Studies and Exercises in Formal Logic. By J. T. N.
Keynes, MA. (Macmillan.)—This book will be found a most valuable aid towards the comprehension of a difficult and most important branch of the Science of Thought. The exercises are not only well chosen for the purpose in view, but many of them constitute intrinsically interesting problems, and there are but few of them in the solution of which the student of the social and political questions of the day may not pro- fitably employ himself, and thus test his capacity for accurate argu- mentation. Part IV., dealing with "Complex Inferences," is, perhaps, the most valuable portion of the book. In practical life, we are con- cerned chiefly with questions of a more or less complicated character, and much of the difficulty that attends the re-solution of the problems raised by the intricate interactions of the forces of modern society would be removed were the disputants duly provided with the skill that can only be acquired by studying and practising the principles and methods which Mr. Keynes has so abundantly illustrated in his last dozen chapters. Of "Formal Logic," what may be termed the formal difficulties, increase with the development of its exposition, while the real difficulties are encountered at the outset. Hence the earlier chap- ters of Mr. Keynes' book are more open to exception than the later section. We have not space to note more than one or two of the ex- ceptions we should ourselves be inclined to take. The definition of a word, as an articulate sound (or its written equivalent), constituting (by itself or with other words) a name or forming a sentence, is certainly insufficient. An interjection is an articulate sound, but it is not a word. So is a sentence ; sentences, indeed, probably preceded words. In fact, it is by no means easy to define the expression " werd." It is the creation of grammarians, the result of the analysis of the sen- tence. Some writers, like Retif de la Bretonne, regarded and wrote many common sentences as composite words. It is, perhaps, best to be content with defining " words " as the ultimate elements of speech, though the definition is not for all languages absolutely correct. Again, it is as misleading (in a work on logic) to talk of the written equivalent of an articulate sound as a word, as it would be to speak of the picture of a man as being a man. Nor can the definition of a name quoted from Hobbes be accepted as satisfactory. A name is hardly ever a word taken "at pleasure," that is, capriciously, as a mark, but a speech-sound chosen and preserved by a sort of natural selection, or merely by a process of history, to mark a state of con- sciousness. Mr. Keynes is, no doubt, right in denying connotation to proper names. Proper names often have a connotation attached to them, but only when they are used as types of a class. They are fre- quently "elliptic," the context supplying or indicating the comple- mentary denotation. The distinction between singular and general collective names which have furnished so much material for contro- versy, is acutely stated to lie in the collective or distributive use of such names. The book, indeed, is fall of sagacious observations of this kind, the result of wide reading and accurate and painstaking reflection. The question of the reality of propositions in connection with formal logic is discussed at considerable length, and the conclusion arrived at is that propositions so considered are not real—that is, do not in- volve existence in fact or imagination. A proposition that is not real, however, is a mere statement in the air; and it would, perhaps, be more accurate to say that formal logic is concerned not with unreal propositions, but with the formal qualities of-real propositions. The syllogism is only cursorily treated. It seems to be admitted that every syllogism is reducible to Barbara ; and if so, it must result that the syllogism is nothing more than the expression of the truism that what is predicated of a class may be predicated of its parts. It is a process of explication, rather than of proof in the ordinary sense, yet it is none the less an important means of adding to our know- ledge. The whole of geometry is, in one sense, contained in the axioms and postulates, but the fact that the three angles of a triangle equal two right angles is, nevertheless, a real acces- sion to the sum of human knowledge. One reflection suggested by the perusal of the earlier chapters is the difficulty the student mast feel with regard to the numerous elementary and fundamental points on which the pundits of the science are hopelessly at variance with each other. We doubt whether examiners are always sufficiently- alive to this difficulty, and make the proper allowances in cases where the candidate has been taught, and adopts in his answers, theories other than what his examiner accepts.
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