OF THE INTELLECTUAL POWERS ACCORDING TO PLATO. 599 



and reflections in water, and in polished bodies ; and by things, I mean that of which these images 

 are the resemblances ; as animals, plants, things made by man. This difference corresponds to 

 the difference of Knowledge and mere Opinion; and the Opinable is to the Knowable as the 

 Image to the Reality. 11 



This analogy is assented to by Glaucon ; and thus there is assumed a ground for a further 

 construction of the diagram. 



" Now," he says, " we have to divide the segment which represents Intelligible Things in the 

 same way in which we have divided that which represents Visible Things. The one part must 

 represent the knowledge which the mind gets by dealing as it were with images, and by 

 reasoning downwards from Principles ; the other that which it has by dealing with the Ideas 

 themselves, and going to First Principles. 



" The one part depends upon assumptions or hypotheses*, the other is unhypothetical or 

 absolute truth. 



" One kind of Intelligible Things, then, is Conceptions ; for instance, geometrical conceptions 

 of figures, by means of which we reason downwards, assuming certain First Principles. 



" Now the other kind of Intelligible Things is this : — that which the Reason includes in 

 virtue of its power of reasoning, when it regards the assumptions of the Sciences as, what they 

 are, assumptions only ; and uses them as occasions and starting points, that from these it may 

 ascend to the absolute. {aw-n-oOeTov, unhypothetical) which does not depend upon assumption, but 

 is the origin of scientific truth. The Reason takes hold of this first principle of truth ; and 

 availing itself of all the connections and relations of this principle, it proceeds to the conclusion ; 

 using no sensible image in doing this, but contemplating the Ideas alone ; and with these Ideas 

 the process begins, goes on, and terminates." 



This account of the matter will probably seem to require at least further explanation ; and 

 that accordingly is acknowledged in the Dialogue itself. Glaucon says : 



" I apprehend your meaning in a certain degree, but not very clearly, for the matter is 

 somewhat abstruse. You wish to prove that the knowledge which, by the Reason, we acquire, 

 of Real Existence and Intelligible Things, is of a higher degree of certainty than the knowledge 

 which belongs to what are commonly called Sciences. Such sciences, you say, have certain 

 assumptions for their bases ; and these assumptions are, by the students of such sciences, appre- 

 hended, not by Sense (that is, the Bodily Senses), but by a Mental Operation, — by Conception. 

 But inasmuch as such students ascend no higher than the assumptions, and do not go to the 

 First Principles of Truth, they do not seem to you to have true knowledge — intuitive insight — 

 Notts — on the subject of their reasonings, though the subjects are intelligible, along with their 

 principle. And you call this habit and practice of the Geometers and others by the name Con- 

 ception, not Intuition j ,■ taking Conception to be something between Opinion on the one side, and 

 Intuitive Insight on the other." 



* It is plain that Plato, by Hypotheses, in this place, means 

 the usual foundations of Arithmetic and Geometry i namely, 

 Definitions and Postulates. He says that "the arithmeticians 

 and geometers take as hypotheses (inrodifievoi) odd and even, 

 and the three kinds of angles, (right, acute, and obtuse;) and 

 figures, (as a triangle, a square,) and the like." I say his " hypo- 



theses" are the Definitions and Postulates, not the Axioms : for 

 the Axioms of Arithmetic and Geometry belong to the Higher 

 Faculty, which ascends to First Principles. But this Faculty 

 operates rather in using these axioms than in enunciating them. 

 It knows them implicitly rather than expresses them explicitly, 

 j* oidvotau cc\V oil vovv. 



Vol. IX. Part IV. 77 



