Determinables and Determinates

views updated

DETERMINABLES AND DETERMINATES

The terminology of "determinables and determinates" existed in scholastic philosophy, but the modern use of these terms originated with the Cambridge (U.K.) philosopher and logician W. E. Johnson, who revived the terminology in his Logic (1921). Johnson said, "I propose to call such terms as colour and shape determinables in relation to such terms as red or circular which will be called determinates. " Some other determinables are size, weight, age, number, and texture. The terminology has since passed into philosophical currency and is now used to mark both the relation between determinate and determinable qualities and the relation between the corresponding words.

The chief features of this relation that Johnson and his successors have found interesting are:

It is logically distinct from the relation of genus to species. The denotation of a species term is marked off within the denotation of a genus term by the possession of properties known as differentia. The species is thus to be construed as formed by the conjunction of two logically independent terms, either of which can, depending on the purposes at hand, be construed as genus or differentia. For example, the species term man is defined as the conjunction of the terms rational and animal. However, the determinate term red is not definable by conjoining the determinable term color with any other independent term. To put this point another way: Whereas we can say, "All humans are animals which are rational," no analogous statement can be made beginning, "All red things are colored things which are." Any term that could fill the gap would have to be synonymous with red. Red things do not possess some trait other than their redness that, when conjoined with their coloredness, makes them by definition red. Both the genus-species relation and the determinable-determinate relation are relations of the less specific to the more specific; but in the former case the specification is provided by some property logically independent of the genus, whereas in the latter case the determinate cannot be specified by adding additional independent properties to the determinable.

This characteristic has been emphasized by Johnson, John Cook Wilson, A. Prior, and John R. Searle; and it is this feature that chiefly justifies the introduction of this terminology as an addition to the traditional arsenal. Attempts have been made—by Searle, for example—to give a rigorous formal definition of the determinable relation utilizing this feature; but it is not clear to what extent they have succeeded.

(2) Determinates under the same determinable are incompatible. For example, the same object cannot be simultaneously red and green at the same point; and a man six feet tall cannot be simultaneously five feet tall. It might seem that counterexamples could be produced to this point since, for example, an object can be both red and scarlet, and red and scarlet are both determinates of color. However, such counterexamples are easily disposed of on the basis of the fact that scarlet is a shade of red, and hence red is a determinable of scarlet.

We must distinguish the relation in which red stands to scarlet from the relation in which color stands to either red or scarlet. Both are cases of the determinable relation, but they are significantly different. We may think of color terminology as providing us with a hierarchy of terms, many of which will stand in the determinable relation to each other as the specification of shades progresses from the less precise to the more precise. But at the top of the hierarchy stands the term color, which we may describe as an absolute determinable of all the other members of the hierarchy, including such lower-order determinables as "red" and their determinates, such as "scarlet."

Our original point can then be restated by saying that determinates under the same determinable are incompatible unless one of the determinates is a lower-order determinable of the other. In the literature of this subject, the counterexamples are usually avoided by saying that any two exact determinates—for example, exact shades of color—are incompatible. However, it is not clear what exact is supposed to mean in this context.

(3) Absolute determinables play a special role vis-à-vis their determinates. This role may be expressed by saying that, in general, for any determinate term neither that term nor its negation is predicable of an entity unless the corresponding absolute determinable term is true of that entity. For example, both the sentence "The number seventeen is red" and the sentence "The number seventeen is not red" sound linguistically odd because numbers are not the sort of entities that can be colored. Lacking the appropriate absolute determinable, neither a determinate term nor its negation is true of the entity in question.

To have a convenient formulation of this point, we may say that the predication of any determinate term or its negation of an object presupposes that the corresponding absolute determinable term is true of that object. We define presupposition as follows: A term A presupposes a term B if and only if it is a necessary condition of A 's being either true or false of an object x that B is true of x. Thus, in short and in general, determinates presuppose their absolute determinables. No doubt certain qualifications would have to be made to account for the operation of this principle in a natural language. For example, perhaps what is presupposed by red is more accurately expressed by colorable rather than by colored.

Aside from the intrinsic interest of these distinctions, they have proved useful in other areas of philosophy. John Locke's very puzzling discussion of primary and secondary qualities can be illuminated by pointing out that he fails to make sufficient use of the distinction between determinable and determinate qualities. When, for example, he says the primary qualities of a material body are inseparable from it in whatever state it may be, he clearly does not mean that a body must have this or that determinate shape or size as opposed to some other shape or size, but rather that it must have the absolute determinables of the primary qualities: It is a necessary condition of something's being a material object that it have some shape or other, some size or other, and so on.

Again, it is useful to point out that absolute determinables are closely related to categories. The notion of a category (or at least one philosophically important notion of a category) is the notion of a class of objects of which a given term can be significantly predicated. Thus, for example, correlative with the notion of red is the notion of things that can significantly be called red; these things are the members of the category associated with red. But a necessary condition of something's being a member of the class of things that can be significantly called "red" is that the absolute determinable of red must be true of that thing since, as we saw above, determinates presuppose their absolute determinables. Because a category (of the sort we are considering) is always a category relative to a certain term, and because a determinate term presupposes its absolute determinable, the absolute determinables provide a set of necessary conditions for category membership relative to the determinate terms.

Where the absolute determinable provides not only a necessary but also a sufficient condition of predictability of the determinate term, the absolute determinable will simply denote the members of the category associated with the determinate term. Thus, assuming colored (or colorable ) is the only presupposed term of red, the category associated with red, and with any other determinate of color, is only the class of objects that are (or could be) colored.