Page:Mind (Old Series) Volume 12.djvu/481

 468 NEW BOOKS. Four friends, " Ralph," " Wilfrid," " Lothaire " and " Harold," having wearied of desultory philosophical talk, agree to explain to one another their " characteristic vein of thought" ; seeing that, in the absence of real understanding of this, " perhaps each one of us, if the truth were known, looks upon the sayings of his neighbour somewhat as on brilliant sparks destined to light up the darkness one instant and then die out, whereas his own wisdom seems to him a steady, continuous light, because he knows where and how high the fire burns whence it emanates". The result of this agreement is a debate continued on two nights till dawn, in which the debaters strive, not to convert one another but to attain perfect clearness as to their ultimate views of things. " Ralph " is the evolutionary moralist, who asserts the supremacy of a universal law of progress to which individuals must conform in order to attain happiness. "Harold" is the "anarchist" or antinomian, who maintains that " there are rules and laws, but there is no such thing as the Rule or the Law," and who would reserve a place of honour for "the holy ghost of destruction". "Lothaire," personally inclined to a mystical acceptance of some form of religious faith, and disposed to hold that logically this would be defensible, does not insist on his own idea, but seeks rather to explain his friends more clearly to each other. " Wilfrid/' the " atheorist," contends that all philosophy and science too is "a deed of speech," and has simply a practical or poetical value, all ideas having equal theoretical justification ; even the principle of the creative action of speech being, as soon as it is laid down as a separate principle, an " idol " like all other principles, and only defen- sible because for itself it claims to be nothing more than one idol along with others. The author treats all his characters with the utmost fairness. Although it is, no doubt, possible to detect a " vein of thought " of his own running through the dialogues, he does not display this by allowing any one of the debaters a victory over the rest. The " debate " is what it sets out to be, a disinterested exhibition of certain types of thought about life as proceeding from the predominance of particular moods. It has both literary charm and philosophical suggestiveness. The Conception of the Infinite, and the Solution of the Mathematical Antino- mies : A Study in Psychological Analysis. By GEORGE S. FULLERTON, A.M., B.D., Adjunct Professor of Philosophy in the University of Pennsylvania. Philadelphia : J. B. Lippincott & Co., 1887. Pp. 131. The author here publishes in its complete form a discussion of " the con- ception of the infinite," the concluding chapter of which has already appeared as an article in MIND (Vol. xi. 186). His main contention is that we have " the notion of unlimited possibility of quantity, a notion which, be it marked, is strictly qualitative " ; and that this, and not the vain effort to imagine an infinite series as a whole, is the essential constituent of the mental state that has reference to infinity. What marks this state off from other qualitative conceptions is "its necessary reference to quantity, though not itself quantitative ". By this exclusion of the notion of " a quantitative whole " from the conception of infinity, the difficulties as to the comparison of infinites are first cleared up. Not being quantitative wholes, infinites admit of no quantitative comparison among themselves ; while they are alike in respect of the quality of allowing progression, in at least one direction, without end ; for, this being supposed, a limit anywhere else does not prevent them from being infinites all the same. " In general, wherever the limit is removed in any one direction, whether in the case of lines, of surfaces or of solids, the object can no longer be regarded as a quantitative whole, and is not to be considered finite ". In chapters iii. and iv. (" The Antinomies of Hamilton," " Kant, Mill and Clifford," pp. 34-