more from George Cantor

### Single Idea 10232

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

Full Idea

Cantor's theorem entails that there are more property extensions than objects. So there are not enough objects in any domain to serve as extensions for that domain. So Frege's view that numbers are objects led to the Caesar problem.

Clarification

How do we know that Julius Caesar is not a number?

Gist of Idea

Property extensions outstrip objects, so shortage of objects caused the Caesar problem

Source

report of George Cantor (works [1880]) by Stewart Shapiro - Philosophy of Mathematics 4.6

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.127

A Reaction

So the possibility that Caesar might have to be a number arises because otherwise we are threatening to run out of numbers? Is that really the problem?