Single Idea 9911

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

Questions of the identification of the referents of number words should be dismissed as misguided in just the way that a question about the referents of the parts of a ruler would be seen as misguided.

Gist of Idea

Number words no more have referents than do the parts of a ruler

Source

Paul Benacerraf (What Numbers Could Not Be [1965], IIIC)

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.292


A Reaction

What a very nice simple point. It would be very strange to insist that every single part of the continuum of a ruler should be regarded as an 'object'.