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?