Full Idea
Classical logic (of Whitehead, Russell, Gödel, Church) is a two-valued system of propositional and predicate logic, in which all propositions are exclusively true or false, and quantification and predication are over existent objects only.
Gist of Idea
Classical logic is bivalent, has excluded middle, and only quantifies over existent objects
Source
Dale Jacquette (Intro to I: Classical Logic [2002], p.9)
Book Reference
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.9
A Reaction
All of these get challenged at some point, though the existence requirement is the one I find dubious.