Introduction and Analysis

The awe with which Plato regarded the character of 'the great' Parmenides has extended to the dialogue which he calls by his name. None of the writings of Plato have been more copiously illustrated, both in ancient and modern times, and in none of them have the interpreters been more at variance with one another. Nor is this surprising. For the Parmenides is more fragmentary and isolated than any other dialogue, and the design of the writer is not expressly stated. The date is uncertain; the relation to the other writings of Plato is also uncertain; the connexion between the two parts is at first sight extremely obscure; and in the latter of the two we are left in doubt as to whether Plato is speaking his own sentiments by the lips of Parmenides, and overthrowing him out of his own mouth, or whether he is propounding consequences which would have been admitted by Zeno and Parmenides themselves. The contradictions which follow from the hypotheses of the one and many have been regarded by some as transcendental mysteries; by others as a mere illustration, taken at random, of a new method. They seem to have been inspired by a sort of dialectical frenzy, such as may be supposed to have prevailed in the Megarian School (compare Cratylus, etc.). The criticism on his own doctrine of Ideas has also been considered, not as a real criticism, but as an exuberance of the metaphysical imagination which enabled Plato to go beyond himself. To the latter part of the dialogue we may certainly apply the words in which he himself describes the earlier philosophers in the Sophist: 'They went on their way rather regardless of whether we understood them or not.'

The awe Plato felt for the character of 'the great' Parmenides has extended to the dialogue named after him. None of Plato's writings have received more extensive commentary, both in ancient and modern times. Nor have interpreters disagreed more about any of them. This is not surprising. The Parmenides is more fragmentary and isolated than any other dialogue, and Plato does not state his purpose explicitly. The date of the dialogue is uncertain, as is its relationship to Plato's other writings. At first, the connection between its two parts is extremely obscure. In the second part, we are left uncertain about Plato's intentions. Is he expressing his own views through Parmenides and making Parmenides refute himself? Or is he presenting conclusions that Zeno and Parmenides themselves would have accepted? Some have regarded the contradictions arising from the hypotheses of the one and the many as transcendental mysteries. Others see them as just a randomly chosen example of a new method. The contradictions seem to have been inspired by a kind of dialectical frenzy. We might suppose that such a frenzy prevailed in the Megarian School (compare Cratylus, etc.). Some have also viewed Plato's criticism of his own doctrine of Ideas as something other than genuine criticism. They see it as an outpouring of metaphysical imagination that allowed Plato to go beyond himself. We can certainly apply Plato's own words about the earlier philosophers in the Sophist to the latter part of the dialogue: 'They went on their way rather regardless of whether we understood them or not.'

The Parmenides in point of style is one of the best of the Platonic writings; the first portion of the dialogue is in no way defective in ease and grace and dramatic interest; nor in the second part, where there was no room for such qualities, is there any want of clearness or precision. The latter half is an exquisite mosaic, of which the small pieces are with the utmost fineness and regularity adapted to one another. Like the Protagoras, Phaedo, and others, the whole is a narrated dialogue, combining with the mere recital of the words spoken, the observations of the reciter on the effect produced by them. Thus we are informed by him that Zeno and Parmenides were not altogether pleased at the request of Socrates that they would examine into the nature of the one and many in the sphere of Ideas, although they received his suggestion with approving smiles. And we are glad to be told that Parmenides was 'aged but well-favoured,' and that Zeno was 'very good-looking'; also that Parmenides affected to decline the great argument, on which, as Zeno knew from experience, he was not unwilling to enter. The character of Antiphon, the half-brother of Plato, who had once been inclined to philosophy, but has now shown the hereditary disposition for horses, is very naturally described. He is the sole depositary of the famous dialogue; but, although he receives the strangers like a courteous gentleman, he is impatient of the trouble of reciting it. As they enter, he has been giving orders to a bridle-maker; by this slight touch Plato verifies the previous description of him. After a little persuasion he is induced to favour the Clazomenians, who come from a distance, with a rehearsal. Respecting the visit of Zeno and Parmenides to Athens, we may observe—first, that such a visit is consistent with dates, and may possibly have occurred; secondly, that Plato is very likely to have invented the meeting ('You, Socrates, can easily invent Egyptian tales or anything else,' Phaedrus); thirdly, that no reliance can be placed on the circumstance as determining the date of Parmenides and Zeno; fourthly, that the same occasion appears to be referred to by Plato in two other places (Theaet., Soph.).

In style, the Parmenides is one of Plato's best writings. The first part of the dialogue is graceful and easy to read, and it holds our interest as a drama. The second part has no room for those qualities, but it is clear and precise. The latter half is an exquisite mosaic, whose small pieces fit together with great delicacy and regularity. Like the Protagoras, Phaedo, and other works, it is a narrated dialogue. Along with the words spoken, the narrator describes their effect. For example, the narrator tells us that Zeno and Parmenides were not entirely pleased by a request from Socrates. He had asked them to examine the nature of the one and the many in the realm of Ideas. Yet they received his suggestion with approving smiles. We are glad to learn that Parmenides was 'old but handsome,' and that Zeno was 'very good-looking.' We also learn that Parmenides pretended to decline the great argument. As Zeno knew from experience, Parmenides was not unwilling to take it up. The character of Antiphon, Plato's half-brother, is described very naturally. He had once been interested in philosophy, but has now shown his family's inherited fondness for horses. He is the only person who knows the famous dialogue. Although he receives the strangers like a courteous gentleman, he resents the trouble of reciting it. As they enter, he has been giving orders to a bridle-maker. With this small detail, Plato confirms his earlier description of Antiphon. After a little persuasion, Antiphon agrees to recite the dialogue for the Clazomenians, who have come from far away. As for the visit of Zeno and Parmenides to Athens, we may note four points. First, such a visit is consistent with the dates and may have happened. Second, Plato is very likely to have invented the meeting. As the Phaedrus says, 'You, Socrates, can easily invent Egyptian tales or anything else.' Third, the visit cannot be relied on to establish the dates of Parmenides and Zeno. Fourth, Plato seems to refer to the same occasion in two other places (Theaet., Soph.).

Many interpreters have regarded the Parmenides as a 'reductio ad absurdum' of the Eleatic philosophy. But would Plato have been likely to place this in the mouth of the great Parmenides himself, who appeared to him, in Homeric language, to be 'venerable and awful,' and to have a 'glorious depth of mind'? (Theaet.). It may be admitted that he has ascribed to an Eleatic stranger in the Sophist opinions which went beyond the doctrines of the Eleatics. But the Eleatic stranger expressly criticises the doctrines in which he had been brought up; he admits that he is going to 'lay hands on his father Parmenides.' Nothing of this kind is said of Zeno and Parmenides. How then, without a word of explanation, could Plato assign to them the refutation of their own tenets?

Many interpreters have seen the Parmenides as a 'reductio ad absurdum' of Eleatic philosophy. But would Plato likely have put such a refutation in the mouth of the great Parmenides himself? Plato saw him, in Homeric language, as 'venerable and awful' and as having a 'glorious depth of mind' (Theaet.). It may be admitted that Plato gave an Eleatic stranger in the Sophist views that went beyond Eleatic doctrines. But the Eleatic stranger explicitly criticizes the doctrines he was raised with. He admits that he is going to 'lay hands on his father Parmenides.' Nothing of this kind is said of Zeno and Parmenides. How, then, could Plato have them refute their own beliefs without a word of explanation?

The conclusion at which we must arrive is that the Parmenides is not a refutation of the Eleatic philosophy. Nor would such an explanation afford any satisfactory connexion of the first and second parts of the dialogue. And it is quite inconsistent with Plato's own relation to the Eleatics. For of all the pre-Socratic philosophers, he speaks of them with the greatest respect. But he could hardly have passed upon them a more unmeaning slight than to ascribe to their great master tenets the reverse of those which he actually held.

We must conclude that the Parmenides is not a refutation of Eleatic philosophy. Nor would that explanation satisfactorily connect the first and second parts of the dialogue. It is also quite inconsistent with Plato's own relationship to the Eleatics. For he speaks of them with the greatest respect of all the pre-Socratic philosophers. But he could hardly have insulted them more pointlessly than by attributing to their great master beliefs opposite to those he actually held.

