Our every assertion or thought involves "properties" or relations. Most simply, we predicate some property of some thing: Earth is round. Sometimes we refer to properties by name or by description: Red is the color of blood. Sometimes our quantifiers range over properties: Galaxies come in many shapes and sizes.

This familiarity with properties, however, does not reveal what properties are. Indeed, the question is equivocal, both in ordinary and in philosophical discourse. There are different conceptions of properties, equally legitimate, corresponding to the different roles that properties have been called upon to play (Bealer 1982; Lewis 1983, 1986). And for each conception there are different theories as to what sort of entity, if any, is best suited to play the role. The most fundamental division is between abundant and sparse conceptions of properties. On an abundant conception every meaningful predicate expresses some property or relation, including "is blue or round...