Single Idea 8203

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory]

Full Idea

The arithmetic of ratios and irrational and imaginary numbers can all be reduced by definition to the theory of classes of positive integers, and this can in turn be reduced to pure set theory.

Gist of Idea

All the arithmetical entities can be reduced to classes of integers, and hence to sets

Source

Willard Quine (Vagaries of Definition [1972], p.53)

Book Reference

Quine,Willard: 'Ways of Paradox and other essays' [Harvard 1976], p.53


A Reaction

This summarises Quine's ontology of mathematics, which tries to eliminate virtually everything, but has to affirm the existence of sets. Can you count sets and their members, if the sets are used to define the numbers?