I think this is just a special case of the “problem of universals” which mediaeval philosophers endlessly debated, and which goes back to Plato and Aristotle in

I think this is just a special case of the “problem of universals” which mediaeval philosophers endlessly debated, and which goes back to Plato and Aristotle in ancient Greece. However you choose to answer that more fundamental question is largely going to dictate how you answer this one.