 But, of course, many philosophers have wanted more than these essentially psychological gains. They have hoped that analytic claims might provide a basis for a priori knowledge of domains that exist independently of us and are not exhausted by our concepts. An important case in point would seem to be the very case of arithmetic that motivated much of the discussion of the analytic in the first place. Recent work of Crispin Wright (1983) and others on the logicist program has shown how a version of Frege’s program might be rescued by appealing not to his problematic Basic Law V, but instead merely to what is called “Hume’s Principle,” or the claim that for the number of Fs to be equal to the number of Gs is for there to be a “one-to-one correspondence” between the Fs and the Gs (as in the case of the fingers of a normal right and left hand), even in infinite cases. According to what is now regarded as “Frege’s Theorem,” the Peano axioms for arithmetic can be derived from this principle in standard second-order logic (see Frege’s theorem and foundations for arithmetic).