Two Studies in Metaphysics

TWO STUDIES IN METAPHYSICS I MATHEMATICAL AND METAPHYSICAL ANALOGY IN ST. THOMAS IT is a significant fact that St. Thomas, following Aristotle, uses the words " analogy " and " proportion " interchangeably ; that is, he takes them to be synonymous. For instance , in his Commentary/ on the Metaphysics we find the expression " proportion or analogy " (proportiorte~ vel analogia ); 1 in his Commentary on the Ethics, the expression" according to analogy, that is, the same proportion" (secundum analogiam, idest proportionem eamdem) ;2 and lest there be any doubt about the matter at all, in the Quaestiones Disputatae De Veritate we have the categorical statement that " according to analogy " means nothing else than " according to proportion." 8 Ordinarily, however, we think of "proportion" as being primarily and above all a mathematical term, and the theory of proportion as belonging primarily and in the strict sense to the science .of mathematics, and in particular to geometry . Hence if by "analogy" St. Thomas only means "proportion ," then it would seem that if the theory of analogy has any really scientific application in philosophy, this application must consist in some sort of extension· of the .mathematical notion of analogy into the domain of philosophical science. One may well ask, however, how any such extension could possibly be valid, for is it not true that in philosophy we are outside the 1 In V Metaph., lect. 8, Cathala ed., n. 879. • In IV Ethic., lect. 7, n. 96. In his Commentaries on the Physics and the De Coelo et Mundo of Aristotle, see also: I Phys., lect. 18, n. 7 (Leonine ed.); 1.18, n. 9; I De C. et M., I. 14, ns. .3-4; ll, I. 11, n. 4; and in his Comp. Theol. see ch. 27. Cf. also Opusc. De Prin. Nat., in fine. 8 Q. ft, 11, corpus. 564 TWO STUDIES IN METAPHYSICS 565 order of quantity in the ordinary mathematical sense? Is this not especially true in metaphysics? Certainly, in philosophy we have attained to a level of abstraction outside or above the corporeal order, but where there are no bodies, how can there be any quantity? Where there is no quantity, how can there be any proportions or " analogies " in a truly scientific sense-in any sense other than a merely literary or metaphorical one? If "analogy" does have a truly philosophical role, that role must be something more than, and other than, that of a mere figure of speech, no matter how suggestive it may be. Nevertheless, it is true that St. Thomas defines analogy in terms of proportion. In fact, he says that " properly speaking, proportion is nothing else than the relation of quantity to quantity, as for instance, in the case of one (quantity) being the equal of another, or the triple of it." 4 It is, as he says in the Summa Theologica, " a certain relation of one quantity to another, according as the double, triple, and equal, are species of proportion ." 5 Obviously, it is here a question of predicamental or dimensive quantity, i.e., of that quantity which depends on extension and is applicable only to bodies; so "proportion" here signifies a definite, precise, determinate relation of one dimensive quantity, continuous or discrete, to another, e. g., the relation of a surface to a surface or of a number to a number.6 Now this is proportion taken according to the first imposition of the name.7 In this sense proportion is univocal; it applies only to the class of dimensive quantities, with respect to which it always has the same meaning, namely, definite or fixed :relation of one quantity to another (certa habitudo unius quantitatis ad alteram), and this holds whether the quantity in • DeVer., q. 8, a. 1, ad 6um. • I, q. 12, a. 1, ad 4um. • Number in the properly mathematical sense is an abstraction from real, discrete, dimensive quantity, and therefore applies properly only to the latter. (See below note H.) 1 See J. M. Ramirez: "De Analogia ... ," in La Ciencia Tomista, vol. xxiv, il· ~3. 566 JAMES F. ANDERSON question be " commensurable " or " incommensurable." 8 Always it is a question of ratio in the strict Euclidean sense,9 namely of a determinate...