That Plato's notion, however, cannot have been exactly either of these is, I think, plain. The colloquial method of stimulating and testing the progress of the student in Dialectic is implied, in the sequel of this discussion of the effect of scientific study. And the method of Dialogue, as the instrument of instruction, being thus supposed, the continuation of the account in the Republic, implies that Plato expected persons to be made dialectical by the study of the exact sciences in a comprehensive spirit. After insisting on Geometry and other sciences, he says (Rep. VII. § 16): "The synoptical man is dialectical; and he who is not the one, is not the other."
But, we may ask, does a knowledge of sciences lead naturally to a knowledge of Ideas, as absolute realities from which First Principles flow? And supposing this to be true, as the Platonic Philosophy supposes, is the Idea of the Good, as the source of moral truths, to be thus attained to? That it is, is the teaching of Plato, here and elsewhere; but have the speculations of subsequent philosophers in the same direction given any confirmation of this lofty assumption?
In reply to this inquiry, I should venture to say, that this assumption appears to be a remnant of the Socratic doctrine from which Plato began his speculations, that Virtue is a kind of knowledge; and that all attempts to verify the assumption have failed. What Plato added to the Socratic notion was, that the inquiry after The Good, the Supreme Good, was to be aided by the analogy or suggestions of those sciences which deal with necessary and eternal truths; the supreme good being of the nature of those necessary and eternal truths. This notion is a striking one, as a suggestion, but it has always failed, I think, in the attempts to work it out. Those who in modern times, as Cudworth and Samuel Clarke, have supposed an analogy between the necessary truths of Geometry and the truths of Morality, though they have used the like expressions concerning the one and the other class of truths, have failed to convey clear doctrines and steady convictions to their readers; and have now, I believe, few or no followers.
The result of our investigation appears to be, that though Plato added much to the matter by means of which the mind was to be improved and disciplined in its research after Principles and Definitions, he did not establish any form of Method according to which the inquiry must be conducted, and by which it might be aided. The most definite notion of Dialectic still remained the same with the original informal view which Socrates had taken of it, as Xenophon tells us, (Mem. IV. 5, 11) when he says: "He said that Dialectic (τὸ διαλέγεσθαι) was so called because it is an inquiry pursued by persons who take counsel together, separating the subjects considered according to their kinds (διαλέγοντας). He held accordingly that men should try to be well prepared for such a process, and should pursue it with diligence: by this means, he thought, they would become good men, fitted for responsible offices of command, and truly dialectical" (διαλέκτικωτάτους). And this is, I conceive, the answer to Mr. Grote's interrogatory exclamation (Vol. VIII. p. 577): "Surely the Etymology here given by Xenophon or Socrates of the word (διαλέγεσθαι) cannot be considered as satisfactory." The two notions, of investigatory Dialogue, and Distribution of notions according to their kinds, which are thus asserted to be connected in etymology, were, among the followers of Socrates, connected in fact; the dialectic dialogue was supposed to involve of course the dialectic division of the subject.
Appendix C.
OF THE INTELLECTUAL POWERS ACCORDING TO PLATO.
(Cam. Phil. Soc. Nov. 10, 1856.)
In the Seventh Book of Plato's Republic, we have certain sciences described as the instruments of a philosophical and intellectual education; and we have a certain other intellectual employment spoken of, namely, Dialectic, as the means of carrying the mind beyond these sciences, and of enabling it to see the sources of those truths which the sciences assume as their first principles. These points have been discussed in the two preceding papers. But this scheme of the highest kind of philosophical education proceeds upon a certain view of the nature and degrees of knowledge, and of the powers by which we know; which view had been presented in a great measure in the Sixth Book; this view I shall now attempt to illustrate.
To analyse the knowing powers of man is a task so difficult, that we need not be surprised if there is much obscurity in this portion of Plato's writings. But as a reason for examining what he has said, we must recollect that if there be in it anything on this subject which was true then, it is true still; and also, that if we know any truth on that subject now, we shall find something corresponding to that truth in the best speculations of sagacious ancient writers, like Plato. It may therefore be worth while to discuss the Platonic doctrines on this matter, and to inquire how they are to be expressed in modern phraseology.
Plato's doctrine will perhaps be most clearly understood, if we begin by considering the diagram by which he illustrates the different degrees of knowledge[341]. He sets out from the distinction of visible and intelligible things. There are visible objects, squares and triangles, for instance; but these are not the squares and triangles about which the Geometer reasons. The exactness of his reasoning does not depend on the exactness of his diagrams. He reasons from certain mental squares and triangles, as he conceives and understands them. "Thus there are visible and there are intelligible things. There is a visible and an intelligible world[342]: and there are two different regions about which our knowledge is concerned. Now take a line divided into two unequal segments to represent these two regions: and again, divide each segment in the same ratio. The parts of each segment are to represent differences of clearness and distinctness, and in the visible world these parts are things and images. By images I mean shadows, and reflections in water, and in polished bodies; and by things, I mean that of which these images are the resemblances; as animals, plants, things made by man. This difference corresponds to the difference of Knowledge and mere Opinion; and the Opinable is to the Knowable as the Image to the Reality."