Page:Philosophical Review Volume 9.djvu/566

550 extension greater than that of the other two terms; and finally, in the third figure, the middle term itself has the least extension of all the terms. But this tabulation will serve at the same time to disclose the principles underlying the classification which led to the division of syllogisms into the three figures: it is the relation as regards extension in which the middle term stands to the other terms."

This explanation, which may now be fairly said to be established, receives striking confirmation from the apt interpretation given by Dr. Maier of the meaning of the so-called of the terms in the three figures. He shows (pp. 53, ff.) that it refers to the order of the letters of the alphabet which are conventionally used by Aristotle in three groups,, for the first figure ;, for the second ; , for the third. Thus, then, in accordance with this scheme for the first figure, the middle term,, will also regularly occupy the middle place in the order of occurrence as the terms appear in the series presented by the schematized syllogism.

With this notice we may now content ourselves. The typography of the book is rather unusually good. A very few errors of consequence appear, two of which may be noted. On p. 37, line 6, nicht seems to have fallen out before "völlig" and, on p. 114, note 2., announced in the text, does not appear at the foot of the page. In conclusion we may say, what really need not be said after the favorable words already spoken, that Dr. Maier has undoubtedly given us the best book on the subject of Aristotle's logic.

In his preface Professor Hoffman states that the object of his book is "to point out with clearness what it is that constitutes a science, and to set forth with some detail what are the grounds upon which every science rests, and what are the principles and rules that must be followed in order to construct one. It is maintained from the first chapter to the last that every department of knowledge is capable of scientific treatment, and must be so treated before any great advance can be made towards a consistent and rational conception of the universe." He also states that the book is "the outcome of a series of lectures given to my classes in Union College to supplement their work in Formal Logic." The general character of the book would lead us to estimate it as such a supplement.

What constitutes a science is outlined in the first chapter. A science involves (1) a knowledge of facts, (2) that these facts be capable of verification, (3) that the knowledge of them be classified, and (4) that they be put together in a system. These constituents yield the following definition: