ARISTOTLE'S PRIOR AND POSTERIOR ANALYTICS

RELATION OF PRIOR TO POSTERIOR ANALYTICS 15This has nothing to do with a chain of Fonns such as is contemplatedin Plato's uvvaywY'i and omtp£u", where each link is aspecification of the one above it.Now what does the Metaphysics say? In Ll10qbq - 21 Aristotlementions the same view, ascribing it to 'some people', but notrepudiating it for himself-though he probably would haverepudiated one phrase here used of the simpler entities, viz. thatthey are 'inhering parts' of the more complex; for the view towhich he holds throughout his works is that while points areinvolved in the being of lines, lines in that of planes, and planesin that of solids, they are not component parts of them, since forinstance no series of points having no dimension could make upa line having one dimension.M et. A. 992"10-19 is a difficult passage, in which Aristotle is notstating his own view but criticizing that of the Platonists. Thepoint he seems to be making is this: The Platonists derive lines,planes, solids from different material principles (in addition toformal principles with which he is not at the moment concerned)­lines from the long and short, planes from the broad and narrow,solids from the deep and shallow. How then can they explainthe presence of lines on a plane, or of lines and planes in a solid?On the other hand, if they changed their view and treated thedeep and shallow as a species of the broad and narrow, they wouldbe in an equal difficulty; for it would follow that the solid is akind of plane, which it is not. The view implied as Aristotle'sown is that undoubtedly the planes presuppose lines, and thesolids planes, but that equally certainly the plane is not a kind ofline nor the solid a kind of plane.Now this view is not the repudiation of anything that is said inthe Posterior A nalytics. What Aristotle says I is that the line ispresent in the being and in the definition of the triangle, and thepoint in that of the line. But this is not to say that the triangle,for instance, is a species of the line, but only that there could notbe a triangle unless there were lines, and that the triangle couldnot be defined except as a figure bounded by three straigh t lines;i.e., Aristotle is not describing points, lines, plane figures asfonning a Platonic chain of Fonns at all. In fact there is no workin which he maintains the difference of ytVTJ more finnly than hedoes in the Posterior Analytics. The theory expressed in theProtrepticus and referred to in M et. A and LI, if it had treated theI 73"35.