Paul of Venice on the definition of accidents

Paul's systematic presentation of Aristotle's philosophy is confronted with several puzzles. Substances are definitionally prior to accidents, Paul maintains, because the definitions of accidents include reference to substance. The reference of an accidents to its corresponding substance is an «aptitudinal inherence». By stating that aptitudinal inherence is not included in the definitions of type-accidents, Paul can state that type-accidents do not share in any common notion. Type-accidents, qua such, also include quantities that do not inhere in any primary substance, but are mere mathematical objects. Hence, aptitudinal inherence cannot be included in the definition of type-accidents, qua type-accidents. Paul's solution showcases the resources of a systematizing reading of Aristotle and of the Aristotelian tradition.