Full Idea
'Theaetetus is a member of the set of seated objects' doesn't mention the predicate 'sits', but has a new predicate 'is a member of', with no given semantic role. We are back with Plato's problem with the predicate 'instantiates'.
Gist of Idea
Treating predicates as sets drops the predicate for a new predicate 'is a member of', which is no help
Source
Donald Davidson (Truth and Predication [2005], 7)
Book Reference
Davidson,Donald: 'Truth and Predication' [Belknap Harvard 2005], p.158
A Reaction
Plato's problem is the 'third man' problem - a regress in the explanation. In other words, if we are trying to explain predication, treating predicates as sets gets us nowhere. Just as I always thought. But you have to want explanations.