Whence Particularity?

Whence Particularity?

Imagine a world consisting only of general properties: what would it take for particulars to be added to this world? How could you convert a general world stocked with universals into a world containing particular things—things that instantiate universals? What is the metaphysical basis of particularity? Plato invited us to think of universals as primary, with particulars “participating” in them, but he neglected to explain how a world of universals could give rise to a world of particulars—what operations on universals generate particulars?

            One answer would be that particulars require a completely separate act of creation: you have to introduce particulars into the world de novo not by operations on universals; they are primitive existences. There is no explanation of the existence of particulars that starts with the existence of universals. Another answer is that we simply have to invoke set formation: a particular is just a set of universals—all those universals the particular instantiates. This is the familiar “bundle theory” of objects. On this view the move from universals to particulars is quick and easy, requiring no substantial new ontological input: we just form sets of universals (or acknowledge that they already exist without any intervention). The first view fails to register the intimate connection between particulars and universals (there are no “bare particulars”), while the second view wrongly assimilates particulars to universals, making particulars into abstract entities, as well as misconstruing the nature of instantiation (as if instantiating a property were the same thing as having it as a member). What we need is a theory that stands between these two extremes—that intelligibly derives particulars from universals, but without identifying the two.

            What kind of theory would do the trick? Consider an Aristotelian perspective that takes particulars as primary and regards universals as derivative: universals exist in virtue of the existence of particulars. Particulars bear similarity relations and that is all the existence of universals amounts to: all you need to get a world with universals is a world with particulars and a similarity relation—universals are just respects of similarity. You don’t need to invoke a separate act of creation that makes no reference to particulars—you show intelligible derivation, ontological dependence. The question is whether there is anything analogous that can be said from a Platonic perspective: can Plato provide a convincing explanation of the existence of particulars, given his metaphysics?

Let me compare the question to this question: What does it take to convert a language containing only general terms into a language containing singular terms? One answer would be: you have to add a new supply of singular terms, not drawing upon the prior resources of the language. Another answer would be: just form sets of general terms. Neither answer is plausible or necessary; rather, we can suggest the following: introduce quantifiers and a uniqueness device (primitive or defined by identity) and form definite descriptions. Thus we tap into the resources of the language by specifying operations on these resources—notably variable-binding. Indeed, this was implicit in the original language, since the general terms would contain free variables to mark argument-places—expressions just itching to be bound by quantifiers. Singularity was implicit in generality—singular terms were waiting in the wings. Yet there is a real step here, not merely agglomeration of what existed before.

            In that spirit, then, consider this proposal: particulars result from the joint operation of instantiation and bundling. First, we stipulate that a universal U is instantiated at a place x: for example, x instantiates Red. We have added space and the instantiation relation to the contents of the world we are considering, thus deriving places being U at t. That is not sufficient for particulars, however, since it might just amount to feature placing, as in “It’s cold”—the presence of a property at a location not the instantiation of a property by an object. An object never consists of a single property being exemplified at a place—that is at most property instantiation without thing-hood. What we need is bundling: several properties have to be co-exemplified—for example, Red, Cubical, and 100lbs. Then we have a particular, but not before. Thus universals give rise to particulars in two steps: first localized instantiation, second discrete bundling (these are logical not temporal steps). There was a genuine insight in the bundle theory, namely that particulars are plural with respect their properties, but it failed to recognize that instantiation is essential to being a particular; we need to combine these two operations. Notice that the operations go beyond the mere existence of universals: they are higher-order operations–properties of properties.  [1] When God was figuring out how to create a universe containing particulars he hit on a clever plan: first introduce universals in all their abstract purity, then arrange for them to be instantiated as pluralities. Nothing else needs to be done, but nothing less is required (he saw immediately that set formation wouldn’t do the trick). And actually the plan was implicit in the first ontological stage, since universals inherently contain a place for particulars to slot into—they are essentially instantiable. Plus they naturally cluster into groups: they are receptive to co-instantiation. They just need to form a pack and latch onto a location and a particular will instantly materialize. Beautiful!

            A couple of points should be noted. First, there are two sorts of bundling: automatic and adventitious. For many properties, if they are instantiated, certain other properties must also be: for example, if color properties are instantiated, then shape properties must also be. So we will automatically have a particular if a color property is instantiated.  [2] By contrast, bundling can be of properties contingently connected—for example, color and taste: this is adventitious bundling. Either kind is sufficient for bringing a particular into existence; both go beyond the instantiation of a single property. Second, there is a sense in which feature placing is more basic than object instantiation: exemplification at a place is logically prior to instantiation by an object.  [3] Particulars emerge from feature placing conjoined with bundling, so feature placing is the primary mode of instantiation: places come before objects. Thus space is the metaphysical foundation of particularity: particulars exist (partly) in virtue of the distribution of properties in space. Particulars are what happen to space when properties bundle at locations. An atom, say, is a bunch of properties instantiated at a place—we wouldn’t get a particular if the properties were instantiated at different places. A particular is the coming together of a group of properties at a particular spot.

            According to this theory (the “instantiated bundle theory”), a particular is not something beneath the properties it instantiates, but neither is it the same as the properties it instantiates. It is the logical product of instantiation at a place and agglomeration. A particular is certainly not a blank tablet awaiting properties before it acquires a nature; every particular intrinsically requires the instantiation of certain properties. Properties play a basic role in constituting particulars in virtue of two aspects of their nature: their propensity to be instantiated and their propensity to combine. If they lacked either aspect, they would be incapable of forming particulars—which is to say they would be impossible. They are hospitable toward space and gregarious among themselves—thus they contrive to create the world of particulars. Those elevated forms know how to descend and gather, producing particularity from generality.

Colin McGinn       

  [1] Instantiation is a property of a property (like existence on some views), but so is bundling: the bundling operation works on properties to produce ensembles of properties.

  [2] It is a question how many discrete properties are needed to constitute a particular—more than two presumably. From several to infinitely many seems like a safe answer.

  [3] This is the ontological analogue of the view that there is a pre-referential level of language at which features are ascribed to the world without any objects being identified (“Red here”, “It’s hot”).