Two preliminary remarks may be made. First, that whatever latitude we may allow to Plato in bringing together by a 'tour de force,' as in the Phaedrus, dissimilar themes, yet he always in some way seeks to find a connexion for them. Many threads join together in one the love and dialectic of the Phaedrus. We cannot conceive that the great artist would place in juxtaposition two absolutely divided and incoherent subjects. And hence we are led to make a second remark: viz. that no explanation of the Parmenides can be satisfactory which does not indicate the connexion of the first and second parts. To suppose that Plato would first go out of his way to make Parmenides attack the Platonic Ideas, and then proceed to a similar but more fatal assault on his own doctrine of Being, appears to be the height of absurdity.

Two preliminary remarks may be made. First, Plato sometimes brings dissimilar themes together by a 'tour de force', as in the Phaedrus. However much freedom we allow him in doing so, he always seeks some connection between them. Many threads join love and dialectic in the Phaedrus. We cannot imagine that the great artist would put two completely separate and unrelated subjects side by side. This leads to a second remark: no explanation of the Parmenides can be satisfactory unless it shows how its two parts connect. Suppose Plato first went out of his way to have Parmenides attack the Platonic Ideas. Suppose he then made a similar but more devastating attack on his own doctrine of Being. This seems the height of absurdity.

Perhaps there is no passage in Plato showing greater metaphysical power than that in which he assails his own theory of Ideas. The arguments are nearly, if not quite, those of Aristotle; they are the objections which naturally occur to a modern student of philosophy. Many persons will be surprised to find Plato criticizing the very conceptions which have been supposed in after ages to be peculiarly characteristic of him. How can he have placed himself so completely without them? How can he have ever persisted in them after seeing the fatal objections which might be urged against them? The consideration of this difficulty has led a recent critic (Ueberweg), who in general accepts the authorised canon of the Platonic writings, to condemn the Parmenides as spurious. The accidental want of external evidence, at first sight, seems to favour this opinion.

Perhaps no passage in Plato shows greater metaphysical power than his attack on his own theory of Ideas. His arguments are nearly, if not quite, the same as Aristotle’s. They are the objections that would naturally occur to a modern student of philosophy. Many people will be surprised to find Plato criticizing the very ideas later ages regarded as uniquely characteristic of him. How could he have stood so completely outside those ideas? How could he have continued to believe in them after seeing the fatal objections that could be raised against them? This difficulty has led a recent critic, Ueberweg, to reject the Parmenides as spurious. Ueberweg generally accepts the recognized canon of Plato’s writings. At first glance, the lack of external evidence, which is accidental, seems to support his view.

In answer, it might be sufficient to say, that no ancient writing of equal length and excellence is known to be spurious. Nor is the silence of Aristotle to be hastily assumed; there is at least a doubt whether his use of the same arguments does not involve the inference that he knew the work. And, if the Parmenides is spurious, like Ueberweg, we are led on further than we originally intended, to pass a similar condemnation on the Theaetetus and Sophist, and therefore on the Politicus (compare Theaet., Soph.). But the objection is in reality fanciful, and rests on the assumption that the doctrine of the Ideas was held by Plato throughout his life in the same form. For the truth is, that the Platonic Ideas were in constant process of growth and transmutation; sometimes veiled in poetry and mythology, then again emerging as fixed Ideas, in some passages regarded as absolute and eternal, and in others as relative to the human mind, existing in and derived from external objects as well as transcending them. The anamnesis of the Ideas is chiefly insisted upon in the mythical portions of the dialogues, and really occupies a very small space in the entire works of Plato. Their transcendental existence is not asserted, and is therefore implicitly denied in the Philebus; different forms are ascribed to them in the Republic, and they are mentioned in the Theaetetus, the Sophist, the Politicus, and the Laws, much as Universals would be spoken of in modern books. Indeed, there are very faint traces of the transcendental doctrine of Ideas, that is, of their existence apart from the mind, in any of Plato's writings, with the exception of the Meno, the Phaedrus, the Phaedo, and in portions of the Republic. The stereotyped form which Aristotle has given to them is not found in Plato (compare Essay on the Platonic Ideas in the Introduction to the Meno.)

