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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 Ref
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.
| 10232 | Property extensions outstrip objects, so shortage of objects caused the Caesar problem [Cantor, by Shapiro] |
| 10030 | 'Julius Caesar' isn't a number because numbers inherit properties of 0 and successor [Frege, by George/Velleman] |
| 8690 | From within logic, how can we tell whether an arbitrary object like Julius Caesar is a number? [Frege, by Friend] |
| 10219 | Frege said 2 is the extension of all pairs (so Julius Caesar isn't 2, because he's not an extension) [Frege, by Shapiro] |
| 13889 | Fregean numbers are numbers, and not 'Caesar', because they correlate 1-1 [Frege, by Wright,C] |
| 18142 | One-one correlations imply normal arithmetic, but don't explain our concept of a number [Frege, by Bostock] |
| 11030 | The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on Frege] |
| 9046 | Our definition will not tell us whether or not Julius Caesar is a number [Frege] |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| 13888 | If numbers are extensions, Frege must first solve the Caesar problem for extensions [Wright,C] |
| 8787 | The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright] |
| 18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
| 17997 | Some suggest that the Julius Caesar problem involves category mistakes [Magidor] |