There are no distributable properties?

Prima facie, there are distributional properties, distributable properties, and they are distinct. It is one thing, Josh Parsons (2004) suggests, to have a redness distribution (say, to be red in such-and-such places but not in others) and another to be just plain red. What I’m interesting in is the claim that there are no distributable properties; there are just distributional properties. Is this a coherent proposal?

One might object as follows. Suppose that D is a distributional property. Intuitively, the instantiation of D involves a distribution of instances of some distributable property D*. On the current proposal, there simply is no property like D*, so the instantiation of D cannot literally involve a distribution of D*-instances. But then how are we to understand what it is for D to be instantiated in the first place? Just as distributors need material to distribute, distributional properties need distributable properties distribute.

I think the thing to say in response to this concern is that it mistakenly, though understandably, assumes that the sense in which distributional properties are ‘distributional’ lines up closely with the everyday sense of the term. Instead, we should think of ‘distributional property’ more as a technical term.

I do not mean to suggest, however, that the notion of distributional property we are working with here is obscure. Suppose that Frank, pointing to Gary who is grimacing and then to Albert who is smiling, says, “There is pain to the left and pleasure to the right.” One might claim in this case that a proper part of the world consisting of Frank, Gary, and Albert involves a distribution of distributable properties including being in pain and having pleasure. Let us call this way of understanding distributional properties the ordinary conception of distributional properties.

One might claim instead that the proper part of the world mentioned above instantiates the distributional property being in pain-to-the-left-and-pleasure-to-the-right. Here the idea is that the truth-maker for Frank’s claim is that the Frank-Gary-Albert fusion instantiates the single aforementioned property. In this case the fusion does not instantiate being in pain and having pleasure qua distributable properties because there are no such properties. To contrast this conception of distributional properties with the ordinary one, call it the minimalist conception (given its commitment to distributional properties but not distributable properties).

Both the ordinary conception and the minimalist conception, as far as I can tell, are coherent, so it seems to me that so far we have not been given a good reason to think that the claim that there are distributional properties but no distributable properties is incoherent. What do you all think?

-Kelly