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