[empath75]

That problem applies with any arbitrary category. If you look at any color, you're going to describe it as whatever color category its closest to. If it's more red than yellow, you might call it orange, I might call it red, someone else might call it orange-red, or I dunno 'pumpkin'. Language is imprecise.

[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'.