 These three parts of Dedekind’s approach may not seem extraordinary to a contemporary mathematician. But that is just testimony to how much modern mathematics has been shaped by his work. His approach was certainly seen as novel, even revolutionary, at the time. Some negative reactions to it, by finitist and constructivist thinkers, have already been mentioned. The extent to which Dedekind’s approach diverged from what had been common stands out further if we remember two traditional, widely shared assumptions: that mathematics is the science of number and magnitude; and that it has essentially to do with calculating and other algorithmic procedures. Relative to such assumptions, Dedekind’s approach to mathematics involves a radical transformation and liberation (Stein 1988, Tait 1996).