Do Determinables Exist?

Gillett, C. and B. Rives (2005). "The Non-Existence of Determinables: Or, a World of Absolute Determinates as Default Hypothesis." Nous 39(3): 483-504.

They argue that there are no determinables, only determinates, on grounds of ontological parsimony. In their opinion, positing determinables on top of determinates leads to "double counting" of causal powers and consequent causal overdetermination (which are unacceptable).

They discuss both dispositional theories of properties (properties are the causal powers they contribute to entities) and categorical theories (properties are the categorical or qualitative bases for the causal powers they contribute to entities). They argue that their argument applies to both kinds of theory of property.

They discuss and reject Shoemaker's "subset" view, according to which determinables are properties constituted by a subset of the causal powers that constitute their determinates. They argue that even the subset view leads to double counting of causal powers. (Shoemaker's view is a version of a dispositional theory, but I imagine that an analogous subset view could be formulated within the framework of a categorical theory of properties.)

Unfortunately, I was not persuaded and remain inclined towards the subset view. (I'd like to remain neutral between categorical and dispositional theories if possible; I will discuss the dispositional version for simplicity.) If we maintain that determinables are constituted by a subset of the causal powers that constitute determinates, it seems to me that causal powers are only counted once, not twice. If you consider all relevant causal powers, you are considering a determinate. If you consider only some of them, you are considering a determinable. Determinables exist because the causal powers that constitute them exist; it's just that there are other relevant causal powers beyond them. Hence, there is neither double-counting of causal powers nor causal overdetermination.

Or am I missing something?