At the close of the sixth book of the Republic (pp. 509-511 Steph.; pp. 321-325 Bekk.) Plato distinguishes the sensuous and the intellectual in our knowledge more exactly, so that in each sphere he again presents two modes of consciousness. “In the sensuous (ὁρατόν) the one division is the external manifestation, for in it are shadows, reflections in water, and also in solid, smooth, and polished bodies, and the like. The second section, of which this is only the resemblance, includes animals, plants” (this concrete life), “and everything in art. The intelligible (νοητόν) is also divided into two parts. In the one sub-division the soul uses the sensuous figures given before, and is obliged to work on hypotheses (ἐξ ὑποθέσεων) because it does not go to the principle but to the result.” Reflection, which is not on its own account sensuous, but undoubtedly belongs to thought, mingles thought with the first sensuous consciousness, although its object is not as yet a pure existence of the understanding. “The other division” (what is thought in the soul itself) “is that in which the soul, proceeding from an hypothesis, makes its way (μέθοδον) to a principle which is above hypotheses, not by means of images, as in the former cases, but through the ideas themselves. Those who study geometry, arithmetic, and kindred sciences, assume the odd and the even, the figures, three kinds of angles, and the like. And since they start from these hypotheses, they do not think it necessary to give any account of them, for everybody is supposed to know them. You further know that they make use of figures which are risible, and speak of them, although they are not thinking of them, but of the ideals which they represent; for they think of the” (absolute) “square itself and of its diagonals, and not of the” (sensuous) “images that they draw. And so it is with other things.” Thus, according to Plato, this is certainly the place where real knowledge begins, because we have nothing further to do with the sensuous as such; at the same time this is not the true knowledge which considers the spiritual universal on its own account, but the arguing and reasoning knowledge that forms universal laws and particular kinds or species out of what is sensuous. “These figures which they draw or make, and which also have shadows and images in water, they use only as images, and seek to behold their originals, which can only be seen with the understanding” (διανοίᾳ).—“That is true.”—“This I have named above that species of the intelligible, in inquiring into which the soul is compelled to use hypotheses, not proceeding to a first principle, because it is not able to get above those hypotheses, but employing those secondary images as images which are made absolutely similar to the originals in every respect”—“I understand that you are speaking of geometry and the kindred arts”—“Now learn about the other division of the intelligible in which reason (λόγος) itself is concerned, since