REVIEWS OF BOOKS.
The body of this work (pp. 1-441) consists of a short critical Conclusion (pp. 431-441), preceded by nine expository chapters dealing with the following subjects: (i) The Syllogistic, (2) the 'Combinatoria,' (3) the Universal Language, (4) the Universal Characteristic, (5) the Encyclopædia, (6) the 'General Science,' (7) the Universal Mathematics, (8) the Logical Calculus, (9) the Geometrical Calculus. Then follow (pp. 443-538) five Appendices: (1) Abstract of the Classical Logic, (2) Leibniz and Hobbes, their Logic, their Nominalism, (3) Some Mathematical Discoveries of Leibniz, connected with the Combinatoria and the Characteristic, (4) On Leibniz as Founder of Academies, (5) On the Geometrical Calculus of Grassmann. The work closes (pp. 539-608) with twenty notes, a table of bibliographical abbreviations, a table of correspondence between the editions of Gerhardt and Erdmann, indexes, etc.
The book is, from every point of view, a noteworthy one. It is the product of an author who is at once—a rare combination—a trained mathematician, logician, and philosopher. It is the result of laborious and scholarly research, including a careful study of many important unpublished writings of Leibniz, neglected even by Gerhardt. Out of a great wealth of material all pertinent facts have been seized upon, admirably marshalled without apparent distortion or undue emphasis, and the whole presented in a charmingly lucid style. And finally, the conclusions reached are revolutionary; if accepted, the traditional interpretation of much of the contents of Leibniz's philosophy and the usual account of its evolution must be discarded.
The book originated in an attempt to make a study of Leibniz as a precursor of modern Symbolical Logic, to analyze his Logical Calculus and his Geometrical Calculus, and to reconstruct the conception of his Universal Characteristic. In carrying out this design, M. Couturat was led to examine the unpublished writings of Leibniz contained in the library at Hanover, being greatly aided in doing so by Herr Bodemann's catalogue. He found that the various editors of Leibniz's works, such as Raspe, Erdmann, and even Gerhardt, had particularly neglected in their editions the logical writings; that, for one manuscript on logic which they had published, they had left a score of
