Sokrates here impugns the doctrine of Zeno. He affirms the Platonic theory of ideas separate from sensible objects, yet participable by them.

Sokrates, depicted here as a young man, impugns this doctrine of Zeno: and maintains that the two worlds, though naturally disjoined, were not incommunicable. He advances the Platonic theory of Ideas: that is, an intelligible world of many separate self-existent Forms or Ideas, apprehended by reason only — and a sensible world of particular objects, each participating in one or more of these Forms or Ideas. “What you say (he remarks to Zeno), is true of the world of Forms or Ideas: the Form of Likeness per se can never be unlike, nor can the Form of Unlikeness be ever like. But in regard to the sensible world, there is nothing to hinder you and me, and other objects which rank and are numbered as separate individuals, from participating both in the Form of likeness and in the Form of unlikeness.3 In so far as I, an individual object, participate in the Form of Likeness, I am properly called like; in so far as I participate in the Form of Unlikeness, I am called unlike. So about One and Many, Great and Little, and so forth: I, the same individual, may participate in many different and opposite Forms, and may derive from them different and opposite denominations. I am one and many — like and unlike — great and little — all at the same time. But no such combination is possible between the Forms themselves, self-existent and opposite: the Form of Likeness cannot become unlike, nor vice versâ. The Forms themselves stand permanently apart, incapable of fusion or coalescence with each other: but different and even opposite Forms may lend themselves to participation and partnership in the same sensible individual object.”4

Parmenides and Zeno admire the philosophical ardour of Sokrates. Parmenides advances objections against the Platonic theory of Ideas.

Parmenides and Zeno are represented as listening with surprise and interest to this language of Sokrates, recognising two distinct worlds: one, of invisible but intelligible Forms, — the other that of sensible objects, participating in these Forms. “Your ardour for philosophy” (observes Parmenides to Sokrates), “is admirable. Is this distinction your own?”5

Plato now puts into the mouth of Parmenides — the advocate of One absolute and unchangeable Ens, separated by an impassable gulf from the sensible world of transitory and variable appearances or phenomena — objections against what is called the Platonic theory of Ideas: that is, the theory of an intelligible world, comprising an indefinite number of distinct intelligible and unchangeable Forms — in partial relation and communication with another world of sensible objects, each of which participates in one or more of these Forms. We thus have the Absolute One pitted against the Absolute Many.

What Ideas does Sokrates recognise? Of the Just and Good? Yes. Of Man, Horse, &c.? Doubtful. Of Hair, Mud, &c.? No.

What number and variety of these intelligible Forms do you recognise — (asks Parmenides)? Likeness and Unlikeness — One and Many — Just, Beautiful, Good, &c. — are all these Forms absolute and existent per se? Sokr. — Certainly they are. Parm. — Do you farther recognise an absolute and self-existent Form of Man, apart from us and all other individuals? — or a Form of fire, water, and the like? Sokr. — I do not well know how to answer:— I have often been embarrassed with the question. Parm. — Farther, do there exist distinct intelligible Forms of hair, mud, dirt, and all the other mean and contemptible objects of sense which we see around? Sokr. — No — certainly — no such Forms as these exist. Such objects are as we see them, and nothing beyond: it would be too absurd to suppose Forms of such like things.6 Nevertheless there are times when I have misgivings on the point; and when I suspect that there must be Forms of them as well as of the others. When such reflections cross my mind, I shrink from the absurdity of the doctrine, and try to confine my attention to Forms like those which you mentioned first.

Parmenides declares that no object in nature is mean to the philosopher.

Parm. — You are still young, Sokrates:— you still defer to the common sentiments of mankind. But the time will come when philosophy will take stronger hold of you, and will teach you that no object in nature is mean or contemptible in her view.7

Remarks upon this — Contrast between emotional and scientific classification.

This remark deserves attention. Plato points out the radical distinction, and frequent antipathy between classifications constructed by science, and those which grow up spontaneously under the associating influence of a common emotion. What he calls “the opinions of men,” — in other words, the associations naturally working in an untaught and unlettered mind — bring together the ideas of objects according as they suggest a like emotion — veneration, love, fear, antipathy, contempt, laughter, &c.8 As things which inspire like emotions are thrown into the same category and receive the same denomination, so the opposite proceeding inspires great repugnance, when things creating antipathetic emotions are forced into the same category. A large proportion of objects in nature come to be regarded as unworthy of any serious attention, and fit only to serve for discharging on them our laughter, contempt, or antipathy. The investigation of the structure and manifestations of insects is one of the marked features which Aristophanes ridicules in Sokrates: moreover the same poet also brings odium on the philosopher for alleged study of astronomy and meteorology — the heavenly bodies being as it were at the opposite emotional pole, objects of such reverential admiration and worship, that it was impious to watch or investigate them, or calculate their proceedings beforehand.9 The extent to which anatomy and physiology were shut out from study in antiquity, and have continued to be partially so even in modern times, is well known. And the proportion of phenomena is both great and important, connected with the social relations, which are excluded both from formal registration and from scientific review; kept away from all rational analysis either of causes or remedies, because of the strong repugnances connected with them. This emotional view of nature is here noted by Plato as conflicting with the scientific. No object (he says) is mean in the eyes of philosophy. He remarks to the same effect in the Sophistês and Politikus, and the remark is illustrated by the classifying processes there exhibited:10 mean objects and esteemed objects being placed side by side.

