Full Idea
Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables.
Gist of Idea
Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables
Source
Willard Quine (Carnap and Logical Truth [1954], II)
Book Reference
Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.110
A Reaction
Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand.