On the Philosophy of Discovery, Chapters Historical and Critical

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.

"If each of several things have a part of the Idea of Equality, it will be Equal to something, in virtue of something which is less than Equality."

And in the same way with regard to the Idea of Smallness.

"If each thing be small by having a part of the Idea of Smallness, Smallness itself will be greater than the small thing, since that is a part of itself."

These ingenious results of the partibility of Ideas remind us of the ingenuity shown in the Greek geometry, especially the Fifth Book of Euclid. They are represented as not resisted by Socrates (§ 12): "In what way, Socrates, can things participate in Ideas, if they cannot do so either integrally or partibly?" "By my troth," says Socrates, "it does not seem easy to tell." Parmenides, who completely takes the conduct of the Dialogue, then turns to another part of the subject and propounds other arguments. "What do you say to this?" he asks.

"There is an Ideal Greatness, and there are many things, separate from it, and Great by virtue of it. But now if you look at Greatness and the Great things together, since they are all Great, they must be Great in virtue of some higher Idea of Greatness which includes both. And thus you have a Second Idea of Greatness; and in like manner you will have a third, and so on indefinitely."

This also, as an argument against the separate existence of Ideas, Socrates is represented as unable to answer. He replies interrogatively:

"Why, Parmenides, is not each of these Ideas a Thought, which, by its nature, cannot exist in anything except in the Mind? In that case your consequences would not follow."

This is an answer which changes the course of the reasoning: but still, not much to the advantage of the Ideal Theory. Parmenides is still ready with very perplexing arguments. (§ 13.)

"The Ideas, then," he says, "are Thoughts. They must be Thoughts of something. They are Thoughts of something, then, which exists in all the special things; some one thing which the Thought perceives in all the special things; and this one Thought thus involved in all, is the Idea. But then, if the special things, as you say, participate in the Idea, they participate in the Thought; and thus, all objects are made up of Thoughts, and all things think; or else, there are thoughts in things which do not think."

This argument drives Socrates from the position that Ideas are Thoughts, and he moves to another, that they are Paradigms, Exemplars of the qualities of things, to which the things themselves are like, and their being thus like, is their participating in the Idea. But here too, he has no better success. Parmenides argues thus:

"If the Object be like the Idea, the Idea must be like the Object. And since the Object and the Idea are like, they must, according to your doctrine, participate in the Idea of Likeness. And thus you have one Idea participating in another Idea, and so on in infinitum." Socrates is obliged to allow that this demolishes the notion of objects partaking in their Ideas by likeness: and that he must seek some other way. "You see then, O Socrates," says Parmenides, "what difficulties follow, if any one asserts the independent existence of Ideas!" Socrates allows that this is true. "And yet," says Parmenides, "you do not half perceive the difficulties which follow from this doctrine of Ideas." Socrates expresses a wish to know to what Parmenides refers; and the aged sage replies by explaining that if Ideas exist independently of us, we can never know anything about them: and that even the Gods could not know anything about man. This argument, though somewhat obscure, is evidently stated with perfect earnestness, and Socrates is represented as giving his assent to it. "And yet," says Parmenides (end of § 18), "if any one gives up entirely the doctrine of Ideas, how is any reasoning possible?"

All the way through this discussion, Parmenides appears as vastly superior to Socrates; as seeing completely the tendency of every line of reasoning, while Socrates is driven blindly from one position to another; and as kindly and graciously advising a young man respecting the proper aims of his philosophical career; as well as clearly pointing out the consequences of his assumptions. Nothing can be more complete than the higher position assigned to Parmenides in the Dialogue.

This has not been overlooked by the Editors and Commentators of Plato. To take for example one of the latest; in Steinhart's Introduction to Hieronymus Müller's translation of Parmenides (Leipzig, 1852), p. 261, he says: "It strikes us, at first, as strange, that Plato here seems to come forward as the assailant of his own doctrine of Ideas. For the difficulties which he makes Parmenides propound against that doctrine are by no means sophistical or superficial, but substantial and to the point. Moreover there is among all these objections, which are partly derived from the Megarics, scarce one which does not appear again in the penetrating and comprehensive argumentations of Aristotle against the Platonic Doctrine of Ideas."

