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Single Idea 13889

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem ]

Full Idea

We cannot reasonably suppose that any numerical singular term has the same reference as 'Caesar', because Frege's numbers (unlike persons) are to be identified and distinguished by appeal to facts about 1-1 correlation among concepts.

Gist of Idea

Fregean numbers are numbers, and not 'Caesar', because they correlate 1-1

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv

Book Ref

Wright,Crispin: 'Frege's Conception of Numbers' [Scots Philosophical Monographs 1983], p.114

The 13 ideas with the same theme [explain why Julius Caesar can't be a number]:

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]