Aristotle's Theory Unity of Science

39 Genus, Abstraction, and Commensurabilitychanges in the affections. A wing may be longer or shorter without ceasingto be a wing. Commensurability, then, is a mark of genus.Aristotle recognizes degrees of abstractability according to how easilythe proposed object can be removed from the per se connections that bindit to its substrate and how easily this new object forms a commensurablegenus. Let us consider three cases drawn from a wide range of contexts,which illustrate the varying degrees to which semi-abstracts maintain perse connection with their substrate .1. Change is impossible to abstract, and so does not even qualify as a semiabstract.What it is to be a change is completely embedded in the specificinstance, its primary recipient. One cannot remove change from its perse and qua connections to its substrate. This is indicated by the factthat change is only commensurable within the genus of its substrate,and different kinds of change, such as alteration and locomotion, areincommensurable with each other.2. The value of manufactured goods is only slightly easier to abstract.Manufactured goods cannot form a single genus, because they performa great variety of functions. Their value is dependent on theirfunction, and so value is per se and qua related to each specific kindof good. But their exchange value in barter must be commensurable ifexchange is to occur. Nevertheless, exchange value, though common, isnot conceivable apart from the specific goods to be exchanged. Value iscommensurable, but it is dependent upon the specific goods, and cannotbe abstracted even conceptually from their manifold specific variety.3. In the case of animal locomotion there is a series of abstractions thatfall short of mathematical completeness, but are more separable thanchange or exchange value. Because the series of abstractions neverleaves the natural domain, each new abstraction remains a hylomorphiccompound, but they become increasingly general and increasingly focusedupon the form. Accordingly, the abstracts always serve as causesfor the substrate, although their per se relations with the substratebecome less direct. As the qua-level changes, the basis for commensurationalso changes.1. Speed of ChangeIn one of the more important and searching passages for issues concerningabstraction, Physics VIl.4, Aristotle argues that the forms of change(alteration, locomotion, etc.) must be specifically identical in order tobe commensurable. The chapter begins with an aporia: is every change