Of course, both this writer and other commentators on Plato offer something as a solution of this difficulty. But though these explanations are subtle and ingenious, they appear to leave no satisfactory or permanent impression on the mind. I must avow that, to me, they appear insufficient and empty; and I cannot help believing that the solution is of a more simple and direct kind. It may seem bold to maintain an opinion different from that of so many eminent scholars; but I think that the solution which I offer, will derive confirmation from a consideration of the whole Dialogue; and therefore I shall venture to propound it in a distinct and positive form. It is this:

I conceive that the Parmenides is not a Platonic Dialogue at all; but Antiplatonic, or more properly, Eleatic: written, not by Plato, in order to explain and prove his Theory of Ideas, but by some one, probably an admirer of Parmenides and Zeno, in order to show how strong were his master's arguments against the Platonists and how weak their objections to the Eleatic doctrine.

I conceive that this view throws an especial light on every part of the Dialogue, as a brief survey of it will show. Parmenides and Zeno come to Athens to the Panathenaic festival: Parmenides already an old man, with a silver head, dignified and benevolent in his appearance, looking five and sixty years old: Zeno about forty, tall and handsome. They are the guests of Pythodorus, outside the Wall, in the Ceramicus; and there they are visited by Socrates then young, and others who wish to hear the written discourses of Zeno. These discourses are explanations of the philosophy of Parmenides, which he had delivered in verse.

Socrates is represented as showing, from the first, a disposition to criticize Zeno's dissertation very closely; and without any prelude or preparation, he applies the Doctrine of Ideas to refute the Eleatic Doctrine that All Things are One. (§ 3.) When he had heard to the end, he begged to have the first Proposition of the First Book read again. And then, "How is it, O Zeno, that you say, That if the Things which exist are Many, and not One, they must be at the same time like and unlike? Is this your argument? Or do I misunderstand you?" "No," says Zeno, "you understand quite rightly." Socrates then turns to Parmenides, and says, somewhat rudely, as it seems, "Zeno is a great friend of yours, Parmenides: he shows his friendship not only in other ways, but also in what he writes. For he says the same things which you say, though he pretends that he does not. You say, in your poems, that All Things are One, and give striking proofs: he says that existences are not many, and he gives many and good proofs. You seem to soar above us, but you do not really differ." Zeno takes this sally good-humouredly, and tells him that he pursues the scent with the keenness of a Laconian hound. "But," says he (§ 6), "there really is less of ostentation in my writing than you think. My Essay was merely written as a defence of Parmenides long ago, when I was young; and is not a piece of display composed now that I am older. And it was stolen from me by some one; so that I had no choice about publishing it."

Here we have, as I conceive, Socrates already represented as placed in a disadvantageous position, by his abruptness, rude allusions, and readiness to put bad interpretations on what is done. For this, Zeno's gentle pleasantry is a rebuke. Socrates, however, forthwith rushes into the argument; arguing, as I have said, for his own Theory.

"Tell me," he says, "do you not think there is an Idea of Likeness, and an Idea of Unlikeness? And that everything partakes of these Ideas? The things which partake of Unlikeness are unlike. If all things partake of both Ideas, they are both like and unlike; and where is the wonder? (§ 7.) If you could show that Likeness itself was Unlikeness, it would be a prodigy; but if things which partake of these opposites, have both the opposite qualities, it appears to me, Zeno, to involve no absurdity.

"So if Oneness itself were to be shown to be Maniness" (I hope I may use this word, rather than multiplicity) "I should be surprised; but if any one say that I am at the same time one and many, where is the wonder? For I partake of maniness: my right side is different from my left side, my upper from my under parts. But I also partake of Oneness, for I am here One of us seven. So that both are true. And so if any one say that stocks and stones, and the like, are both one and many,—not saying that Oneness is Maniness, nor Maniness Oneness, he says nothing wonderful: he says what all will allow. (§ 8.) If then, as I said before, any one should take separately the Ideas or Essence of Things, as Likeness and Unlikeness, Maniness and Oneness, Rest and Motion, and the like, and then should show that these can mix and separate again, I should be wonderfully surprised, O Zeno: for I reckon that I have tolerably well made myself master of these subjects³²³. I should be much more surprised if any one could show me this contradiction involved in the Ideas themselves; in the object of the Reason, as well as in Visible objects."

