Problem is, there's only one classification that works. There's only one way of classifying organisms such that they all fit into one category, and stay there no matter which characters you use.
If you classify by, e.g., taste, then color, then number of eyes, then furriness, you get one classification scheme. Then, if you try number of eyes first, then furriness, then taste, then color, you get a different one.
If you classify by objective physical characters, you only get one classification scheme (out of astronomically huge numbers of them). That's how you know your classification criteria are objective.



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