ABSTRACT
This chapter provides Richard Dedekind’s characterization of his project as showing that arithmetic, understood in an inclusive sense, is “part of logic”, and shows that project into the context of broader developments in 19th-century mathematics. It looks at Dedekind’s procedure, including the fact that it involves set-theoretic “constructions” and a certain kind of “abstraction”. The chapter provides a brief summary of later appropriations and developments of Dedekind’s contributions. It presents the background for the question of how Dedekind—and parallel to him, Gottlob Frege—must have understood “logic” for their logicist projects to make sense, namely in a wider sense than the one dominant in the 20th century. The chapter deals with some general observations, both about the contested status of the notion of “logic”, i.e. a lack of consensus about its nature that is often underestimated, and about its historical and philosophical relationship to modern mathematics.
