There is more difficulty in comprehending how he arrived at the first term of the series, which is nowhere else mentioned, and has no reference to any other part of his system. Nor indeed does the relation of shadows to objects correspond to the relation of numbers to ideas. Probably Plato has been led by the love of analogy (“Timaeus,” 32 B) to make four terms instead of three, although the objects perceived in both divisions of the lower sphere are equally objects of sense. He is also preparing the way, as his manner is, for the shadows of images at the beginning of the seventh book, and the imitation of an imitation in the tenth. The line may be regarded as reaching from unity to infinity, and is divided into two unequal parts, and subdivided into two more; each lower sphere is the multiplication of the preceding. Of the four faculties, faith in the lower division has an intermediate position (compare for the use of the word faith or belief, πίστις, “Timaeus,” 29 C, 37 B), contrasting equally with the vagueness of the perception of shadows (εἰκασία) and the higher certainty of understanding (διάνοια) and reason (νοῦς).
The difference between understanding and mind or reason (νοῦς) is analogous to the difference between acquiring knowledge in the parts and the contemplation of the whole. True knowledge is a whole, and is at rest; consistency and universality are the tests of truth. To this self-evidencing knowledge of the whole the faculty of mind is supposed to correspond. But there is a knowledge of the understanding which is incomplete and in motion always, because unable to rest in the subordinate ideas. Those ideas are called both images and hypotheses—images because they are clothed in sense, hypotheses because they are assumptions only, until they are brought into connection with the idea of good.
The general meaning of the passage 508–511, so far as the thought contained in it admits of being translated into the terms of modern philosophy, may be described or explained as follows:—There is a truth, one and self-existent, to which by the help of a ladder let down from above, the human intelligence may ascend. This unity is like the sun in the heavens, the light by which all things are seen, the being by which they are created and sustained. It is the idea of good. And the steps of the ladder leading up to this highest or universal existence are the mathematical sciences, which also contain in themselves an element of the universal. These, too, we see in a new manner when we connect them with the idea of good. They then cease to be hypotheses or pictures, and become essential parts of a higher truth which is at once their first principle and their final cause.
We cannot give any more precise meaning to this remarkable passage, but we may trace in it several rudiments or vestiges of thought which are common to us and to Plato: such as (1) the unity and correlation of the sciences, or rather of science, for in Plato’s time they were not yet parted off or distinguished; (2) the existence of a Divine Power, or life or idea or cause or reason, not yet conceived or no longer conceived as in the “Timaeus” and elsewhere under the form of a person; (3) the recognition of the hypothetical and conditional character of the mathematical sciences, and in a measure of every science when isolated from the rest; (4) the conviction of a truth which is invisible, and of a law, though hardly a law of nature, which permeates the intellectual rather than the visible world.
The method of Socrates is hesitating and tentative, awaiting the fuller explanation of the idea of good, and of the nature of dialectic in the seventh book. The imperfect intelligence of Glaucon, and the reluctance of Socrates to make a beginning, mark the difficulty of the subject. The allusion to Theages’ bridle, and to the internal oracle, or demonic sign, of Socrates, which here, as always in Plato, is only prohibitory; the remark that the salvation of any remnant of good in the present evil state of the world is due to God only; the reference to a future state of existence, 498 D, which is unknown to Glaucon in the tenth book, 608 D, and in which the discussions of Socrates and his disciples would be resumed; the surprise in the answers at 487 E and 497 B; the fanciful irony of Socrates, where he pretends that he can only describe the strange position of the philosopher in a figure of speech; the original observation that the Sophists, after all, are only the representatives and not the leaders of public opinion; the picture of the philosopher standing aside in
