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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 Ref
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]