A modern definition of "species" generally gives a set of objective criteria that you can use to determine if two organisms are the same species (such as "can they produce fertile offspring"). Is there any definition of race like this? Genuine question, I don't think I've ever seen a definition of race more specific than "a collection of people with similar physical characteristics" or something like that, and I can't find one now. There's lots of definitions of what all the different races are, but none of what a "race" actually is.

Is there any definition of race where, given two people, you can apply some criteria to determine whether or not they are the same race? The criteria can't be "look at the definitions of each race and categorize the two people" because that's circular, how were those particular categories chosen? With species, you can determine that a bird and a fish are different species without knowing what birds and fish are.