Full Idea
It is in the spirit of bivalence not just to treat each closed sentence as true or false; as Frege stressed, each general term must be definitely true or false of each object, specificiable or not.
Gist of Idea
Bivalence applies not just to sentences, but that general terms are true or false of each object
Source
Willard Quine (What Price Bivalence? [1981], p.36)
Book Reference
Quine,Willard: 'Theories and Things' [Harvard 1981], p.36
A Reaction
But note that this is only the 'spirit' of the thing. If you had (as I do) doubts about whether predicates actually refer to genuine 'properties', you may want to stick to the whole sentence view, and not be so fine-grained.