*THE POPULAR SCIENCE MONTHLY.*

*many*logical methods of treatment possible in a hand-book of zoölogy, many are easy to follow out, and that one, which aims at presenting a logical classification of the kind spoken of by Mill, in which objects 'are arranged in such groups, and those groups in such an order as shall best conduce to the ascertainment and remembrance of their laws,' is a very difficult one to follow out. This kind of classification involves nothing less than an attempt (however inadequate) to trace the animal pedigree; for the laws to be ascertained and remembered are the laws of heredity and adaptation. We may regret, then, that so able a zoologist as Prof. Carus has remained in the old grooves and not ventured on to the inevitable track where Gegenbaur and Haeckel have preceded him."

Problems of Life and Mind. By George Henry Lewes. First Series, Vol. II. Boston: J. R. Osgood & Co., pp. 487. Price, $3.

The "problems" discussed by Mr. Lewes in the two volumes which constitute his first series are six in number. Of these, the first, "Limitations of Knowledge," was considered in the preceding volume; the rest are considered in the volume before us. The author's purpose in this series is "to lay down the foundations of a creed, by exhibiting the method which determines all successful inquiry, and by specifying certain general results reached on that method." Thoroughly imbued with the scientific spirit, Mr. Lewes applies to metaphysical discussions the same methods which have in modern times given such brilliant results in the field of natural science. The problems which he discusses are among the most intricate which have worried the mind of man from the dawn of reason. They have been the object of profound study ever since philosophy first had a place in human thought; men have viewed them from every side, and attempted their solution in every conceivable way, but still they remain in all their pristine obscurity. The scientific method of investigation has at last been brought to bear upon these problems, and already we seem to be gaining some headway, under the guidance of Spencer, Bain, Lewes, and their fellows.

The first problem discussed in the volume before us is that of *Certitude.* The author's one test of truth, or of certitude, is the principle of equivalence. When two terms have the same import, i. e., are *equivalent* they may be predicated of one another; and all errors, both in reasoning and conduct, arise from assuming equivalence in terms where it does not exist. Mathematical truths are exact, necessary, only when the terms in which they are stated are equivalent; mathematical propositions become inexact, or contingent, whenever they are applied to cases involving conditions not included in the terms. The objection might be made that this reduces truth to an identical proposition—"a thing is itself." Yet, in propounding any truth, what more does one intend than to express *what the facts are;* and what is a statement of facts more than the assertion *that they are what they are?* When the two terms of a proposition can be thus shown to be equivalent, the proposition is a truth, and we possess certitude of it. Mr. Lewes shows that this principle of equivalence is the same as the Universal Postulate of Herbert Spencer, of which it is merely the positive statement. Our author's principle is, "Truth is the equivalence of its terms." He states Spencer's principle as follows: "Whenever a subject and predicate are so united that the one term is incapable of appearing to thought without the other, the proposition is necessary; and its negative being unthinkable, the proposition itself must be true." Our author further shows that the three scholastic principles, Identity, Contradiction, and Ratio Sufficiens, are all reducible to the principle of equivalence.