260 CRITICAL NOTICES : view that others are not very useful results, I think, from his neglect of modern researches on the transtinite, the principles of geometry, and kindred subjects. This neglect appears, for example,, in the remark (p. 103) that " most of the strange and inadmissible paradoxes of the various non-Euclidean geometries " result from confusions as to the infinite and the infinitesimal. As a matter of fact, most modern writers treat non-Euclidean geometry purely projectively or descriptively, so that no metrical ideas occur in their work ; consequently the infinite and the infinitesimal are not involved at all. The present work is not quite in line with those of other current writers on symbolic logic ; but it has merits which most of their works do not have, and it serves in any case to prevent the subject from getting into a groove. And since one never knows what will be the line of advance, it is always most rash to condemn what is not quite in the fashion of the moment. In this case, the points of difference are small compared to the points of agreement, and the book will be found highly instructive by beginners, and stimulating, by all readers. B. RUSSELL.
