more on this theme     |     more from this thinker


Single Idea 10264

[filed under theme 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'

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.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).


The 4 ideas from 'Constructibility and Mathematical Existence'

We could talk of open sentences, instead of sets [Chihara, by Shapiro]
Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]