On the Philosophy of Discovery, Chapters Historical and Critical

by William Whewell

To this the Platonist replied, that the phenomena which present themselves to the senses partake, in a certain manner, of Ideas, and thus include so much of the nature of Ideas, that they include also an element of Truth. The geometrical diagram of Triangles and Squares which is drawn in the sand of the floor of the Gymnasium, partakes of the nature of the true Ideal Triangles and Squares, so that it presents an imitation and suggestion of the truths which are true of them. The real triangles and squares are in the mind: they are, as we have said, objects, not in the Visible, but in the Intelligible World. But the Visible Triangles and Squares make us call to mind the Intelligible; and thus the objects of sense suggest, and, in a way, exemplify the eternal truths.

This I conceive to be the simplest and directest ground of two primary parts of the Theory of Ideas;—The Eternal Ideas constituting an Intelligible World; and the Participation in these Ideas ascribed to the objects of the world of sense. And it is plain that so far, the Theory meets what, I conceive, was its primary purpose; it answers the questions, How can we have certain knowledge, though we cannot get it from Sense? and, How can we have knowledge, at least apparent, though imperfect, about the world of sense?

But is this the ground on which Plato himself rests the truth of his Theory of Ideas? As I have said, I have no doubt that these were the questions which suggested the Theory; and it is perpetually applied in such a manner as to show that it was held by Plato in this sense. But his applications of the Theory refer very often to another part of it;—to the Ideas, not of Triangles and Squares, of space and its affections; but to the Ideas of Relations—as the Relations of Like and Unlike, Greater and Less; or to things quite different from the things of which geometry treats, for instance, to Tables and Chairs, and other matters, with regard to which no demonstration is possible, and no general truth (still less necessary an eternal truth) capable of being asserted.

I conceive that the Theory of Ideas, thus asserted and thus supported, stands upon very much weaker ground than it does, when it is asserted concerning the objects of thought about which necessary and demonstrable truths are attainable. And in order to devise arguments against this part of the Theory, and to trace the contradictions to which it leads, we have no occasion to task our own ingenuity. We find it done to our hands, not only in Aristotle, the open opponent of the Theory of Ideas, but in works which stand among the Platonic Dialogues themselves. And I wish especially to point out some of the arguments against the Ideal Theory, which are given in one of the most noted of the Platonic Dialogues, the Parmenides.

The Parmenides contains a narrative of a Dialogue held between Parmenides and Zeno, the Eleatic Philosophers, on the one side, and Socrates, along with several other persons, on the other. It may be regarded as divided into two main portions; the first, in which the Theory of Ideas is attacked by Parmenides, and defended by Socrates; the second, in which Parmenides discusses, at length, the Eleatic doctrine that All things are One. It is the former part, the discussion of the Theory of Ideas, to which I especially wish to direct attention at present: and in the first place, to that extension of the Theory of Ideas, to things of which no general truth is possible; such as I have mentioned, tables and chairs. Plato often speaks of a Table, by way of example, as a thing of which there must be an Idea, not taken from any special Table or assemblage of Tables; but an Ideal Table, such that all Tables are Tables by participating in the nature of this Idea. Now the question is, whether there is any force, or indeed any sense, in this assumption; and this question is discussed in the Parmenides. Socrates is there represented as very confident in the existence of Ideas of the highest and largest kind, the Just, the Fair, the Good, and the like. Parmenides asks him how far he follows his theory. Is there, he asks, an Idea of Man, which is distinct from us men? an Idea of Fire? of Water? "In truth," replies Socrates, "I have often hesitated, Parmenides, about these, whether we are to allow such Ideas." When Plato had proceeded to teach that there is an Idea of a Table, of course he could not reject such Ideas as Man, and Fire, and Water. Parmenides, proceeding in the same line, pushes him further still. "Do you doubt," says he, "whether there are Ideas of things apparently worthless and vile? Is there an Idea of a Hair? of Mud? of Filth?" Socrates has not the courage to accept such an extension of the theory. He says, "By no means. These are not Ideas. These are nothing more than just what we see them. I have often been perplexed what to think on this subject. But after standing to this a while, I have fled the thought, for fear of falling into an unfathomable abyss of absurdities." On this, Parmenides rebukes him for his want of consistency. "Ah Socrates," he says, "you are yet young; and philosophy has not yet taken possession of you as I think she will one day do--when you will have learned to find nothing despicable in any of these things. But now your youth inclines you to regard the opinions of men." It is indeed plain, that if we are to assume an Idea of a Chair or a Table, we can find no boundary line which will exclude Ideas of everything for which we have a name, however worthless or offensive. And this is an argument against the assumption of such Ideas, which will convince most persons of the groundlessness of the assumption:—the more so, as for the assumption of such Ideas, it does not appear that Plato offers any argument whatever; nor does this assumption solve any problem, or remove any difficulty[322]. Parmenides, then, had reason to say that consistency required Socrates, if he assumed any such Ideas, to assume all. And I conceive his reply to be to this effect; and to be thus a reductio ad absurdum of the Theory of Ideas in this sense. According to the opinions of those who see in the Parmenides an exposition of Platonic doctrines, I believe that Parmenides is conceived in this passage, to suggest to Socrates what is necessary for the completion of the Theory of Ideas. But upon either supposition, I wish especially to draw the attention of my readers to the position of superiority in the Dialogue in which Parmenides is here placed with regard to Socrates.

Parmenides then proceeds to propound to Socrates difficulties with regard to the Ideal Theory, in another of its aspects;—namely, when it assumes Ideas of Relations of things; and here also, I wish especially to have it considered how far the answers of Socrates to these objections are really satisfactory and conclusive.

"Tell me," says he (§ 10, Bekker), "You conceive that there are certain Ideas, and that things partaking of these Ideas, are called by the corresponding names;—an Idea of Likeness, things partaking of which are called Like;—of Greatness, whence they are Great: of Beauty, whence they are Beautiful?" Socrates assents, naturally: this being the simple and universal statement of the Theory, in this case. But then comes one of the real difficulties of the Theory. Since the special things participate of the General Idea, has each got the whole of the Idea, which is, of course, One; or has each a part of the Idea? "For," says Parmenides, "can there be any other way of participation than these two?" Socrates replies by a similitude: "The Idea, though One, may be wholly in each object, as the Day, one and the same, is wholly in each place." The physical illustration, Parmenides damages by making it more physical still. "You are ingenious, Socrates," he says, (§ 11) "in making the same thing be in many places at the same time. If you had a number of persons wrapped up in a sail or web, would you say that each of them had the whole of it? Is not the case similar?" Socrates cannot deny that it is. "But in this case, each person has only a part of the whole; and thus your Ideas are partible." To this, Socrates is represented as assenting in the briefest possible phrase; and thus, here again, as I conceive, Parmenides retains his superiority over Socrates in the Dialogue.

There are many other arguments urged against the Ideal Theory by Parmenides. The next is a consequence of this partibility of Ideas, thus supposed to be proved, and is ingenious enough. It is this:

"If the Idea of Greatness be distributed among things that are Great, so that each has a part of it, each separate thing will be Great in virtue of a part of Greatness which is less than Greatness itself. Is not this absurd?" Socrates submissively allows that it is.

And the same argument is applied in the case of the Idea of Equality.