 The later Wittgenstein, however, wishes to ‘warn’ us that our thinking is saturated with the idea of “[a]rithmetic as the natural history (mineralogy) of numbers” (RFM IV, §11). When, for instance, Wittgenstein discusses the claim that fractions cannot be ordered by magnitude, he says that this sounds ‘remarkable’ in a way that a mundane proposition of the differential calculus does not, for the latter proposition is associated with an application in physics, 