When we talk about objects we often make a distinction between the object and the properties it has, as if the object is one thing and the properties it has are another. This way of thinking about objects and properties is captured by the formal notation Pa (the object a has the property P). This implies that objects and properties are basically independent of each other, and that objects exist as a separate kind of thing, distinct from their properties, and possibly that they could exist even without any properties at all. We can call this understanding of properties and object the central substance model.
As the picture shows in this model the object (a.k.a. a substance) is like some kind of focal point that all the properties are tied to. Certainly this is the intuitive picture that arises from the way we talk about properties and objects. After all, if there wasn’t some object at the center of things what would it mean to say that a single object had two different properties? But, despite its intuitive nature, this model doesn’t hold up to close scrutiny. Just what are these objects, considered by themselves and stripped of all their properties? Certainly they aren’t the fundamental physical constituents of nature, because those fundamental constituents are defined as much as anything else by the properties they have. And how could these objects or substances be distinguished from one another, such that properties could be had by one and not another, since without properties they are all basically the same?
Thus we may be motivated to simply drop the central substance out of the equation. After all it is doing very little work, since the only way we know objects is through their properties, and thus claim that all an object is is a collection of properties. This leaves us with the bundle of properties model.
Now the properties form a bundle, but without a central substance which they all are applied to. Although this model conforms to our epistemological situation with respect to objects and properties (how we come to know them) it leaves some important questions unanswered. Why are certain properties a bundle and not others? Why do they stay as a bundle?
One middle ground between a pure bundle of properties model and a central substance model is the essential properties model.
Under this system properties are divided into two kinds, the essential and accidental. The essential properties, in the center, define what the object is, and must be had by that object necessarily if it is to be what it is. In contrast we have the accidental properties, which are had only contingently, meaning that the object could very well not have had them and still been the same object. Obviously this view is proposed with an eye to answering a different sort of question than the ones we are after here, namely what makes an object what it is. Even so, we can see it as a kind of compromise between the two, with the essential properties somehow forming a single object which the accidental properties them adhere to, playing the same role as the indescribable substance in the central substance model. Unfortunately we are left asking all the same questions about the bundle of essential properties, namely what makes it a bundle, ect. And of course we now also have to ask which properties are essential, what makes them essential, how do we know that they are essential, and so on, leaving us possibly worse off then we would be if we simply adopted one of the other two views.
Finally then we have the connection properties model.
This way of understanding objects and properties is closest to the bundle of properties model. But instead of assuming that the bundle of properties simple is a bundle fundamentally it posits a transitive, reflexive, and symmetric relation between instances of properties (C, obviously not all connections drawn in). Again why this relation exists or holds between property instances is left as fundamental, so we may not be completely satisfied. But it does answer many of our other questions. First of all we can say why certain properties seem to go together by appealing to a relation of connection, meaning that we can define what it means for two properties to apply to the same object in terms of this connection relation. And, more importantly, we can formulate a system of physical laws that takes a collection of point locations (L) and then operates on them depending on their connected properties to generate subsequent states of affairs. So while this may not answer all of our questions about the bundle of properties model, such as why properties are bundled in the way that they are, it can be a suitable description of the real world, involving only things we can directly observe, instances of properties and the fact that collections of them go together, while leaving out that which we can’t, namely indescribable substances. And if we can model the world with it then that is all that we need, because properties and objects were never meant to explain how the world actually works, but rather to be a way to think clearly and consistently about it. And I think the central substance view does mislead us about the world, because while we can reduce talk about properties to talk about similarities (specifically in causal effect), and thus do away with them as extra entities above and beyond the physical world there is no such way to deal with the objects or substances themselves.
Finally, a quick note concerning the identity of indiscernibles. Under the first view of properties, the central substance view, indiscernibles need not be identical, because they may have different substances even if they share all of the same properties. However on the bundle of properties model, or one of its variants, indiscernible objects must be identical, since all there is to the object is its properties, and we have just ascertained that those are the same. I think that this is another point in favor of the bundle of properties model or one of its derivatives.