Aristote et la hiérarchie des sciences

«You cannot prove anything by crossing from another kind – e.g. something geometrical by arithmetic. There are three things involved in demonstration: one, what is being demonstrated, or the conclusion (this is what holds of some kind in itself); one, the axioms (axioms are the items from which the demonstrations proceed); third, the underlying kind whose attributes – i.e. the items incidental to it in itself – the demonstrations make plain» (Aristotle, Posterior Analytics 75a38-b2). However, Aristotle accepts an exception: the case of the sciences having a hierarchical relationship, such that one falls under the other. In this case it is possible to prove by crossing from another kind. Throughout Posterior Analytics Aristotle presents several examples of sciences having this relationship. My goal is to analyse such examples in order to show the importance and coherence of the Aristotelian theory of the hierarchy of sciences.