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Full Idea
Chihara's system is a version of type theory. Translate thus: replace variables of sets of type n with level n variables over open sentences, replace membership/predication with satisfaction, and high quantifiers with constructability quantifiers.
Clarification
For 'constructibility quantifiers' see Idea 10264
Gist of Idea
Chihara's system is a variant of type theory, from which he can translate sentences
Source
report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.231
8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |