The paper scrutinizes Frege’s Euclideanism—his view of arithmetic and geometry as resting on a small number of self-evident axioms from which nonself-evident theorems can be proved. Frege’s notions of self-evidence and axiom are discussed in some detail. Elements in Frege’s position that are in apparent tension with his Euclideanism are considered—his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that… Expand