The Logic in Dedekind’s Logicism

Any history of logic from Kant to the 20th century needs to take into account the emergence of logicism, since it is largely in this context that logic as we know it became prominent. Usually Gottlob Frege and Bertrand Russell are seen as its two main representatives, especially early on, and the more recent rise of neo-logicism, in writings by Crispin Wright, Bob Hale and others, proceeds along Fregean lines as well. In this chapter, I will focus on Richard Dedekind instead. Today Dedekind is sometimes mentioned in connection with logicism; yet at the end of the 19th century, he was the most prominent logicist, ahead of Frege. This alone invites further reflection. Reconsidering Dedekind also leads naturally to questions about what was, or could be, understood by “logic” in this context. Addressing them will involve developments in 19thcentury mathematics that are relevant in two respects: by forming core parts of the background for the emergence of modern logic; and by pointing towards a distinction between two conceptions of logic that deserve more attention, both historically and philosophically.