Abstract

The paper argues for three things. First, that the abstract concepts of ancient Greek and modern mathematics are fundamentally different. The general treatment of mathematical things in ancient Greek mathematics manifestly does not presuppose a general mathematical object, while in modern mathematics the generality of the method presupposes precisely such a general mathematical object. Two, that this difference in abstract concepts of mathematics makes a difference in our understanding of a discipline other than mathematics, specifically, in the discipline of history. And, three, that what is at issue in this difference is whether it is necessary for human beings to understand themselves from the perspective of history in order to understand themselves properly as human