[n0us]

Is it categories themselves that are arbitrary or the set of items belonging to a category are arbitrary? Do you mean that the meaning of a statement is imprecise in that it is vague or ambiguous? Or do you mean that the way that humans employ language to convey concepts is imprecise?

You are thinking like a psychologist or a linguist. I'm not denying that many people view this is a tedious and seemingly silly thing to argue about but you can't metaphorically just throw up you hands and claim that it doesn't matter as a valid counter argument when you are doing philosophy.

[mannykannot]

You make philosophy sound like a form of OCD, obsessing about putting everything in its place.

The answer to your questions is 'all of the above, to some degree'.