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Single Idea 7731

[from 'Grundlagen der Arithmetik (Foundations)' by Gottlob Frege, in 6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism ]

Full Idea

If the number one is a property of external things, how can one pair of boots be the same as two boots? ...but if the number one is subjective, then the number a thing has for me need not be the same number the object has for you.

Gist of Idea

How can numbers be external (one pair of boots is two boots), or subjective (and so relative)?

Source

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

Book Reference

Weiner,Joan: 'Frege' [OUP 1999], p.54


A Reaction

This nicely captures the initial dilemma over the nature of numbers. It is the commonest dilemma in all of philosophy, struggling between subjective and objective accounts of things. Hence Putnam's nice definition of philosophy (Idea 2352).

Related Idea

Idea 2352 The job of the philosopher is to distinguish facts about the world from conventions [Putnam]