De la logique à la théologie, cinq études sur Aristote (review)

508 HISTORY OF PHILOSOPHY In making their selection the editors have, with the two exceptions ment;oned, chosen well. I should like to have seen J. S. Morrison's "Pythagoras of Samos" (Class. Quart., 1956) included, and H. C. Baldry's "Embryological Analogies in Presocratic Cosmogony" (Class. Quart., 1932); but there is small room for complaint, and one can look forward with confidence to the second volume in which we are promised, among other things, a translation of Fr~inkel's "Parmenidesstudien" and an Index to both volumes. JOHN M. ROBINSON Windham College De la logique ~ la thdologie, cinq dtudes sur Aristote. By Jules Vuillemin. (Paris: Flammarion, 1967. Pp. 235) Professor Vuillemin has added to his extensive works on philosophy and mathematics a detailed examination of certain elements of Aristotle's logic and metaphysics. The subjects of the five studies are: (1) "Analogy," (2) "Aristotle's System of the Categories and Its Logical and Metaphysical Significance," (3) "On the Infinite Regress as a Method of Refutation," (4) "The Theory of Mixed Relations," and (5) "The Theology of Aristotle." Although the studies were written separately and can be read accordingly, they are closely interrelated, providing a distinct unity to the book. Throughout, Vuillemin uses contemporary logic and mathematics in support of his analyses. In the first study, the source of Aristotle's view of analogy is found in the Eudoxean theory of proportion. Vuillemin is primarily interested, however, in Aristotle's use of analogy in attempting to transcend the restriction of every true science to one genus, an attempt which fails. The study of the Categories, the longest of the book, is the most minute with which this reader is acquainted. In an extraordinarily detailed analysis, Vuillemin rejects the notion that the Categories is simply a classification of terms of the Greek language. Rather, it is a tightly knit theory of judgment involving the terms of judgment, which are also the terms of being. One of the most important bases of the theory, which Vuillemin feels has not been adequately treated, is Aristotle's distinction between "being said of a subject" (essential predication) and "being in a subject" (accidental predication). Vuillemin's dissection of this distinction in relation to the categories in terms of the language of contemporary logic is indeed ingenious. He finds the distinction rooted in Aristotle's metaphysics. The preeminence of essential predication in Aristotle's logic is based upon the privileged position accorded to primary substance. With respect to the infinite regress as a method of refutation, Aristotle argued that no actual infinite series exists but rather that an infinite series can exist only potentially. Vuillemin points out that modern mathematicians have effectively shown that there are infinite series and infinite numbers. Thus arguments based upon the impossibility of an actual infinite series must fail. In the fourth study Vuillemin finds that Aristotle in his view of knowing uses a theory of mixed relations which falters both from the standpoint of logic and psychology . The study of Aristotle's theology is limited to arguments for the existence of the Unmoved Mover in Metaphysics A and Physics VH and VIII. The detail of the analysis is comparable to that of the Categories. The argument in the Metaphysics, for example, is laid out in a series of 29 propositions, some of which have subsidiary propositions. BOOK REVIEWS 509 A reader will have to decide for himself whether every step of the analysis reflects the text. In considering the three arguments for the Unmoved Mover, Vuillemin finds that they depend upon the following propositions (p. 210): 1. The physical principle of the existence of motion. 2. The logical principle of noncontradiction. 3. The logical impossibility of the actual infinite. 4. The principle of economy (nature uses a minimum of principles and does nothing in vain). 5. The principle of the priority of substance. 6. The principle of the priority of actuality. 7. The principle of analogy. 8. The definition of motion. According to Vuillemin, the arguments fail because, of the principles cited, the third, fourth, sixth, and seventh are defective. These brief comments can only suggest the closely reasoned arguments throughout this book, especially in the studies of the Categories...