Theories about properties generally come in two varieties. First we have the theories that explain properties by appeal to universals (or forms). The idea of a universal, in this context, is that of something that exists in addition to the object. All objects that have a particular property are related to a single universal in some way, and in virtue of that relationship possess the property in question. (I know that not all theories that use the term “universals” describe them in this way, but it’s the kind of theory that springs to mind for me when I consider the term, so I’m sticking with it here.) Other theories describe properties as part of the object. They claim that if we have two white books there is a property of whiteness in one and a property of whiteness in the other, and that these two properties are numerically distinct. What exactly these properties are and how they are embedded in the object varies from theory to theory naturally. (On a previous occasion I outlined a theory about properties of the second sort, which defined them as patterns of (causal) effects that the object was responsible for.)
Both approaches have their strengths and weaknesses. Let’s begin with the universals approach. The strength of the universals approach is that it can easily explain how two objects have the same properties, and thus how they are similar to each other, by pointing to the fact that they are related to one and the same universal. Why are these two white books similar? Because they participate in the same form of whiteness – end of story. The problem with this approach is, first, that it is metaphysically loaded, and, secondly, that it leaves a good deal unexplained when it comes to the relationship between objects and universals. The theory is metaphysically loaded because it introduces new objects: universals and their relations, which are distinct from the existing objects, and which some new place must be found for. I’ll ignore that problem here, at least for the moment. The second set of issues, those stemming from the relationship between universals and objects, often comes from integrating this theory with other theories, such as those about change or essential properties. Under this approach every property of the object is pulled off of it, and becomes a relationship and a universal. This creates problems because it means that we are left with an object that is bare – an object that has no properties of its own. If every object is bare it would seem that they are indistinguishable from one another. So what makes one object related to a particular universal while its identical twin is related to a different universal? Or, in other words, why is an object related to the universals that it is? It’s hard to connect a theory that appeals to universals with other philosophical positions without raising these issues. For example, if you were a substance dualist, and you appealed to universals, you would have to answer the question: why can’t one and the same object be related to both mental and physical universals?
Taking the position that properties are in the objects themselves turns the weakness of the universals position into strengths, but unfortunately also turns its strengths into weaknesses. If properties are explained as being part of objects then the question of why an object has them essentially disappears. You wouldn’t, for example, be stumped by the question “why is page 5 part of this book?”, you could appeal to the book’s history whereby various parts became stuck together. Similarly, you can tell a story about properties where various properties become bound up and dislodged from each other (making an object a properties bundle in essentially the same way a book is a pages bundle). This makes talking about change, for example, extremely easy. And it also resolves the problems that arise from treating objects as additional bare particulars. However, solving these problems comes at a cost. Now it is difficult to describe how two objects can be similar or have the same properties. Consider our two white books. Under this theory they both have a whiteness part. But what makes those whiteness parts the same property of whiteness? Nothing, it would seem. The fact that we talk about them as both being whiteness parts does not mean that there is any grounding in the theory for doing so. Now it is not impossible to tack on a solution to this problem. We could, for example, say that these property-parts are both related to the same universal of whiteness (raising for property-parts the same problems that solution raised for objects). But, unfortunately, these solutions tend to be extremely complicated and metaphysically loaded.
Either way we go, then, there are problems. Of course these problems have solutions – many solutions in fact. Many have attempted to tack on more complicated frameworks to these initially simply solutions in an attempt to bury the problems mentioned above. These solutions are not successful. Some simply raise new problems as they deal with the existing ones. Others become so baroque and metaphysically loaded that they defeat the point of having a metaphysical theory about properties and objects in the first place. And, to refresh your memory, the point of such a theory is to be a useful tool for thought; to a guide that allows us to deal with properties and object in other contexts cleanly and smoothly, allowing us to focus on the issues at hand rather than problems arising from wrestling with properties and objects. A theory that is too complicated defeats that purpose. It is not a convenient tool for thought; it becomes a system that uses us rather than allowing us to use it. By being metaphysically loaded it has the tendency to decide issues for us, rather than allowing us to decide them. And by being baroque it means that to invoke the system is to spend as more time working with it than with the issues we invoked it to assist us with. Thus such solutions fail us as philosophy, even if they have consistent answers to all the questions we might pose to them.
Let’s consider a third approach. We’ll start with the same basic idea as the properties-as-parts approach: each object is a collection of properties, each of which is a part of the object, and which collectively are the object. This leaves us with the problem of explaining how objects can be said to share the same properties. Here is where we can take a different path: let’s simply bite the bullet and assert that they simply share the same properties. That’s right, whiteness is a part of a book, and if we have two white books whiteness is a part of both of them, and, perhaps counter-intuitively, the same whiteness part is in both. I say this is counter-intuitive because if we have two white books it seems quite clear that they don’t overlap, and that each is independent of the other. But this intuitive sense in which they don’t overlap is only a spatiotemporal one. Instead of thinking of objects as sitting in space-time think of them as sitting in property space. For the sake of simplicity think of property space as a big sheet of paper, on which are written the names of different properties. (And if you want to be fancy you can think of these properties as organized such that the property of being a cat is a large region, inside of which are the smaller regions that correspond to being a particular species of cat.) And think of an object as a loose loop of string. The string lies on top of property space, and all the properties that fall within that loop are properties the object has. Our two white books are two such loops of string. Now, for the most part, these loops don’t overlap; they don’t surround the same spatial location, for example. However, when it comes to the property of being white they do; they both include the same region of property-space. And in that way they share the same part. Of course just because they share the same part in this sense doesn’t mean that one white book can influence another in some spooky way. An object under this view is a division in property-space. The object, the division, is mutable, but property-space is not. So even though they share a part in common, whiteness, whiteness itself is immutable (although whether an object is white is mutable), and thus they cannot be influenced by their part in common.
I won’t pretend that the above is beyond our ability to pose problems for it. For example, this view can pose difficulties when trying to explain how all properties ultimately reduce to physical properties. At the very least this introduces complexities such as a mapping between physical space and property-space and the necessity of dealing with a structure of property space such that not all divisions of it are admissible as objects. (Clearly such a structure is necessary, otherwise you could have an object that had the property of being a white-book without having the property of being white.) Another problem that has to go unaddressed is that of how the world is divided into objects. This is the problem of saying why the four pennies on the table form a group with the property of four-ness and why they aren’t considered to be part of a larger group that contains the penny in my pocket as well (manifesting five-ness), the one stuck under the table (manifesting six-ness), and so on. Obviously any solution to that has consequences for which properties there are and which objects have them. But since the best solution is generally to admit that how the world is divided into object is conventional this makes all of the schemes discussed here for explaining properties and objects unworkable (since they must all be relativized to the mind in some way while at the same time explaining how it is an objective fact that this book is white; not an easy task).
But the purpose of a philosophical theory (or perspective, as I like to call them) is not to answer every question that can be raised; it is to be a useful intellectual tool. In this specific case the point of the tool is to cleanly handle properties and objects whenever they arise. I submit that the position described here is genuinely useful in this capacity since issues of reduction and the relativity of objects don’t come up that often (outside of contexts that are heavily philosophical) and that it is more useful than the first two approaches described because it is roughly as simple as they are and works in all the situations they do, as well as some in which they don’t (such as when they lead to questions about why an object has the properties it does or in what way two objects have the same properties).