Rather than lie sleeplessly in bed, I thought I would instead share the source of my insomniac puzzlement here:
Let's say that concepts or categories (I will use the terms interchangeably) have instances, and, moreover, that the instances of a concept can be good or bad instances, that is, instances can exemplify to a greater or lesser degree the excellences that would belong to a paradigm exemplar instance of the category. (There can be instances of pencils. These instances might be more or less worthy as the sorts of writing instruments which pencils will ideally be. Some pencils are dull, or have points which break easily, or are too light; other pencils are sharp, and keep their point tolerably well, and leave an appropriately dark mark on the paper. The former sorts of pencils are good/better examples of pencils, the latter are bad/worse examples.) We can, in other words, distinguish bad from good (or better from worse) instances of a category. If you reflectively introspect, you will find that the ground of this distinction is given in nothing but the very category itself. (To judge our dull, easily-broken pencil as a bad pencil, we do not need to appeal to any idea other than the idea of a pencil itself.) It appears, then, that a category can get inside of itself for the purpose of making sub-distinctions / sub-categorizations, as between good or bad instances of itself. How is this possible?
(The problem would go away if we said, for example, that the bad instances of a category are not really instances of that category. But I don't think this move is really open to us, as convenient as it would nevertheless be; on reflection, you will not be able to shake the impression that bad pencils are still, for all that they are bad, nevertheless pencils.)