 Like for Frege, the other main logicist in the nineteenth century, “logic” is  more encompassing for Dedekind than often assumed today (as comprising only first-order logic). Both thinkers take the notions of object, set, and function to be fundamental for human thought and, as such, to fall within the range of logic. Each of them then develops a version of set theory (a theory of “systems”, “extensions”, or “classes”)  seen as part of logic. Also for both, logic in this encompassing sense is independent of intuitive considerations and, specifically, of traditional Euclidean geometry (understood to be  grounded in pure or empirical intuition). A main goal in reducing analysis and arithmetic to logic is, thus, to establish that those fields too are independent of intuition (cf. Demopoulos &amp;  Clark 2005).