Parmenides now produces various objections against the Platonic variety of dualism: the two distinct but partially inter-communicating worlds — one, of separate, permanent, unchangeable, Forms or Ideas — the other, of individual objects, transient and variable; participating in, and receiving denomination from, these Forms.

Objections of Parmenides — How can objects participate in the Ideas. Each cannot have the whole Idea, nor a part thereof.

1. How (asks Parmenides) can such participation take place? Is the entire Form in each individual object? No: for one and the same Form cannot be at the same time in many distant objects. A part of it therefore must be in one object; another part in another. But this assumes that the Form is divisible — or is not essentially One. Equality is in all equal objects: but how can a part of the Form equality, less than the whole, make objects equal? Again, littleness is in all little objects: that is, a part of the Form littleness is in each. But the Form littleness cannot have parts; because, if it had, the entire Form would be greater than any of its parts, — and the Form littleness cannot be greater than any thing. Moreover, if one part of littleness were added to other parts, the sum of the two would be less, and not greater, than either of the factors. It is plain that none of these Forms can be divisible, or can have parts. Objects therefore cannot participate in the Form by parts or piecemeal. But neither can each object possess the entire Form. Accordingly, since there remains no third possibility, objects cannot participate in the Forms at all.11

Comparing the Idea with the sensible objects partaking in the Idea, there is a likeness between them which must be represented by a higher Idea — and so on ad infinitum.

2. Parmenides now passes to a second argument. The reason why you assume that each one of these Forms exists, is — That when you contemplate many similar objects, one and the same ideal phantom or Concept is suggested by all.12 Thus, when you see many great objects, one common impression of greatness arises from all. Hence you conclude that The Great, or the Form of Greatness, exists as One. But if you take this Form of Greatness, and consider it in comparison with each or all the great individual objects, it will have in common with them something that makes it great. You must therefore search for some higher Form, which represents what belongs in common both to the Form of Greatness and to individual great objects. And this higher Form again, when compared with the rest, will have something in common which must be represented by a Form yet higher: so that there will be an infinite series of Forms, ascending higher and higher, of which you will never reach the topmost.13

Are the Ideas conceptions of the mind, and nothing more? Impossible.

3. Perhaps (suggests Sokrates) each of these Forms is a Conception of the mind and nothing beyond: the Form is not competent to exist out of the mind.14 How? (replies Parmenides.) There cannot be in the mind any Conception, which is a Conception of nothing. Every Conception must be of something really existing: in this case, it is a Conception of some one thing, which you conceive as belonging in common to each and all the objects considered. The Something thus conceived as perpetually One and the same in all, is, the Form. Besides, if you think that individual objects participate in the Forms, and that these Forms are Conceptions of the mind, — you must suppose, either that all objects are made up of Conceptions, and are therefore themselves Concipients: or else that these Forms, though Conceptions, are incapable of conceiving. Neither one nor the other is admissible.15

The Ideas are types or exemplars, and objects partake of them by being likened to them. Impossible.

4. Probably the case stands thus (says Sokrates). These Forms are constants and fixtures in nature, as models or patterns. Particular objects are copies or likenesses of them: and the participation of such objects in the Form consists in being made like to it.16 In that case (replies Parmenides), the Form must itself be like to the objects which have been made like to it. Comparing the Form with the objects, that in which they resemble must itself be a Form: and thus you will have a higher Form above the first Form — and so upwards in the ascending line. This follows necessarily from the hypothesis that the Form is like the objects. The participation of objects in the Form, therefore, cannot consist in being likened to it.17

If Ideas exist, they cannot be knowable by us. We can know only what is relative to ourselves. Individuals are relative to individuals: Ideas relative to Ideas.

