著者

井上 直昭

出版者

日本科学哲学会

雑誌

科学哲学 (ISSN:02893428)

巻号頁・発行日

vol.36, no.1, pp.17-28, 2003-07-25 (Released:2009-05-29)

参考文献数

16

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This paper deals with Frege's stipulation in his Grundgesetze der Arithmetik I section 10, in which he gives way out of Julius Caesar Problem. There it seems as if he restricted the problem to the case of the truth values, so some consider Frege not wrestling with it squarely in Grundgesetze. But in the second footnote of the section he says clearly that it is possible to adopt his stipulation to the cases of any objects given us independently of the course of values. I will show that his account is correct and it is able to find out a consistency model in which both the stipulation and Quine's axiom of the existence of non-class objects presented in Mathematical Logic hold. With this result I suppose that we are able to take a good understanding for interpretation of that footnote.

著者

井上 直昭

出版者

日本科学哲学会

雑誌

科学哲学 (ISSN:02893428)

巻号頁・発行日

vol.35, no.1, pp.15-26, 2002-05-25 (Released:2009-05-29)

参考文献数

24

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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.

著者

井上 直昭

出版者

日本科学哲学会

雑誌

科学哲学 (ISSN:02893428)

巻号頁・発行日

vol.34, no.1, pp.49-60, 2001-05-30 (Released:2009-05-29)

参考文献数

7

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This paper deals with the so-called Julius Caesar Problem. Crispin Wright has recently shown that it is possible to derive the axioms of second-order arithmetic from a principle which is called Hume's Principle (HP). Depending upon this result, Wright resurrected a version of Fregean logicistic project. But historical Frege suspected HP as not a fundamental law of arithmetic in the face of Caesar Problem in his Die Grundlagen der Arithmetik section 66. He supposed, I think, that this problem was to be solved through axiom V, the basic law in his Grundgesetze der Arithmetik. But this strategy failed because of the inconsistency of axiom V. And this failure must be seen from a point of view of semantic ill-foundedness, which in general would be included in Fregean abstract principle. This difficulty is an important reason for Russell's Paradox, thus makes it impossible to give any answer to Julius Caesar Problem.