Single Idea 10219

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

Full Idea

Frege proposed that the number 2 is a certain extension, the collection of all pairs. Thus, 2 is not Julius Caesar because, presumably, persons are not extensions.

Gist of Idea

Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension)

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Stewart Shapiro - Philosophy of Mathematics 3.2

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.78


A Reaction

Unfortunately, as Shapiro notes, Frege's account of extension went horribly wrong. Nevertheless, this seems to show why the Julius Caesar problem does not matter for Frege, though it might matter for the neo-logicists.