Full Idea
In studying second-order logic one can think of relations and functions as extensional or intensional, or one can leave it open. Little turns on this here, and so words like 'property', 'class', and 'set' are used interchangeably.
Gist of Idea
Logicians use 'property' and 'set' interchangeably, with little hanging on it
Source
Stewart Shapiro (Higher-Order Logic [2001], 2.2.1)
Book Reference
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.36
A Reaction
Important. Students of the metaphysics of properties, who arrive with limited experience of logic, are bewildered by this attitude. Note that the metaphysics is left wide open, so never let logicians hijack the metaphysical problem of properties.