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Abstract

In Die Grundlagen, Frege takes the Julius Caesar problem to eliminate HP – the number of Fs is the same as the number of Gs if, and only if, the Fs and Gs are in one-one correspondence – as an explanation of the notion of cardinal number and, therefore, as the most fundamental principle of arithmetic. But similar problems arise with respect to the infamous Basic Law V. The present paper investigates Frege's many discussions of the Caesar problem, to which he returns at several points throughout his career. I suggest that the crucial difference between HP and Basic Law V is, in the end, dialectical, not substantive.