Determinables and Determinates [addendum]
The relation between determinates and determinables has certain interesting formal and modal features. It is controversial whether these features are to be explained in terms of something more basic or whether they are primitive.
Formally speaking, the determinate-determinable relation is transitive, asymmetric, and irreflexive. Because scarlet is a determinate of red and red is a determinate of color, scarlet is a determinate of color. Because scarlet is a determinate of red, red is not a determinate of scarlet. And nothing is a determinate of itself.
Modally speaking, three features are worthy of note. First, if anything has some property, p, then it also has every property, q, of which p is a determinate. Thus, of necessity, scarlet things are red and colored. Second, the relation guarantees the exclusion of codeterminates. Nothing can have two determinates under a single determinable (provided the determinates are not themselves determination related). Thus, nothing can be both scarlet and crimson, because both are codeterminates of color. Third, and more controversially, any object with a determinable property must have a property that is a determinate of that property. Furthermore, there must be an exactly determinate property under every determinable.
It may be that the modal and formal structure of the determinate-determinable relation is brute, but two theories suggest otherwise. According to David M. Armstrong (1997), codeterminates under a single determinable are partially identical. Having five grams of mass just consists in having one gram of mass five times over. So, the exclusion relation is neatly explained by appeal to familiar facts about identity. Nothing can be five grams of mass and one gram of mass for the same reason that no room can have exactly one lectern and exactly five lecterns. However, the notion of partial identity for properties, as opposed to individuals, remains unclear.
Sydney Shoemaker (1984, 1998) holds that properties are individuated by the causal powers they bestow on objects that instantiate them. This theory of properties provides a ready explanation of the nature of the determinate-determinable relation: The powers endowed by a determinable property are a proper subset of the powers endowed by a determinate of that property (2001). For example, scarlet bestows the power to trigger scarlet detectors as well as red and color detectors. Some of the modal and formal features of the relation are then explicable simply by appeal to set theory, with its transitive, asymmetric, and irreflexive relation of proper subsethood. For example, if anything is scarlet, then it is also red, because if anything has the set of causal powers endowed by scarlet, then it has every subset of the causal powers in that set, and one of those subsets corresponds to red. The exclusion of codeterminates requires another explanation, however, which appeals to the individuation of powers. If an object were both scarlet and crimson, it would have incompatible causal powers, that is, it would be disposed to act in contradictory ways in the identical circumstances.
This reduction of the determinate-determinable relation would be more satisfying were the causal theory of properties that underwrites it less controversial. Among the more surprising consequences of the theory is that the laws of nature are strictly metaphysically necessary. Moreover, the theory is not perfectly general, but applies only to certain properties. The causal relation itself, along with purely formal properties like self-identity, cannot be correlated with a unique set of powers, but such noncausal properties may nevertheless stand in determinate-determinable relations.
One other characteristic is worthy of note: Determinates and determinables do not compete for causal efficacy. If a scarlet patch sets off a red detector, it is appropriate both to say the detector was triggered by the red and that the detector was triggered by the scarlet. The overdetermination here is harmless, which raises the possibility that the relation may be appropriated by nonreductive physicalists seeking a way to preserve the causal efficacy of the mental in a physical world; perhaps physical properties are determinates of mental determinables (Yablo 1992).
The fit is not quite right, however. To repeat the point made earlier, the determinate-determinable relation is not the genus-species relation, nor is it merely one of greater and lesser generality. A perfectly determinate shape may be realized in different materials, but the conjunctions of that shape with different types of material do not form further determinates of shape. Likewise, mental properties may still admit multiple physical realizations even if they are perfect determinates of thought (Funkhouser).
Armstrong, David M.; Properties; Set Theory; Shoemaker, Sydney.
Bibliography
Armstrong, David M. A World of States of Affairs. New York: Cambridge University Press, 1997.
Funkhouser, Eric. "The Determinate-Determinable Relation." Forthcoming, Nous.
Shoemaker, Sydney. "Causal and Metaphysical Necessity." Pacific Philosophical Quarterly 79 (1998): 59–77.
Shoemaker, Sydney. "Causality and Properties." In Identity, Cause, and Mind: Philosophical Essays. New York: Cambridge University Press, 1984.
Shoemaker, Sydney. "Realization and Mental Causation." In Physicalism and Its Discontents, edited by Carl Gillett and Barry Loewer. New York: Cambridge University Press, 2001.
Yablo, Stephen. "Mental Causation." Philosophical Review 101 (1992): 245–280.
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