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roystgnr comments on Concepts Don't Work That Way - Less Wrong
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I think this is a little unfair. For example, I know exactly what the category 'fish' contains. It contains eels and it contains flounders, without question. If someone gives me a new creature, there are things that I can do to ascertain whether it is a fish. The only question is how quickly I could do this.
We pattern-match on 'has fins', 'moves via tail', etc. because we can do that fast, and because animals with those traits are likely to share other traits like 'is billaterally symetrical' (and perhaps 'disease is more likely to be communicable from similarly shaped creatures'). But that doesn't mean the hard-and-fast 'fish' category is meaningless; there is a reason dolphins aren't fish.
I'm guessing you'd quickly say "yes" for Panderichthys and "no" for Acanthostega... but what about Tiktaalik? Or if that's too easy to answer (which answer?), pick any clear amphibian and start looking at its ancestors. Is there a clear line where "this is not a fish, but its mother is"?
We think of ring species as rare populations with interesting spatial distributions, but thanks to common descent every living thing is part of one big multi-ring species with a very interesting space-time distribution. It's hard to categorize living things, in part because the obvious ideas for equivalence relations turned out to not be inherently transitive.