Single Idea 8652

[catalogued under 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism]

Full Idea

Individual numbers are objects, as is indicated by the use of the definite article in expressions like 'the number two', and by the impossibility of speaking of ones, twos, etc. in the plural.

Gist of Idea

Numbers are objects, because they can take the definite article, and can't be plurals

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §68 n)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.80


A Reaction

Hm. The beginnings of linguistic philosophy, with all its problems. It is well known that 'for the sake of the children' doesn't make an ontological commitment to 'sakes'. The children might 'enter in threes', but the second half is a good point.