Aristotle's Theory Unity of Science

21 Genus, Abstraction, and Commensurabilitysays, 'it is necessary for the extreme and the middle terms to come fromthe same genus' (APo I.7 7SblO-ll). Aristotle explains in more detail·howthe identity of a science is determined by the genus:A science (f7TLUT~,U:1J) is one if it is of one genus (EVO~ yivov!O) - of whatever thingsare composed from the primitives and are parts or attributes of these in themselves(.!Cae' aimi). One science is different from another if their principles depend neitheron the same things nor the ones on the others. There is evidence for this whenone comes to the non-demonstrables; for these must be in the same genus as thethings demonstrated. And there is evidence for this when the things that are provedthrough them are in the same genus and of a kind. (APo 1.28)It is an important point made clear in this passage that this sense of 'genus/the identity condition of a science, is not the same as the sense in which agroup is divided into species by differentiae. This' genus' includes a subject,its principles, its parts, and its attributes. Many of these will not be in thesame divisionary genus, and will not even be in the same category as thesubject itself. Whereas members of a divisionary genus like animal are allsimilar and share some characteristics, members of a scientific genus arerelated to one another by per se relations. 12The terms of a single science, then, all belong in the same genus,because they are related per se and qua the subject. Conversely, terms thatare not related per se and qua the subject do not belong in the genus.What is not related per se is incidental (APo 1.4 73b4-S), and since it isimpossible to demonstrate anything with incidental premisses, one can onlydemonstrate with terms from the same genus. Each thing must be provedfrom its own principles (A Po 1.9 7Sb37-38), and the principles used mustbe coextensive with the subject. Aristotle repeatedly warns about breakingthis rule: what is proved must not be proved of a subject narrower inextension than the predicate:One cannot, therefore, prove anything by crossing from another genus (E~ aAAOVyivovS' flETaj3a.vTa) - e.g. something geometrical by arithmetic ... For this reasonone cannot prove by geometry that there is a single science of opposites, nor even12 For further comments, see McKirahan 1992, 61-2. The senses of the tenn are hardlyexclusive, and as Andrew Coles has pointed out to me they are central to two momentsof a single inquiry. The first, the divisionary moment in which subjects are connectedwith attributes at various levels of generality, requires that a genus be divisible intospecies. After this stage each level becomes a genus-subject of demonstration. Seeespecially Lennox 1987a.