Hale on Caesar. (English) Zbl 0938.01016

This paper is about the problem if the principle: The number of \(Fs\) is the same as the number of \(Gs\) just in case the \(Fs\) can be one-one correlated with the \(Gs\),
suffices as an explication of the concept of number. This problem was brought up by G. Frege in his Grundlagen der Arithmetik, and Frege explained why - in his opinion - the answer must be negative. Recently, Crispin Wright and Bob Hale expressed their disagreement with Frege. They invoke a so-called Sortal Inclusion Principle in order to defend their positive answer to the above question. The authors now explain why they find the position taken by Wright and Hale unsatisfying.


01A55 History of mathematics in the 19th century
00A30 Philosophy of mathematics
03-03 History of mathematical logic and foundations
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