work it out by patient and laborious research. No way was open to him except the diligent comparison and analysis of propositions. And though all students have now become familiar with the various classes of terms and propositions, together with their principal characteristics and relations, yet to frame and designate such classes for the first time without any precedent to follow, to determine for each the rules and conditions of logical convertibility, to put together the constituents of the Syllogism, with its graduation of Figures and difference of Modes, and with a selection, justified by reasons given, between the valid and the invalid modes--all this implies a high order of original systematizing genius, and must have required the most laborious and multiplied comparisons between propositions in detail.