Single Idea 18151

[catalogued under 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory]

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]