Full Idea
The 'Julius Caesar problem' in Frege's theory is that from within logic we cannot tell if an arbitrary objects such as Julius Caesar is a number or not. Logic itself cannot tell us enough to distinguish numbers from other sorts of objects.
Gist of Idea
From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number?
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michèle Friend - Introducing the Philosophy of Mathematics 3.4
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.66
A Reaction
What a delightful problem (raised by Frege himself). A theory can look beautiful till you ask a question like this. Only a logician would, I suspect, get into this mess. Numbers can be used to count or order things! "I've got Caesar pencils"?