Contemporary debates over categorical properties – mention of such properties, even – very often involves people talking past one another.
This did not used to be the case. It used to be that everyone knew what a categorical property was supposed to be. As it happens, they also used to know at least enough about what a dispositional property is supposed to be to know that they denied that such properties exist — which is to say that they denied that the world includes things (“things” as loosely construed as you like) that are inherently active in different kinds of ways. (And everyone understood what it meant to deny that.)
But time marches on.
Nowadays, there are multiple definitions of “categorical property” in play, and it is worth being sure about which one any given interlocutor is using. Here is a short list:
(1) a categorical property is one the having of which does not pertain to what its bearer can or can potentially do;
(2) a categorical property is a property that cannot itself do anything;
(3) a categorical property is a property the identity of which is not the same in all possible worlds, &/or is not essential to that property;
(4) a categorical property is a property that has no identity other than that of formal self-identity.
These definitions get mixed and matched and deployed in all manner of unfortunate discussion. Thinker A rejects pandispositionalism on the basis of (1). Thinker B endorses it on the basis of (4). Etc. (It should be easy to see, too, how confusion at this level winds up figuring in what has come to be called the debate over so-called “pure powers.”)
I expect to post more on this topic – and please, please feel free to weigh in – but for now let me just say that the categorical properties that everyone used to believe in when they didn’t believe in powers — those were categorical properties as per (1). That this is so, or was so, only makes sense, given that passivists deny that things have real powers to do, and passivism was then an unquestioned orthodoxy in the relevant circles. (No. It is not permissible to re-define “do” here. Not unless you are a sophist. :-) )