Single Idea 18143

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

Full Idea

The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set).

Gist of Idea

Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set!

Source

David Bostock (Philosophy of Mathematics [2009], 9.A.2)

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.267


A Reaction

The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else?