On Properties of Sets of Properties

If I understood it right, part of the core of Zalta's LOGOS Colloquium today was the thesis that his abstract objects were not mere sets of properties. I wasn't completely clear about exactly his reasons for this, but he mentioned the contention that sets can not exemplify any of its members. Apologies in advance if I am missing something basic, but is this really so? Take P to be the property of being a set mentioned at The bLOGOS and consider its singleton. Isn't it both the case that P is a member of {P} and that {P} exemplifies P? No?