It may be remarked that Socrates delivers all this argumentation with the repetitions which it involves, and the vehemence of its manner, without waiting for a reply to any of his interrogations; instead of making every step the result of a concession of his opponent, as is the case in the Dialogues where he is represented as triumphant. Every reader of Plato will recollect also that in those Dialogues, the triumph of temper on the part of Socrates is represented as still more remarkable than the triumph of argument. No vehemence or rudeness on the part of his adversaries prevents his calmly following his reasoning; and he parries coarseness by compliment. Now in this Dialogue, it is remarkable that this kind of triumph is given to the adversaries of Socrates. "When Socrates had thus delivered himself," says Pythodorus, the narrator of the conversation, "we thought that Parmenides and Zeno would both be angry. But it was not so. They bestowed entire attention upon him, and often looked at each other, and smiled, as in admiration of Socrates. And when he had ended, Parmenides said: 'O Socrates, what an admirable person you are, for the earnestness with which you reason! Tell me then, Do you then believe the doctrine to which you have been referring;—that there are certain Ideas, existing independent of Things; and that there are, separate from the Ideas, Things which partake of them? And do you think that there is an Idea of Likeness besides the likeness which we have; and a Oneness and a Maniness, and the like? And an Idea of the Right, and the Good, and the Fair, and of other such qualities?'" Socrates says that he does hold this; Parmenides then asks him, how far he carries this doctrine of Ideas, and propounds to him the difficulties which I have already stated; and when Socrates is unable to answer him, lets him off in the kind but patronizing way which I have already described.

To me, comparing this with the intellectual and moral attitude of Socrates in the most dramatic of the other Platonic Dialogues, it is inconceivable, that this representation of Socrates should be Plato's. It is just what Zeno would have written, if he had wished to bestow upon his master Parmenides the calm dignity and irresistible argument which Plato assigns to Socrates. And this character is kept up to the end of the Dialogue. When Socrates (§ 19) has acknowledged that he is at loss which way to turn for his philosophy, Parmenides undertakes, though with kind words, to explain to him by what fundamental error in the course of his speculative habits he has been misled. He says; "You try to make a complete Theory of Ideas, before you have gone through a proper intellectual discipline. The impulse which urges you to such speculations is admirable—is divine. But you must exercise yourself in reasoning which many think trifling, while you are yet young; if you do not, the truth will elude your grasp." Socrates asks submissively what is the course of such discipline: Parmenides replies, "The course pointed out by Zeno, as you have heard." And then, gives him some instructions in what manner he is to test any proposed Theory. Socrates is frightened at the laboriousness and obscurity of the process. He says, "You tell me, Parmenides, of an overwhelming course of study; and I do not well comprehend it. Give me an example of such an examination of a Theory." "It is too great a labour," says he, "for one so old as I am." "Well then, you, Zeno," says Socrates, "will you not give us such an example?" Zeno answers, smiling, that they had better get it from Parmenides himself; and joins in the petition of Socrates to him, that he will instruct them. All the company unite in the request. Parmenides compares himself to an aged racehorse, brought to the course after long disuse, and trembling at the risk; but finally consents. And as an example of a Theory to be examined, takes his own Doctrine, that All Things are One, carrying on the Dialogue thenceforth, not with Socrates, but with Aristoteles (not the Stagirite, but afterwards one of the Thirty), whom he chooses as a younger and more manageable respondent.

The discussion of this Doctrine is of a very subtle kind, and it would be difficult to make it intelligible to a modern reader. Nor is it necessary for my purpose to attempt to do so. It is plain that the discussion is intended seriously, as an example of true philosophy; and each step of the process is represented as irresistible. The Respondent has nothing to say but Yes; or No; How so? Certainly; It does appear; It does not appear. The discussion is carried to a much greater length than all the rest of the Dialogue; and the result of the reasoning is summed up by Parmenides thus: "If One exist, it is Nothing. Whether One exist or do not exist, both It and Other Things both with regard to Themselves and to Each other, All and Everyway are and are not, appear and appear not." And this also is fully assented to; and so the Dialogue ends.

I shall not pretend to explain the Doctrines there examined that One exists, or One does not exist, nor to trace their consequences. But these were Formulæ, as familiar in the Eleatic school, as Ideas in the Platonic; and were undoubtedly regarded by the Megaric contemporaries of Plato as quite worthy of being discussed, after the Theory of Ideas had been overthrown. This, accordingly, appears to be the purport of the Dialogue; and it is pursued, as we see, without any bitterness toward Socrates or his disciples; but with a persuasion that they were poor philosophers, conceited talkers, and weak disputants.

The external circumstances of the Dialogue tend, I conceive, to confirm this opinion, that it is not Plato's. The Dialogue begins, as the Republic begins, with the mention of a Cephalus, and two brothers, Glaucon and Adimantus. But this Cephalus is not the old man of the Piræus, of whom we have so charming a picture in the opening of the Republic. He is from Clazomenæ, and tells us that his fellow-citizens are great lovers of philosophy; a trait of their character which does not appear elsewhere. Even the brothers Glaucon and Adimantus are not the two brothers of Plato who conduct the Dialogue in the later books of the Republic: so at least Ast argues, who holds the genuineness of the Dialogue. This Glaucon and Adimantus are most wantonly introduced; for the sole office they have, is to say that they have a half-brother Antiphon, by a second marriage of their mother. No such half-brother of Plato, and no such marriage of his mother, are noticed in other remains of antiquity. Antiphon is represented as having been the friend of Pythodorus, who was the host of Parmenides and Zeno, as we have seen. And Antiphon, having often heard from Pythodorus the account of the conversation of his guests with Socrates, retained it in his memory, or in his tablets, so as to be able to give the full report of it which we have in the Dialogue Parmenides³²⁴. To me, all this looks like a clumsy imitation of the Introductions to the Platonic Dialogues.

