(Some readers may be interested in the supplementary document Qualitative Essences and a Final Defense for Plantinga).
However, the only clear examples of such belong to necessary beings like the number 2. The real question is whether contingent beings have purely qualitative essences.
A (unary) role is just a "purely qualitative" property of a certain sort, where (as described in more detail in the supplementary document on Qualitative Essences) a purely qualitative property is a property that "involves" no particular individuals.
Hence it does not follow that there are no purely qualitative essences -- perhaps the purely qualitative modal properties of x are sufficient to distinguish it from any of its de facto doppelgängers, i.e., that none of its de facto doppelgängers are modal doppelgängers.
Results strongly suggest that a human judgment is qualitative in essence, closer to a possibilistic than to a probabilistic approach of uncertainly.
Now, there surely are some purely qualitative individual essences, e.g., being smaller than every other prime number.
When we appreciate a painting, Lewis contends, what we contemplate is what this canvas could have in common with some reproduction of it, namely, "that qualitative and abstract essence which is here incorporated, and is theoretically repeatable in some other physical object" (1946, 477).
