Analogy and “Kinds” of Things

Abstract

ANALOGY AND "KINDS" OF THINGS T HE CONSIDERATIONS WHICH follow arose chiefly from reflections on two treatments of the problem of analogy by I. M. Bochenski. The first appeared in this journal over twenty years ago/ and the second formed an appendix to The Logic of Religion.2 Both are excellent analyses of the problem. Nevertheless, there are difficulties which seem to resist solution by means of the proposals put forth by Bochenski. It is these difficulties to which I address myself here, following which I consider three questions which stem from them and are of the utmost importance in achieving a proper cataloging of the problems of analogy. The purpose of such an enterprise is heuristic. It is to be hoped that my remarks, which are not definitive, can contribute somewhat to the motion of the ongoing debate on analogy, whether this be by means of further developing the scheme set forth by Bochenski, or by suggesting some alternate route to the heart of the problem. By way of brief summary of Bochenski's analysis, it should first be noted that it depends upon the following formulation of the workings of language. Words are construed as visual or auditory marks which "mean" certain properties of objects. This relation is expressed in the formulaS (a, f, x), or" a means f in x." Thus, "red" stands for the red of my car. Given a second expression which is meaningful, S (b, g, y) ,3 any relation which might obtain between the two terms a and b would be expressed by the formula R (a, b, f, g, x, y): "a which stands for f in x is related to b which stands for g in y." Univocal 1 "On Analogy," The Thomist, 11 (1948), pp. 424-447. Reprinted in LogicoPhilosophical Studies, ed. A. Menne (Dordrecht, 1961), pp. 97-117. • (New York, 1965), pp. 156-162. 3 Presumably there is a misprint in 50.12 of The Logic of Religion. Cf. "On Analogy," 4. 293 294 JAMES J. HEANEY terms would be those in which a and b were of the same form (" Isomorphic ") , and f and g were identical properties, while x and y were different objects: "red" in "a red house" and "a red car." Ambiguous or equivocal terms, among which he classes analogous expressions, are those in which a and b are isomorphic, while neither the properties f and g nor the objects x and y are identical: " red " in " a red house " and " a red herring." The relation of ambiguity or equivocation can thus be formalized as: (1) Am(a, b,f,g,x,y) for S(a,f,x) · S(b,g,y) ·· I(a,b) · f#g · x#y.4 In the earlier work he then tried to account for analogy in terms of this definition, adding only that there must be some further distinguishing factor to set analogy apart from other instances of equivocation, expressed as: (2) An(a,b,f,g,x,y) =Dt.Am(a,b,f,g,x,y) · F.5 The factor F is then interpreted according to the traditional notions of attribution and proportionality. A third move which appears in the earlier work, and continues on as the basis of the later, is the notion of analogy as "isomorphy." In it, very possibly because of the difficulties involved in treating analogous meaning as a subclass while defining it by means of an added characteristic, Bochenski has opted for a limitation of those terms to he considered analogous to relational predicates alone. Once again, analogy is defined in terms of equivocity, this time with the added stipulations that there must be relations involved, and that a further relation of " isomorphy " must hold between these relations. "Isomorphy" means that the relations have the same formal properties, e. g., transitivity, symmetry, reflexivity, ect., in common. The formula given to describe this is: • The Logic of Religion, 50.14; "On Analogy," 5.4. 5 " On Analogy," 8.2. The notation has been modified in favor of the simplicity of the later treatment. ANALOGY AND "KINDS" OF THINGS Q95 (3) An(a, b, f, g, x, y) = Dt. Ae (a, b, f, g, x...