Aristotle's Theory Unity of Science

35 Genus, Abstraction, and Commensurabilityviz. CB, FB, DB - equal too. Draw the line AEB. Then the triangles are equal; fortheir base AEB is equal. Draw perpendiculars to AEB from the angles; CE from(, FE from F, DE from D. Then these perpendiculars are equal, being in equaltriangles and all in one plane; for they are all at right angles to AEB and meetat the single point E. So if you draw the line it will be a circle and E its centre.(373a6-16)Aristotle concludes with some principles that allow us to interpret thegeometrical proof in optical and natural terms:now B is the sun, A the eye, and the circumference passing through the pointsCFD the cloud from which the visual ray is reflected to the sun. (373al6-19)SuperfiCially it is easy to see just what kind of explanation Aristotle hasin mind when he says that geometry provides the cause for the opticalfact. One common and plausible interpretation argues that in the contextof a demonstrative syllogism, the major and middle terms of thedemonstration will come from geometry, while the minor term will beoptical, and the minor premiss will state that the optical phenomenonfalls under the geometrical explanation.31 Consequently, the demonstrationwill have the same sort of structure as that applying the general2R theorem to the specific case of the isosceles triangle, an applicationargument. But isosceles is a species of triangle, and the application ofthe genus and its properties to the species does not require any furtherexplanation, since the genus-species connection is immediate. By contrast,the connection between optics and geometry is not immediate and requiresexplanation. 32I should like to suggest that, because of the presence of embeddedterms in the proof, this mixed science cannot be a case of simple applicationargument. First of all, at Phys. II.2 194al-12 Aristotle clearlyplaces mixed sciences among those that behave like the snub. In this samepassage he claims that, 'while geometry investigates natural lines but notqua natural, optics investigates mathematical lines, but qua naturaL notqua mathematical.' The difficulty in setting a determinate qua-level forsuch demonstrations is illustrated by his contradictory claim that 'neither31 This is the interpretation given by McKirahan 1978, 201, and Lennox 1986, 48. Lennox1987a, 94, notes the similarity between 2R-isosceles and mixed science, but rightly doesnot identify their structure.32 McKirahan 1992, 178, 184, recognizes that application arguments need not be to species,but does not deal with cases where the application may not be immediate.