Review of Aristotle’s Theory of the Infinite

Aristotle’s Theory of the Infinite. By Abraham Edel. New York: Columbia University Press, 1934. Pp. 102.

The results of this study cannot here be summarized because it is mainly an exposition of the chief sections of Physics III and De Caelo I which deal with Aristotle’s theory of the infinite. To this is related, as necessary to the explanation, an analysis of potentiality into three types, one of which alone affords to the infinite the only kind of existence it can have. Then after giving the positive account of the infinite, and considering the question of an infinite world, Dr. Edel traces the several applications of general theory to specific fields, or, more exactly, the corroboration of the general analysis by independent analyses of the subject-matter of various specific fields.

There are, passim, but preponderantly at the end, correlations of Aristotle’s arguments with modern arguments and modern methods. These comparisons show the adaptability of Aristotelian analysis to the development of modern science, Aristotle’s inadequacy owing to his limited empirical knowledge, for, to quote one such such case: “The substitution of relational patterns of types of motion for elementary qualities has little bearing on the question at issue.” When, however, Dr. Edel attempts to propose a new statement of Aristotle’s view on the finitude of the world, he seems to the reviewer to lose himself in inconclusiveness, notwithstanding some thoughtful and thought-provoking suggestions. Of his work as a whole, he says in the introduction: “At worst, the result is simply another interpretation; at best, a fresh approach to his [Aristotle’s] own way of thinking.” We may well add that, with the textual analysis and his criticisms of other commentators, at worst, the work is good.