 These systems allow for terms corresponding to properties, in particular variables that are meant to range over properties and that can be quantified over. This can be achieved in two ways. Either (option 1; Cocchiarella 1986a) the terms standing for properties are predicates or (option 2; Bealer 1982) such terms are subject terms that can be linked to other subject terms by a special predicate that is meant to express a predication relation (let us use “pred”) pretty much as in standard set theory a special predicate, “\(\in\)”, is used to express the membership relation. To illustrate, given the former option, an assertion such as “there is a property that both John and Mary have” can be rendered as