These primitive intuitions--the simple perceptions of sense, and the à priori intuitions of the reason, which constitute the elements of all our complex notions, have essentially diverse objects--the sensible or ectypal world, seen by the eye and touched by the hand, which Plato calls δοξαστήν--the subject of opinion; and the noetic or archetypal world, perceived by reason, and which he calls διανοητικήν--the subject of rational intuition or science. "It is plain," therefore, argues Plato, "that opinion is a different thing from science. They must, therefore, have a different faculty in reference to a different object--science as regards that which is, so as to know the nature of real being--opinion as regards that which can not be said absolutely to be, or not to be. That which is known and that which is opined can not possibly be the same,... since they are naturally faculties of different things, and both of them are faculties--opinion and science, and each of them different from the other." [529] Here then are two grand divisions of the mental powers--a faculty of apprehending universal and necessary Truth, of intuitively beholding absolute Reality, and a faculty of perceiving sensible objects, and of judging according to appearance.
[Footnote 529: ][ (return) ] Ibid., bk. v. ch. xxi., xxii.
According to the scheme of Plato, these two general divisions of the mental powers are capable of a further subdivision. He says: Consider that there are two kinds of things, the intelligible and the visible; two different regions, the intelligible world and the sensible world. Now take a line divided into two equal segments to represent these two regions, and again divide each segment in the same ratio--both that of the visible and that of the intelligible species. The parts of each segment are to represent differences of clearness and indistinctness. In the visible world the parts are things and images. By images I mean shadows, [530] reflections in water and in polished bodies, and all such like representations; and by things I mean that of which images are resemblances, as animals, plants, and things made by man.
You allow that this difference corresponds to the difference of knowledge and opinion; and the opinionable is to the knowable as the image to the reality. [531]
[Footnote 530: ][ (return) ] As in the simile of the cave ("Republic," bk. vii. ch. i. and ii.).
[Footnote 531: ][ (return) ] The analogy between the "images produced by reflections in water and on polished surfaces" and "the images of external objects produced in the mind by sensation" is more fully presented in the "Timæus," ch. 19.
The eye is a light-bearer, "made of that part of elemental fire which does not burn, but sheds a mild light, like the light of day.... When the light of the day meets the light which beams from the eye, then light meets like, and make a homogeneous body; the external light meeting the internal light, in the direction in which the eye looks. And by this homogeneity like feels like; and if this beam touches any object, or any object touches it, it transmits the motions through the body to the soul, and produces that sensation which we call seeing.... And if (in sleep) some of the strong motions remain in some part of the frame, they produce within us likenesses of external objects,... and thus give rise to dreams.... As to the images produced by mirrors and by smooth surfaces, they are now easily explained, for all such phenomena result from the mutual affinity of the external and internal fires. The light that proceeds from the face (as an object of vision), and the light that proceeds from the eye, become one continuous ray on the smooth surface."
Now we have to divide the segment which represents intelligible things in this way: The one part represents the knowledge which the mind gets by using things as images--the other; that which it has by dealing with the ideas themselves; the one part that which it gets by reasoning downward from principles--the other, the principles themselves; the one part, truth which depends on hypotheses--the other, unhypothetical or absolute truth.
Thus, to explain a problem in geometry, the geometers make certain hypotheses (namely, definitions and postulates) about numbers and angles, and the like, and reason from them--giving no reason for their assumptions, but taking them as evident to all; and, reasoning from them, they prove the propositions which they have in view. And in such reasonings, they use visible figures or diagrams--to reason about a square, for instance, with its diagonals; but these reasonings are not really about these visible figures, but about the mental figures, and which they conceive in thought.
The diagrams which they draw, being visible, are the images of thoughts which the geometer has in his mind, and these images he uses in his reasoning. There may be images of these images--shadows and reflections in water, as of other visible things; but still these diagrams are only images of conceptions.
This, then, is one kind of intelligible things: conceptions--for instance, geometrical conceptions of figures. But in dealing with these the mind depends upon assumptions, and does not ascend to first principles. It does not ascend above these assumptions, but uses images borrowed from a lower region (the visible world), these images being chosen so as to be as distinct as may be.