Full Idea
Chihara proposes to replace all sets by reference to the open sentences that define them.
Clarification
'Open sentences' have variables in them
Gist of Idea
Could we replace sets by the open sentences that define them?
Source
report of Charles Chihara (Ontology and the Vicious Circle Principle [1973]) by David Bostock - Philosophy of Mathematics 9.B.4
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.283
A Reaction
This depends on predicativism, because that stipulates the definitions will be available (cos if it ain't definable it ain't there). Chihara went on to define the open sentences in terms of the possibility of uttering them. Cf. propositional functions.
Related Idea
Idea 18136 If we can only think of what we can describe, predicativism may be implied [Bostock]