Single Idea 8467

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

Full Idea

Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit

Gist of Idea

Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit'

Source

report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3

Book Reference

Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.57


A Reaction

(See Idea 8454 for the categories of numbers). This is a problem for Dummett.

Related Idea

Idea 8454 The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]