Abstract

In Posterior Analytics 1.13, Aristotle introduced a distinction between two kinds of demonstrations: of the fact (quia), and of the reasoned fact (propter quid). Both demonstrations take a syllogistic form, in which the middle term links either two facts (in the case of quia demonstrations) or a proximate cause and a fact (in the case of propter quid demonstrations). While Aristotle stated that all the terms of one demonstration must be taken from within the same subject matter, he admitted some exceptions in which the fact and the reasoned fact are instantiated by terms from different sciences, as when mathematics provides the reason and another science the empirical fact. This was the methodological foundation of the “mixed sciences”, a subject of varying interpretations in the thirteenth century. Roger Bacon (C. 1220–1292), adhering to Robert Grosseteste’s (C. 1168–1563) commentary on Posterior Analytics, presented a unique interpretation of this exception. He replaced propositional demonstrations with geometrical considerations and diagrams, thus producing geometrical arguments for theorems in natural philosophy. I focus on Bacon’s propter quid arguments, as applied in three case studies: (1) the heat caused by a body moving to its natural place; (2) the motion of the scale; (3) and the contraction of water. Based on an analysis of these demonstrations, I argue that Bacon’s interpretation of propter quid demonstration reflects his application of a scientific methodology that imbues geometrical objects with causal power over material bodies.