Ultimately every property is some kind of causal disposition. It is not my purpose to establish that claim here, but claiming otherwise, claiming that there could be two different properties associated with the same causal disposition (or a property associated with no causal dispositions), is absurd. If that were the case how could we know that there were in fact two different properties associated with this single causal disposition? But given that properties are associated with particular causal dispositions we want to know how to identify two properties. This is not, of course, an attempt to determine when two properties always (necessarily) coincide. To do that is easy, we simply look at the causal disposition that defines the two properties, and if it is exactly the same disposition then they are identical. That is not a particularly interesting question, nor is it particularly informative. What is interesting is the cases in which we have two properties, defined as different causal dispositions, which are in some situations identical (or so I would claim).
Here I will lean on color to explain my ideas, since color is a well-understood phenomenon (physically if not psychologically). For the sake of simplicity let us understand being a particular color just as the property of reflecting a particular wavelength of light. And let us also consider the property of being coated in a particular type of paint. The question to ask then is whether an object’s property of being coated in a particular type of paint is identical to its property of being a particular color, despite the fact that being coated in a particular type of paint and being a particular color do not always coincide. At work here is the idea that even though we speak of a property as a general kind of thing most properties do not exist independently. Instead they exist in virtue of a number of microscopic properties of the object, leading us to say that in particular cases that macroscopic property (or at least particular instances of it) is identical to that set of microscopic properties. And different arrangements of microscopic properties may result in the same macroscopic property. Thus we can think of our interaction with macroscopic properties as interactions with particular instances of them, particular arrangements of microscopic properties that give rise to them. (Of course microscopic properties themselves hold in virtue of simpler and simpler properties, until we come to the most fundamental properties, such as “being an electron at a particular location”, which we don’t have enough information to say more about.) Thus while two macroscopic properties may, in general, be different, it is perfectly possible for them to exist in virtue of the same microscopic properties, and hence be identical, in the sense that the particular instances of those macroscopic properties present are identical.
In our example the property of being a particular color holds in virtue of a number of microscopic properties about the shape and density of electrons on the surface of the object. Similarly the property of being coated in a particular paint holds in virtue of microscopic properties involving the placement of various atoms, which involves microscopic properties about the shape and density of electrons on the surface of the object. Thus in our example the property of being a particular color is identical to the property of being coated with a certain type of paint, at least in the case of specific objects (although we may identify them in specific cases in general we would still define them differently).
Now let’s consider an objection to this position, specifically an objection that a “property dualist” about color might make. The property dualist about color is convinced that the property of being a particular color and the property of being coated in a particular type of paint just can’t be identical. Since they aren’t associated with the same causal disposition in general the property dualist about color insists that we can know a priori that they are different properties (they can imagine the object being red without being coated in that particular shade of paint they might say). Of course the property dualist about color is of course confused about the claims we are making, we are claiming that the properties are identical in specific instances because they hold because of the same microscopic facts, which means that whether they could possibly come apart in other situations is irrelevant. That is not the objection the property dualist about color might make; I am just trying to outline a kind of competing position. Now, given this position, they might claim that we have left unexplained the connection between being a particular color and being coated with a particular kind of paint, because certainly we haven’t posited any laws connecting them, nor a causal relationship between the two. But by raising this objection the property dualist about color is assuming what they must prove, namely that they always are different properties. If they were different properties then of course we would need to explain why they occur in conjunction with each other. But the assertion that they are identical in these cases is a complete explanation by itself, assuming that we know what makes a particular set of microscopic properties count as the property of being coated with a particular type of paint, and what makes such a set count as having a particular color (knowing those facts also gives us the epistemic justification to posit an identity in specific cases). Given that making the assertion that a single set of microscopic facts fulfills both roles explains the connection without the need to introduce anything more explaining the connection, which we would have to do if they failed to be identical.