«The measure» of neo-logicism: mathematical aspect

The paper analyzes G. Frege's logicism and neo-logicism of C. Wright and B. Hale. The main aims that have been attributed to Frege's logicism by different scholars are considered. A brief description of these aims is given. The paper is concerned with the mathematical rationale. According to the mathematical rationale, G. Frege believed that whatever admits to proof ought to be proved. And he thought that the propositions of arithmetic, hitherto unproved, admit of proof and should be proved. Aspects of neo-logicism, questioning the feasibility of mathematical aims of G. Frege in the framework of the program, are problematized. It is concluded about the solution of this problem in the framework of the project of neo-logicism of C. Wright and B. Hale.

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