not of knowledge only, but of being, yet greater far than either in dignity and power. 'That is a reach of thought more than human; but, pray, go on with the image, for I suspect that there is more behind.' There is, I said; and bearing in mind our two suns or principles, imagine further their corresponding worlds--one of the visible, the other of the intelligible; you may assist your fancy by figuring the distinction under the image {lxxxviii} of a line divided into two unequal parts, and may again subdivide each part into two lesser segments representative of the stages of knowledge in either sphere. The lower portion of the lower or visible sphere will consist of shadows and reflections, *510* and its upper and smaller portion will contain real objects in the world of nature or of art. The sphere of the intelligible will also have two divisions,--one of mathematics, in which there is no ascent but all is descent; no inquiring into premises, but only drawing of inferences. In this division the mind works with figures and numbers, the images of which are taken not from the shadows, but from the objects, although the truth of them is seen only with the mind's eye; and they are used as hypotheses without being analysed. *511* Whereas in the other division reason uses the hypotheses as stages or steps in the ascent to the idea of good, to which she fastens them, and then again descends, walking firmly in the region of ideas, and of ideas only, in her ascent as well as descent, and finally resting in them. 'I partly understand,' he replied; 'you mean that the ideas of science are superior to the hypothetical, metaphorical conceptions of geometry and the other arts or sciences, whichever is to be the name of them; and the latter conceptions you refuse to make subjects of pure intellect, because they have no first principle, although when resting on a first principle, they pass into the higher sphere.' You understand me very well, I said. And now to those four divisions of knowledge you may assign four corresponding faculties--pure intelligence to the highest sphere; active intelligence to the second; to the third, faith; to the fourth, the perception of shadows--and the clearness of the several faculties will be in the same ratio as the truth of the objects to which they are related.... * * * * * [Sidenote: _Republic VI._ Introduction.]