appended to each chapter a complete and very valuable set of exercises and problems. Dr. Hyslop has given completeness to the work by treating briefly, yet in a very satisfactory way, of the Quantification of the Predicate, and of mathematical and other forms of non-syllogistic reasoning. I consider the book admirably adapted for students of some maturity — undergraduates in their junior or senior year — who can devote a considerable portion of time to the subject.
I wish, however, to call attention to a few of the minor excellencies and defects of the book. One of the modifications which Dr. Hyslop has introduced into logical doctrine, and upon which he lays considerable stress, is the division of general terms or concepts into mathematical generals and strictly logical generals. He does not give any examples of former class, and his definition (" by mathematical general concepts, I mean those which are absolutely alike in their content or intension, or such as are grouped together under the same name, solely on account of their numerical value," p. 75) does not seem intelligible. The meaning, however, seems to be that the so-called mathematical generals do not connote the common qualities of a class, but are formed by the addition of homogeneous units, and so contain their individuals in them and not under them as do strictly logical concepts. But if this is so they are surely not general terms at all, but only an abridged form for a number of singular terms. As for the distinction made (p. 93) between the mathematical and logical genus, it does not seem to mean more than that the genus may be regarded both from the point of view of extension and intension. There may, however, be some advantage in adopting the term Conferentia to denote the genus in the latter sense as opposed to the differentia. In testing the valid moods in the different figures the author would have done better to have followed Überweg. In his treatment of the Sorites he has neglected to point out the rules which this form of reasoning must obey. His classification of fallacies is excellent, the grouping of material fallacies as Fallacies of Equivocation and Fallacies of Presumption being particularly happy. It seems a mistake, however, to substitute for the descriptive "Undistributed Middle," the more technical phrase, "Illicit Process of the Middle Term," as a name for the well-known fallacy.
The author has very carefully and accurately distinguished Induction from other processes not properly reasoning at all, as well as from deductive inferences. "The probability of an inductive inference is the result of an inference from established facts, and so is due to going beyond the premises under the stimulus of certain general principles which may be called the Principles of Induction" (p. 315). In treating of the Inductive Method in the last chapter Dr. Hyslop says that the
