Online research in philosophy

The problem of universals arises when philosophy attempts to give an account of the relationship mind and objects, between language and the world. How do words succeed in being about things? In this paper I show how the problem of universals arises out of a particular theory about the relationship of words to things and that when an alternative theory is accepted the notion of universal dissipates and is replaced by the concept of meaning. Meaning, however, has its own problems. In the end I conclude that there are no universals.

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.

Two texts that raise problems for Alexander of Aphrodisias' theory of universals are examined. "De anima" 90.2-8 appears to suggest that universals are dependent on thought for their existence; this raises questions about the status both of universals and of forms. It is suggested that the passage is best interpreted as indicating that universals are dependent on thought only for their being recognised as universals. The last sentence of "Quaestio" 1.11 seems to assert that if the universal did not exist no individual would exist, thereby contradicting Alexander's position elsewhere. This seems to be a slip resulting from the fact that species with only one member are the exception rather than the rule.

Two texts that raise problems for Alexander of Aphrodisias' theory of universals are examined. "De anima" 90.2-8 appears to suggest that universals are dependent on thought for their existence; this raises questions about the status both of universals and of forms. It is suggested that the passage is best interpreted as indicating that universals are dependent on thought only for their being recognised as universals. The last sentence of "Quaestio" 1.11 seems to assert that if the universal did not exist no individual would exist, thereby contradicting Alexander's position elsewhere. This seems to be a slip resulting from the fact that species with only one member are the exception rather than the rule.

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.

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.

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.