Single Idea 9938

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

Full Idea

Benacerraf raises the question how numbers can be 'objects' if they have no properties except order in a particular ω-sequence.

Gist of Idea

How can numbers be objects if order is their only property?

Source

report of Paul Benacerraf (What Numbers Could Not Be [1965], p.301) by Hilary Putnam - Mathematics without Foundations

Book Reference

'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.301


A Reaction

Frege certainly didn't think that order was their only property (see his 'borehole' metaphor in Grundlagen). It might be better to say that they are objects which only have relational properties.

Related Ideas

Idea 8652 Numbers are objects, because they can take the definite article, and can't be plurals [Frege]

Idea 10043 Mathematical objects are as essential as physical objects are for perception [Gödel]