Online research in philosophy

Armstrong holds the Supervenience Theory of instantiation, namely that the instantiation of universals by particulars supervenes upon what particulars and what universals there are, where supervenience is stipulated to be explanatory or dependent supervenience. I begin by rejecting the Supervenience Theory of instantiation. Having done so it is then tempting to take instantiation as primitive. This has, however, an awkward consequence, undermining one of the main advantages universals have over tropes. So I examine another account hinted at by Armstrong. This is the Operator Theory of instantiation, by which I mean the theory that universals are operators, and that a particular instantiates a monadic universal because the universal operates on the particular, resulting in the state of affairs. On this theory the state of affairs supervenes on the instantiation rather than vice versa. In the second part of the paper I develop this theory of universals as operators, including an account of structural universals, which are useful for accounts of modality and of mathematics.

I attempt to answer the question of what Aristotle's criteria for 'being a substance' are in the Categories. On the basis of close textual analysis, I argue that subjecthood, conceived in a certain way, is the criterion that explains why both concrete objects and substance universals must be regarded as substances. It also explains the substantial primacy of concrete objects. But subjecthood can only function as such a criterion if both the subjecthood of concrete objects and the subjecthood of substance universals can be understood as philosophically significant phenomena. By drawing on Aristotle's essentialism, I argue that such an understanding is possible: the subjecthood of substance universals cannot simply be reduced to that of primary substances. Primary and secondary substances mutually depend on each other for exercising their capacities to function as subjects. Thus, subjecthood can be regarded as a philosophically informative criterion for substancehood in the Categories.

One often hears a complaint about “bare particulars”. This complaint has bugged me for years. I know it bugs others too, but no one seems to have vented in print, so that is what I propose to do. (I hope also to say a few constructive things along the way.) The complaint is aimed at the substratum theory, which says that particulars are, in a certain sense, separate from their universals. If universals and particulars are separate, connected to each other only by a relation of instantiation, then, it is said, the nature of these particulars becomes mysterious. In themselves, they do not have any properties at all. They are nothing but a pincushion into which universals may be poked. They are Locke’s “I know not what” (1689, II, xxiii, §2); they are Plato’s receptacles (Timaeus 48c–53c); they are “bare particulars”.1 Against substratum theory there is the bundle theory, according to which particulars are just bundles of universals. The substratum and bundle theories agree on much. They agree that both universals and particulars exist. And they agree that a particular in some sense has universals. (I use phrases like ‘particular P has universal U ’ and ‘particular P ’s universals’ neutrally as between the substratum and bundle theories.) But the bundle theory says that a particular is exhaustively composed of (i.e., is a mereological fusion of) its universals. The substratum theory, on the other hand, denies this. Take a particular, and mereologically subtract away its universals. Is anything left? According to the bundle theory, no. But according to the substratum theory, something is indeed left. Call this remaining something a thin particular. The thin particular does not contain the universals as parts; it instantiates them.

David Lewis famously argued against structural universals since they allegedly required what he called a composition “sui generis” that differed from standard mereological com¬position. In this paper it is shown that, although traditional Boolean mereology does not describe parthood and composition in its full generality, a better and more comprehensive theory is provided by the foundational theory of categories. In this category-theoretical framework a theory of structural universals can be formulated that overcomes the conceptual difficulties that Lewis and his followers regarded as unsurmountable. As a concrete example of structural universals groups are considered in some detail.

Philosophical theories of the nature of concrete particulars come in two basic kinds, those according to which a concrete particular consists of properties and a bearer of those properties (a substratum), and those according to which a concrete particular consists only of its properties, in a relation of compresence or concurrence. Substrata are theoretical entities defined by their explanatory functions. As such, there is not much disagreement about their nature: they are propertyless, unobservable constituents of concrete particulars that are the bearers of properties 1 and the individuators of distinct particulars. The situation is different with respect to properties. Among realists, some think properties are universals, either transcendent (Platonists) or immanent (Aristotelians), and some 2 think they are particulars (“tropes” ). Of the resultant possible positions on the nature of concrete particulars, six have been the focus of recent philosophical attention. These theories variously identify concrete particulars with (i) material substrata bearing transcendent universals, (ii) material substrata bearing immanent universals, (iii) material substrata bearing abstract particulars, (iv) bundles of transcendent universals, (v) bundles of immanent universals, and (vi) bundles of abstract particulars.

Universals are usually considered to be universal properties. Since tropes are particular properties, if there are only tropes, there are no universals. However, universals might be thought of not only as common properties, but also as common aspects (“determinable universals”) and common wholes (“concrete universals”). The existence of these two latter concepts of universals is fully compatible with the assumption that all properties are particular. This observation makes possible three different trope theories, which accept tropes and no universals, tropes and determinable universals and tropes and concrete universals.