Abstract

The authors explicate Aquinas's conception of mathematics. They show that in his work the Aristotelian conception is prevalent, according to which this discipline is—together with physics and metaphysics—a theoretical science, whose subject is the study of real quantity and its necessary properties. But, alongside this dominant and prevalent conception, Aquinas's work contains a number of indications that cast doubt. These sparse and rather marginal reflections lead the authors to conclude that Aquinas's texts contain a "constructivist" conception of mathematics in rudimentary form. According to this approach, mathematics is not a theoretical science examining real quantity but, rather, a special kind of "art" by means of which mathematical objects are "created." From a constructivist point of view the authors then attempt to formulate a conception of mathematics that would accord with the basic Aristotelian assumptions of Aquinas's thought.