Derived Quantity and Quantity as Such—Notes toward a Thomistic Account of Modern and Classical Mathematics

Abstract

Thomists do not have an account of how modern mathematics relates to classical mathematics or more generally fits into the Aristotelian hierarchy of sciences. Rather than treat primarily of Aquinas’s theses on mathematical abstraction, I turn to considering what modern mathematics is in itself, seen from a broadly classical perspective. I argue that many modern quantities can be considered to be, not quantities as such or in themselves, but derived quantities, i.e., quantities that can be defined wholly in terms of the principles of number or magnitude. I also interpret the parts of modern mathematics that study quantitative change as being properly-speaking parts of natural philosophy, for example, probability theory, statistics, calculus, etc. In conclusion, I consider the place that quantity as such has in the order of the world and why we should expect the world to be highly mathematical, as we have found it to be.