A abstração matemática de Tomás de Aquino

Abstract

The present paper deals with the reception of the mathematical practice in the Aristotelian philosophy of Thomas Aquinas. Thomas's Commentary on Boethius' Treatise on the Trinity allows further reflection on this topic. Mainly, Geometry was the paradigm of mathematical practice in the Middle Ages. In both demonstration and mathematical definitions, form is a central concept. That is why Thomas names this mental activity as an abstraction of form. The paper's central thesis is that mathematical abstraction needs to produce a clearly expressed definition, unlike natural definitions, which admit a confusing stage of conceptual apprehension.

Furthermore, the concept of form is patent in the function of the so-called demonstration by formal causality, a demonstrative process proper to mathematical science and dependent on the produced definition. On the other hand, the demonstration proper of natural science presupposes the moving relation of cause and effect and may use concepts in a more confused stage. Finally, I address the notions of abstraction of form and intelligible matter, considering this detailed analysis of the use of the term form.