Single Idea 18103

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

One can always say 'the number of Jupiter's moons is 4', which is explicitly a statement of identity, and for Frege identity is always to be construed as a relation between objects. This is really all he gives to argue that numbers are objects.

Gist of Idea

Numbers are objects because they partake in identity statements

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 55-57) by David Bostock - Philosophy of Mathematics

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.118


A Reaction

I struggle to understand why numbers turn out to be objects for Frege, given that they are defined in terms of sets of equinumerous sets. Is the number not a property of that meta-set. Bostock confirms my uncertainty. Paraphrase as solution?