1414. Concreteness and Abstractness

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Concreteness and Abstractness

Granted that concreteness is what makes instances of an abstract property instances, rather than abstract properties all over again; and that, by analogy, abstractness is what all abstract properties have in common as over against their instances, what, exactly, are concreteness and abstractness respectively?

An indication of an answer is given by Hartshorne when he observes: "Whereas both individuals and abstractions (other than those of uttermost generality) can have aspects of relativity, can depend in some way and degree upon contingent relations, . . . only individuals, not abstractions, can feel or think or remember"(Creative Synthesis and Philosophic Method: 154). It is clear from this observation that: 

(1) Abstractions of uttermost generality (or what I mean by "transcendentals") have no aspects of relativity, in no way and degree depend upon contingent relations; for while they must indeed be actualized somehow, and all actualization is contingent, the intensional classes of contingent instances that they require only by an utterly generic or indefinite necessity are necessarily nonempty; and this means that they are not properly relative. 

(2) Granted that only individuals can feel or think or remember, the converse is not true, that only entities that can feel or think or remember are individuals. Indeed, this is not true without qualification even for the metaphysical psychicalist insofar, at least, as she or he allows that thinking, if not feeling and remembering, can only be a local, not a cosmic, variable.

(3) But what does characterize all individuals, indeed, all concrete singulars, including events, is that their aspect of relativity is constituted not only by real, internal relations to certain abstracts, but also, in one part, by real, internal relations to other concretes, which they require by an utterly specific or definite necessity. (The other part of their aspect of relativity is constituted by real, internal relations to some concretes or other, which they require by only a more or less generic or indefinite necessity.)

(4) By contrast, what characterizes all abstracts other than those of uttermost generality is that their aspect of relativity is wholly constituted by real, internal relations to some concretes or other, which they require by only a more or less generic or indefinite necessity. Although they have to be actualized somehow, the how is indeterminate. On the other hand, the intensional classes of contingent instances that they thus require by only a more or less generic or indefinite necessity are not necessarily, but only contingently, nonempty; and this means that, unlike abstractions of uttermost generality, they are properly relative. 

Considering these four points, we can say that concreteness is the transcendental property of being relative not only to certain abstracts, but also to certain concretes—both to some concretes that are required by an utterly specific or definite necessity and to yet other concretes that are required by only a more or less generic or indefinite necessity. Abstractness, by contrast, is the transcendental property of being relative to concretes, if thus relative at all, solely to some concretes or other, which are required by only a more or less generic or indefinite necessity. 

Alternatively, abstractness may be understood simply as the transcendental property of being an object and only an object, whereas concreteness may be understood as the transcendental property of being an object that is also a subject, whether individual or event. Although objects do indeed require subjects, they require them by only a more or less generic or indefinite necessity, whereas subjects, by contrast, require objects, concretes as well as abstracts, by an utterly specific or definite necessity.

September 1989; rev. 23 October 1998; 22 July 2002