Single Idea 8636

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One]

Full Idea

We combine 'Solon was wise' and 'Thales was wise' into 'Solon and Thales were wise', but we can't say 'Solon and Thales were one', which implies that 'one' is not a property in the same way 'wise' is.

Gist of Idea

We can say 'a and b are F' if F is 'wise', but not if it is 'one'

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §29)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.40


A Reaction

Maybe 'one' is still a property, but of a different sort. However, Frege builds up a very persuasive case that just because numbers function as adjectives it does not follow that they are properties. See Idea 8637.

Related Idea

Idea 8637 The number 'one' can't be a property, if any object can be viewed as one or not one [Frege]