 It is clear that Dedekind is writing on the presumption—assumed to be so widespread as not to call for any justificatory argument—that one should have no recourse at all to geometric intuitions or first principles when founding the theory of the real numbers. This presumption, said Dedekind, ‘no one will deny’. Dedekind wanted “a purely arithmetical and perfectly rigorous foundation for the principles of infinitesimal analysis” [Emphases  added].[8] 