Single Idea 10030

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem]

Full Idea

'Julius Caesar' is not a natural number in Frege's account because he does not fall under every concept under which 0 falls and which is hereditary with respect to successor.

Gist of Idea

'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.35


A Reaction

Significant for structuralist views. One might say that any object can occupy the structural place of '17', but if you derive your numbers from 0, successor and induction, then the 17-object must also inherit the properties of zero and successors.