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### 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem

#### [explain why Julius Caesar can't be a number]

13 ideas
 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]
 11030 The words 'There are exactly Julius Caesar moons of Mars' are gibberish [Rumfitt on Frege]
 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]
 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]