Aristotle's Theory Unity of Science

15 Genus, Abstraction, and CommensurabilityThere are different degrees of semi-abstraction. By enlisting commensurabilityas a sign of generic unity (i.e., objects in the same genus can becompared directly with one another, while objects from different generacannot) I shall examine abstraction and resistance to abstraction in severalgraduated cases. While mathematicals can easily be abstracted from theirphysical substrate and be compared as quantities, some other objects resistabstraction to a greater or lesser extent. I shall consider three such objects . .First, kinds of change cannot be abstracted from their substrate and cannotbe compared one with another. Next, the exchange value of manufacturedgoods can be abstracted from the proper function of the goods sufficientlyto allow commensuration for the purpose of exchange and trade. Finally,causes of animal locomotion can be abstracted from the instrumental partsof locomotion to the extent that at the upper reaches of abstraction thereremain no per se connections with the specific -instruments. But eachlevel of abstraction from the pans allows for commensuration within thatlevel. By establishing the possibility of semi-abstraction and degrees ofabstractability and by describing them in the theoretical terms of thePosterior Analytics, I shall have identified the fundamental concepts inAristotle's theory of relations among subject-genera.Demarcating the GenusA demonstrative science is constructed out of demonstrative syllogisms.A demonstrative syllogism, in turn, is constructed out of terms that areorganized into premisses and a conclusion. The terms of the premissesare related to one another by necessity. In order to explicate the notionof necessity, Aristotle introduces three relationships between terms in ademonstrative syllogism:Demonstration, therefore, is deduction from what is necessary. We must thereforegrasp what things and what sort of things demonstrations depend 00. And first letus define what we mean by holding in every case (Kanl 7TaVn:lS') and what by initself (peT se; Ka8' a;'To) and what by universally (Ka80Aov) . (APo 1.4 73.24-27;modified Revised Oxford Translation [ROT])Necessity, then, is explicated in terms of the relations holding in everycase, holding in itself, and holding universally. It is not clear from thispassage whether each of these relations by itself is a sufficient conditionof necessity, or whether they are sufficient only as a group. However,they appear to be arranged in order of increasing stringency and, to someextent, inclusion. We may, therefore, leave at least the holding-in-everycaserelation (KarCz. 1TavTo~) safely aside, on the grounds that it is subsumed