more from Charles Chihara

Single Idea 10264

[catalogued under 6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism]

Full Idea

Chihara has proposal a modal primitive, a 'constructability quantifier'. Syntactically it behaves like an ordinary quantifier: Φ is a formula, and x a variable. Then (Cx)Φ is a formula, read as 'it is possible to construct an x such that Φ'.

Gist of Idea

Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ'


report of Charles Chihara (Constructibility and Mathematical Existence [1990]) by Stewart Shapiro - Philosophy of Mathematics 7.4

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.230

A Reaction

We only think natural numbers are infinite because we see no barrier to continuing to count, i.e. to construct new numbers. We accept reals when we know how to construct them. Etc. Sounds promising to me (though not to Shapiro).