Abstract

Jacob Klein’s own account of the change from the ancient to the modern mode of thinking presented in his seminal Greek Mathematical Thought and the Origin of Algebra included the observation that it did not consider the larger perspective of this change. The discussion to follow proposes to view the larger perspective of this transition through the lens provided by the Kantian concept of a “critique” of pure reason. By asking and attempting to answer the question of whether Klein’s account of what he calls the “symbolic abstraction” responsible for the genesis of the modern concept of number can be seen as what Kant characterizes as an “assessment” of pure reason, it is my intent to venture a prolegomenon to a critique of what, following Klein, I want to argue is most properly called “symbolic reason.”