I say nothing of the chronological difficulties which arise from bringing Parmenides and Socrates together, though they are considerable; for they have been explained more or less satisfactorily; and certainly in the Theætetus, Socrates is represented as saying that he when very young had seen Parmenides who was very old³²⁵. Athenæus, however³²⁶, reckons this among Plato's fictions. Schleiermacher gives up the identification and relation of the persons mentioned in the Introduction as an unmanageable story.

I may add that I believe Cicero, who refers to so many of Plato's Dialogues, nowhere refers to the Parmenides. Athenæus does refer to it; and in doing so blames Plato for his coarse imputations on Zeno and Parmenides. According to our view, these are hostile attempts to ascribe rudeness to Socrates or to Plato. Stallbaum acknowledges that Aristotle nowhere refers to this Dialogue.

Appendix B

ON PLATO'S SURVEY OF THE SCIENCES

(Cam. Phil. Soc. April 23, 1855.)

A survey by Plato of the state of the Sciences, as existing in his time, may be regarded as hardly less interesting than Francis Bacon's Review of the condition of the Sciences of his time, contained in the Advancement of Learning. Such a survey we have, in the seventh book of Plato's Republic; and it will be instructive to examine what the Sciences then were, and what Plato aspired to have them become; aiding ourselves by the light afforded by the subsequent history of Science.

In the first place, it is interesting to note, in the two writers, Plato and Bacon, the same deep conviction that the large and profound philosophy which they recommended, had not, in their judgment, been pursued in an adequate and worthy manner, by those who had pursued it at all. The reader of Bacon will recollect the passage in the Novum Organon (Lib. I. Aphorism 80) where he speaks with indignation of the way in which philosophy had been degraded and perverted, by being applied as a mere instrument of utility or of early education: "So that the great mother of the Sciences is thrust down with indignity to the offices of a handmaid;—is made to minister to the labours of medicine or mathematics; or again, to give the first preparatory tinge to the immature minds of youth³²⁷."

In the like spirit, Plato says (Rep. VI. § 11, Bekker's ed.):

"Observe how boldly and fearlessly I set about my explanation of my assertion that philosophers ought to rule the world. For I begin by saying, that the State must begin to treat the study of philosophy in a way opposite to that now practised. Now, those who meddle at all with this study are put upon it when they are children, between the lessons which they receive in the farm-yard and in the shop³²⁸; and as soon as they have been introduced to the hardest part of the subject, are taken off from it, even those who get the most of philosophy. By the hardest part, I mean, the discussion of principles—Dialectic³²⁹. And in their succeeding years, if they are willing to listen to a few lectures of those who make philosophy their business, they think they have done great things, as if it were something foreign to the business of life. And as they advance towards old age, with a very few exceptions, philosophy in them is extinguished: extinguished far more completely than the Heraclitean sun, for theirs is not lighted up again, as that is every morning:" alluding to the opinion which was propounded, by way of carrying the doctrine of the unfixity of sensible objects to an extreme; that the Sun is extinguished every night and lighted again in the morning. In opposition to this practice, Plato holds that philosophy should be the especial employment of men's minds when their bodily strength fails.

What Plato means by Dialectic, which he, in the next Book, calls the highest part of philosophy, and which is, I think, what he here means by the hardest part of philosophy, I may hereafter consider: but at present I wish to pass in review the Sciences which he speaks of, as leading the way to that highest study. These Sciences are Arithmetic, Plane Geometry, Solid Geometry, Astronomy and Harmonics.

The view in which Plato here regards the Sciences is, as the instruments of that culture of the philosophical spirit which is to make the philosopher the fit and natural ruler of the perfect State—the Platonic Polity. It is held that to answer this purpose, the mind must be instructed in something more stable than the knowledge supplied by the senses;—a knowledge of objects which are constantly changing, and which therefore can be no real permanent Knowledge, but only Opinion. The real and permanent Knowledge which we thus require is to be found in certain sciences, which deal with truths necessary and universal, as we should now describe them: and which therefore are, in Plato's language, a knowledge of that which really is³³⁰.

