2002 年 35 巻 1 号 p. 15-26
This paper deals with C. Wright's strategies to establish Frege's logicism. They essentially depend on Frege's Theorem (FT), i.e. the derivability of Peano-Dedekind axioms from the second-order logic plus Hume's principle (HP). HP says that the number of the concept F is identical with that of G if and only if F is equinumerous with G. By regarding HP as the explanatory principle of the number of a concept, Wright seems to assert that FT has already shown that Frege's logicism has been completely established. On the contrary, Frege regarded HP as unsatisfactory for establishing the foundations of arithmetic. It is powerless to decide whether the number of the concept "not identical with itself" is the same as Julius Caesar. This problem is called Julius Caesar problem (JC). Thus if Wright were right, historical Frege would have been rashly convinced that HP alone would not resolve JC, so that there had been no problem such as JC. I think, however, that JC is a genuine trouble to Frege's logicism and then Wright's strategies do not establish it.