5. Here are grave difficulties (continues Parmenides) opposed to this doctrine of yours, affirming the existence of self-existent, substantive, unchangeable, yet participated, Forms. But difficulties still graver remain behind. Such Forms as you describe cannot be cognizable by us: at least it is hard to show how they can be cognizable. Being self-existent and substantive, they are not in us: such of them as are relative, have their relation with each other, not with those particular objects among us, which are called great, little, and so forth, from being supposed to be similar to or participant in the forms, and bearing names the same as those of the Forms. Thus, for example, if I, an individual man, am in the relation of master, I bear that relation to another individual man who is my servant, not to servantship in general (i.e. the Form of servantship, the Servus per se). My servant, again, bears the relation of servant to me, an individual man as master, — not to mastership in general (i.e. to the Form of mastership, the Dominus per se). Both terms of the relation are individual objects. On the other hand, the Forms also bear relation to each other. The Form of servantship (Servus per se) stands in relation to the Form of mastership (Dominus per se). Neither of them correlates with an individual object. The two terms of the relation must be homogeneous, each of them a Form.18

Forms can be known only through the Form of Cognition, which we do not possess.

Now apply this to the case of cognition. The Form of Cognition correlates exclusively with the Form of Truth: the Form of each special Cognition, geometrical or medical, or other, correlates with the Form of Geometry or Medicine. But Cognition as we possess it, correlates only with Truth relatively to us: also, each special Cognition of ours has its special correlating Truth, relatively to us.19 Now the Forms are not in or with us, but apart from us: the Form of Cognition is not our Cognition, the Form of Truth is not our Truth. Forms can be known only through the Form of Cognition, which we do not possess: we cannot therefore know Forms. We have our own cognition, whereby we know what is relative to us; but we know nothing more. Forms, which are not relative to us, lie out of our knowledge. Bonum per se, Pulchrum per se, and the other self-existent Forms or Ideas, are to us altogether unknowable.20

Form of cognition, superior to our Cognition, belongs to the Gods. We cannot know them, nor can they know us.

6. Again, if there be a real self-existent Form of Cognition, apart from that which we or others possess — it must doubtless be far superior in accuracy and perfection to that which we possess.21 The Form of Beauty and the other Forms, must be in like manner superior to that which is found under the same name in individual objects. This perfect Form of Cognition must therefore belong to the Gods, if it belong to any one. But if so, the Gods must have a Form of Truth, the proper object of their Form of Cognition. They cannot know the truth relatively to us, which belongs to our cognition — any more than we can know the more perfect truth belonging to them. So too about other Forms. The perfect Form of mastership belongs to the Gods, correlating with its proper Form of servantship. Their mastership does not correlate with individual objects like us: in other words, they are not our masters, nor are we their servants. Their cognition, again, does not correlate with individual objects like us: in other words, they do not know us, nor do we know them. In like manner, we in our capacity of masters are not masters of them — we as cognizant beings know nothing of them or of that which they know. They can in no way correlate with us, nor can we correlate with them.22

Sum total of objections against the Ideas is grave. But if we do not admit that Ideas exist, and that they are knowable, there can be no dialectic discussion.

Here are some of the objections, Sokrates (concludes Parmenides), which beset your doctrine, that there exist substantive, self-standing, Forms of Ideas, each respectively definable. Many farther objections might also be urged.23 So that a man may reasonably maintain, either that none such exist — or that, granting their existence, they are essentially unknowable by us. He must put forth great ingenuity to satisfy himself of the affirmative; and still more wonderful ingenuity to find arguments for the satisfaction of others, respecting this question.

Nevertheless, on the other side (continues Parmenides), unless we admit the existence of such Forms or Ideas — substantive, eternal, unchangeable, definable — philosophy and dialectic discussion are impossible.24

Dilemma put by Parmenides — Acuteness of his objections.

The doctrine which Parmenides attacks is the genuine Platonic theory of Ideas. His objections are never answered in any part of the Platonic dialogues.

It is true that Sokrates is here introduced as juvenile and untrained; or at least as imperfectly trained. And accordingly, Stallbaum with others think, that this is the reason of his inability to meet the objections: which (they tell us), though ingenious and plausible, yet having no application to the genuine Platonic doctrine about Ideas, might easily have been answered if Plato had thought fit, and are answered in other dialogues.25 But to me it appears, that the doctrine which is challenged in the Parmenidês is the genuine Platonic doctrine about Ideas, as enunciated by Plato in the Republic, Phædon, Philêbus, Timæus, and elsewhere — though a very different doctrine is announced in the Sophistês. Objections are here made against it in the Parmenidês. In what other dialogue has Plato answered them? and what proof can be furnished that he was able to answer them? There are indeed many other dialogues in which a real world of Ideas absolute and unchangeable, is affirmed strenuously and eloquently, with various consequences and accompaniments traced to it: but there are none in which the Parmenidean objections are elucidated, or even recited. In the Phædon, Phædrus, Timæus, Symposion, &c., and elsewhere, Sokrates is made to talk confidently about the existence and even about the cognoscibility of these Ideas; just as if no such objections as those which we read in the Parmenidês could be produced.26 In these other dialogues, Plato accepts implicitly one horn of the Parmenidean dilemma; but without explaining to us upon what grounds he allows himself to neglect the other.