Aristotle's Theory Unity of Science

37 Genus, Abstraction, and Commensurabilityequal lines falling from a point IPO equal rays falling from a light sourceequal rays falling from a light source IPO equal rays falling from the sunequal rays falling from the sun IPO equal rays reflected by mist to the eyeequal rays reflected by mist to the eye IPO halo.These premisses will be explanatory of why halos exhibit this particulargeometrical nature.We now have an explanation of how these mixed sciences may haveboth geometrical and optical explanatory components, and as a result it willnot be possible to say that the explanation resides either at the qua-level ofgeometry or at the qua-level of optics: it resides at both. In a correspondingway we can redescribe Euclid's Optics 23 in a schematic demonstrativefashion:smaller than the diameter IPO circle at the tangent from a pointcircle at the tangent from a point IPO appearance of sphere from one eyesmaller than the diameter !PO appearance of sphere from one eyeAgain the cone shape of the optical field will serve as a principle to explainthe connection between the middle and the minor terms.As Lennox has rightly pointed out, the form of explanation in these'mixed' sciences differs from the application of 2R to isosceles in thathalos are not species or determinate forms of circles. 34 In fact, circle is noteven part of the definition of halo. For this reason, the transference ofper se attributes of common features (geometry) to the instance (halo) isnot an immediate fact, but itself requires explanation. Aristotle describesthe situation in terms of facts and causes, because he is interested inthe reason why the halo takes a circular shape, rather than why it fall sunder geometrical analysis at alL Nevertheless, the example illustrates thatwhere the subordinate science is not a species of the superordinate science,the subordinate science makes a genuine and unique contribution to theunderstanding of why the major term belongs to the subordinate subject.In proving that halos are circular, we are studying halos qua halos, thatis, we are studying what belongs to halos in virtue of their halo nature,but we are proving attributes that extend beyond halos, attributes that arenon-coextensive per se accidents. Owing to the inconcinnity between theper se and qua requirements, the distinction between the mathematical34 1986,41.