Single Idea 7737

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

Full Idea

Identity statements are about objects. If we can say that 1 is identical (or not) to 0, then 1 must be an object.

Gist of Idea

Identities refer to objects, so numbers must be objects

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Joan Weiner - Frege Ch.4

Book Reference

Weiner,Joan: 'Frege' [OUP 1999], p.59


A Reaction

This seems to point to Platonism about numbers, but maybe we can accept it as being about physical objects. If numbers are essentially patterns, then identity is hypothetical one-to-one identity between sets of objects.