This is the object of the Sciences of which Plato speaks. And hence, when he introduces Arithmetic, as the first of the Sciences which are to be employed in this mental discipline, he adds (VII. § 8) that it must be not mere common Arithmetic, but a science which leads to speculative truths³³¹, seen by Intuition³³²; not an Arithmetic which is studied for the sake of buying and selling, as among tradesmen and shopkeepers, but for the sake of pure and real Science³³³.

I shall not dwell upon the details with which he illustrates this view, but proceed to the other Sciences which he mentions.

Geometry is then spoken of, as obviously the next Science in order; and it is asserted that it really does answer the required condition of drawing the mind from visible, mutable phenomena to a permanent reality. Geometers indeed speak of their visible diagrams, as if their problems were certain practical processes; to erect a perpendicular; to construct a square: and the like. But this language, though necessary, is really absurd. The figures are mere aids to their reasonings. Their knowledge is really a knowledge not of visible objects, but of permanent realities: and thus, Geometry is one of the helps by which the mind may be drawn to Truth; by which the philosophical spirit may be formed, which looks upwards instead of downwards.

Astronomy is suggested as the Science next in order, but Socrates, the leader of the dialogue, remarks that there is an intermediate Science first to be considered. Geometry treats of plane figures; Astronomy treats of solids in motion, that is, of spheres in motion; for the astronomy of Plato's time was mainly the doctrine of the sphere. But before treating of solids in motion, we must have a science which treats of solids simply. After taking space of two dimensions, we must take space of three dimensions, length, breadth and depth, as in cubes and the like³³⁴. But such a Science, it is remarked, has not yet been discovered. Plato "notes as deficient" this branch of knowledge; to use the expression employed by Bacon on the like occasions in his Review. Plato goes on to say, that the cultivators of such a science have not received due encouragement; and that though scorned and starved by the public, and not recommended by any obvious utility, it has still made great progress, in virtue of its own attractiveness.

In fact, researches in Solid Geometry had been pursued with great zeal by Plato and his friends, and with remarkable success. The five Regular Solids, the Tetrahedron or Pyramid, Cube, Octahedron, Dodecahedron and Icosahedron, had been discovered; and the curious theorem, that of Regular Solids there can be just so many, these and no others, was known. The doctrine of these Solids was already applied in a way, fanciful and arbitrary, no doubt, but ingenious and lively, to the theory of the Universe. In the Timæus, the elements have these forms assigned to them respectively. Earth has the Cube: Fire has the Pyramid: Water has the Octahedron: Air has the Icosahedron: and the Dodecahedron is the plan of the Universe itself. This application of the doctrine of the Regular Solids shows that the knowledge of those figures was already established; and that Plato had a right to speak of Solid Geometry as a real and interesting Science. And that this subject was so recondite and profound,—that these five Regular Solids had so little application in the geometry which has a bearing on man's ordinary thoughts and actions,—made it all the more natural for Plato to suppose that these solids had a bearing on the constitution of the Universe; and we shall find that such a belief in later times found a ready acceptance in the minds of mathematicians who followed in the Platonic line of speculation.

Plato next proceeds to consider Astronomy; and here we have an amusing touch of philosophical drama. Glaucon, the hearer and pupil in the Dialogue, is desirous of showing that he has profited by what his instructor had said about the real uses of Science. He says Astronomy is a very good branch of education. It is such a very useful science for seamen and husbandmen and the like. Socrates says, with a smile, as we may suppose: "You are very amusing with your zeal for utility. I suppose you are afraid of being condemned by the good people of Athens for diffusing Useless Knowledge." A little afterwards Glaucon tries to do better, but still with no great success. He says, "You blamed me for praising Astronomy awkwardly: but now I will follow your lead. Astronomy is one of the sciences which you require, because it makes men's minds look upwards, and study things above. Any one can see that." "Well," says Socrates, "perhaps any one can see it except me—I cannot see it." Glaucon is surprised, but Socrates goes on: "Your notice of 'the study of things above' is certainly a very magnificent one. You seem to think that if a man bends his head back and looks at the ceiling he 'looks upwards' with his mind as well as his eyes. You may be right and I may be wrong: but I have no notion of any science which makes the mind look upwards, except a science which is about the permanent and the invisible. It makes no difference, as to that matter, whether a man gapes and looks up or shuts his mouth and looks down. If a man merely look up and stare at sensible objects, his mind does not look upwards, even if he were to pursue his studies swimming on his back in the sea."

The Astronomy, then, which merely looks at phenomena does not satisfy Plato. He wants something more. What is it? as Glaucon very naturally asks.