Dude, read your own words: if you offer a 4-way distinction, you cannot publicly use the word “binary”
and not get hassled. There are 5 traditional race categories, which states facts about humans (generally). The recognition of “mixed race” does correctly encode the fact that this is a continuum with certain major clusters and marginal cases.
Theyre binary categories in the sense that either youre in one, or youre not (ie membership is all or nothing). ‘Mixed race’ is a misleading term since it implies that everyone who isnt mixed race is ‘fully’ Caucasion/Negroid/whatever.
Do pick an example that’s better than color: neither race nor (visual) color are arbitrary. These are wholly valid recognitions of fact.
It depends what you mean by ‘recognition of fact’. The way in which we have broken up the racial and colour spectrums isnt based on any ‘fact’ that could make our way right and someone else’s wrong - its just the way that we have come to do things. Its true that people with white skin look different from people with black skin, but this alone doesnt justify our racial categories; short people with black hair look different from tall people with blonde hair, yet we dont class them as being members of a different race. Our notion of race is primarilly (historically) based on skin colour, but theres no objective reason to prefer a categorisation based on skin colour over one based on eye colour or height.
Just because the neo-Dadaist postemodernological deconstructionarians shrilly decry the arbitrariness of race does not make it an arbitrary classification.
If its not arbitrary, then give a rational reason why Negroid has more objective validity as a racial category than Irish redhead.
All of our categories? What is “fuzzy” about the category, “male”?
Sorry, exaggeration. I should have said ‘most’. Anyway, ‘male’ is probably a fuzzy category; see androgeny, hermaphrodites, Klinefelter’s syndrome etc. We could choose to class these people as being ‘male’, ‘female’, or belonging to some third category - theres nothing forcing us to go one way or the other. I dont think theres any rigid biological definition of ‘male’ in the “necessary and sufficient” sense.
Outside of pure biology, it makes sense to say that one person is more masculine than another, even if we would call them both male. We also talk about manly women. This all seems to imply that our ordinary language category of ‘male’ is fuzzy.
Stated more generally, is it your position that the referents of all concepts are selected arbitrarily?
No, of course not. The way we divide up the race and colour spectrums are fairly arbitrary however - our classifications have arisen for historical reasons rather than through rational reflection. If another culture classified races in a different way from us, we couldnt say they are wrong for the same reason we couldnt say a culture which grouped blue and green together was wrong - theres no underlying fact of the matter here. This obviously doesnt extend to most of our concepts though.