I suppose it would be difficult to justify anything post-1950 as a classic, purely because we haven't had time to integrate it into our society (awful turn of phrase, I know, but you get my point). And to clarify I definitely don't want to restrict it to the Romans and Greeks (they have their uses, but a lot of good stuff has been written after Christ too). I'll see if I can get some philosophy in a list.
One problem I've noticed with a lot of classics lists is the focus on getting the complete works of one author, as opposed to a variety. It's not a terrible idea, it might just get a bit tedious, particularly with the heavy stuff like Kant. I tell you, that's somewhere the Greeks and Romans have Renaissance-types beaten.
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