2. Plato supposes that when the tablet has been made blank the artist will fill in the lineaments of the ideal state. Is this a pattern laid up in heaven, or mere vacancy on which he is supposed to gaze with wondering eye? The answer is, that such ideals are framed partly by the omission of particulars, partly by imagination perfecting the form which experience supplies (Phaedo). Plato represents these ideals in a figure as belonging to another world; and in modern times the idea will sometimes seem to precede, at other times to co-operate with the hand of the artist. As in science, so also in creative art, there is a synthetical as well as an analytical method. One man will have the whole in his mind before he begins; to another the processes of mind and hand will be simultaneous.3. There is no difficulty in seeing that Plato's divisions of knowledge are based, first, on the fundamental antithesis of sensible and intellectual which pervades the whole pre-Socratic philosophy; in which is implied also the opposition of the permanent and transient, of the universal and particular. But the age of philosophy in which he lived seemed to require a further distinction;--numbers and figures were beginning to separate from ideas. The world could no longer regard justice as a cube, and was learning to see, though imperfectly, that the abstractions of sense were distinct from the abstractions of mind. Between the Eleatic being or essence and the shadows of phenomena, the Pythagorean principle of number found a place, and was, as Aristotle remarks, a conducting medium from one to the other. Hence Plato is led to introduce a third term which had not hitherto entered into the scheme of his philosophy. He had observed the use of mathematics in education; they were the best preparation for higher studies. The subjective relation between them further suggested an objective one; although the passage from one to the other is really imaginary (Metaph.). For metaphysical and moral philosophy has no connexion with mathematics; number and figure are the abstractions of time and space, not the expressions of purely intellectual conceptions. When divested of metaphor, a straight line or a square has no more to do with right and justice than a crooked line with vice. The figurative association was mistaken for a real one; and thus the three lat-ter divisions of the Platonic proportion were constructed.
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 num-
35
bers to ideas. Probably Plato has been led by the love of analogy (Timaeus) 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 (cp. for the use of the word faith or belief, (Greek), Timaeus), contrasting equally with the vagueness of the perception of shadows (Greek) and the higher certainty of understanding (Greek) and reason (Greek).
The difference between understanding and mind or reason (Greek) 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 connexion with the idea of good.
The general meaning of the passage, 'Noble, then, is the bond which links together sight...And of this kind I spoke as the intelligible...' 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, which is unknown to Glaucon in the tenth book, and in which the discussions of Socrates and his disciples would be resumed; the surprise in the answers; 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 the shower of
sleet under a wall; the figure of 'the great beast' followed by the expression of good-will towards the common people who would not have rejected the philosopher if they had known him; the 'right noble thought' that the highest truths demand the greatest exactness; the hesitation of Socrates in returning once more to his well-worn theme of the idea of good; the ludicrous earnestness of Glaucon; the comparison of philosophy to a deserted maiden who marries beneath her--are some of the most interesting characteristics of
the sixth book.
Yet a few more words may be added, on the old theme, which was so oft discussed in the Socratic circle, of which we, like Glaucon and Adeimantus, would fain, if possible, have a clearer notion. Like them, we are dissatisfied when we are told that the idea of good can only be revealed to a student of the mathematical sciences, and we are inclined to think that neither we nor they could have been led along that path to any satisfactory goal. For we have learned that differences of quantity cannot pass into differences of qual-
ity, and that the mathematical sciences can never rise above themselves into the sphere of our higher thoughts, although they may sometimes furnish symbols and expressions of them, and may train the mind in habits of abstraction and self-concentration. The illusion which was natural to an ancient philosopher has ceased to be an illusion to us. But if the process by which we are supposed to arrive at the idea of good be really imaginary, may not the idea itself be also a mere abstraction? We remark, first, that in all ages, and especially in primitive philosophy, words such as being, essence,
