 One of Hempel’s early influential articles was a defense of logicism, according to which mathematics—with the notable exception of geometry, which he addressed separately—can be reduced to logic (for Hempel, including set theory) as its foundation (Hempel 1945c). Mathematics thus becomes an exemplar of analytic a priori knowledge. Two subtheses should be distinguished: (i) that all mathematical concepts can be defined by means of basic logical concepts; and (ii) that all mathematical theorems can be deduced from basic logical truths. In order to distinguish logicism from formalism, however, the former maintains that there is one system of logic that is fundamental to all inquiries, where all mathematical terms are reducible to logical terms, and all mathematical axioms are derivable from logical ones, which formalism denies (Rech 2004).