In answer, it might be enough to say that no ancient writing of equal length and excellence is known to be spurious. Nor should we hastily assume that Aristotle was silent about it. At the very least, his use of the same arguments may suggest that he knew the work. And if the Parmenides is spurious, we are led, like Ueberweg, further than we originally intended. We must similarly condemn the Theaetetus and Sophist, and therefore the Politicus (compare Theaet., Soph.). But the objection is really fanciful. It rests on the assumption that Plato held the doctrine of the Ideas in the same form throughout his life. In truth, Plato's Ideas were constantly developing and changing. Sometimes they were veiled in poetry and mythology. At other times, they emerged as fixed Ideas. In some passages, they are regarded as absolute and eternal. In others, they are relative to the human mind, existing in and derived from external objects as well as transcending them. The recollection, or anamnesis, of the Ideas is chiefly emphasized in the mythical parts of the dialogues. It occupies very little space in Plato's works as a whole. The Philebus does not assert the transcendental existence of the Ideas and therefore implicitly denies it. The Republic assigns them different forms. In the Theaetetus, the Sophist, the Politicus, and the Laws, they are mentioned much as Universals would be in modern books. Indeed, the transcendental doctrine of Ideas, meaning their existence apart from the mind, leaves very faint traces in Plato's writings. The exceptions are the Meno, the Phaedrus, the Phaedo, and parts of the Republic. The fixed form Aristotle gave the Ideas is not found in Plato (compare Essay on the Platonic Ideas in the Introduction to the Meno).

The full discussion of this subject involves a comprehensive survey of the philosophy of Plato, which would be out of place here. But, without digressing further from the immediate subject of the Parmenides, we may remark that Plato is quite serious in his objections to his own doctrines: nor does Socrates attempt to offer any answer to them. The perplexities which surround the one and many in the sphere of the Ideas are also alluded to in the Philebus, and no answer is given to them. Nor have they ever been answered, nor can they be answered by any one else who separates the phenomenal from the real. To suppose that Plato, at a later period of his life, reached a point of view from which he was able to answer them, is a groundless assumption. The real progress of Plato's own mind has been partly concealed from us by the dogmatic statements of Aristotle, and also by the degeneracy of his own followers, with whom a doctrine of numbers quickly superseded Ideas.

A full discussion of this subject would require a comprehensive survey of Plato’s philosophy, which would be out of place here. But we can make one observation without straying further from the immediate subject of the Parmenides. Plato takes his objections to his own doctrines quite seriously, and Socrates makes no attempt to answer them. The Philebus also mentions the puzzles surrounding the one and the many in the realm of Ideas. It gives no answer to them. Nor have these puzzles ever been answered. Nor can anyone who separates appearances from reality answer them. There is no basis for assuming that Plato later reached a point of view from which he could answer them. Aristotle’s dogmatic statements have partly obscured the actual development of Plato’s thinking. So has the decline of Plato’s own followers, among whom a doctrine of numbers quickly replaced Ideas.

As a preparation for answering some of the difficulties which have been suggested, we may begin by sketching the first portion of the dialogue:—

To prepare to answer some of the difficulties raised, we may begin by outlining the first part of the dialogue:

Cephalus, of Clazomenae in Ionia, the birthplace of Anaxagoras, a citizen of no mean city in the history of philosophy, who is the narrator of the dialogue, describes himself as meeting Adeimantus and Glaucon in the Agora at Athens. 'Welcome, Cephalus: can we do anything for you in Athens?' 'Why, yes: I came to ask a favour of you. First, tell me your half-brother's name, which I have forgotten—he was a mere child when I was last here;—I know his father's, which is Pyrilampes.' 'Yes, and the name of our brother is Antiphon. But why do you ask?' 'Let me introduce to you some countrymen of mine, who are lovers of philosophy; they have heard that Antiphon remembers a conversation of Socrates with Parmenides and Zeno, of which the report came to him from Pythodorus, Zeno's friend.' 'That is quite true.' 'And can they hear the dialogue?' 'Nothing easier; in the days of his youth he made a careful study of the piece; at present, his thoughts have another direction: he takes after his grandfather, and has given up philosophy for horses.'

Cephalus narrates the dialogue. He is from Clazomenae in Ionia, the birthplace of Anaxagoras. Clazomenae is a city of considerable importance in the history of philosophy. Cephalus describes meeting Adeimantus and Glaucon in the Agora at Athens. ‘Welcome, Cephalus. Can we do anything for you in Athens?’ ‘Yes, I came to ask you a favor. First, tell me your half-brother’s name. I have forgotten it. He was just a child when I was last here. I know his father’s name is Pyrilampes.’ ‘Yes, and our brother’s name is Antiphon. But why do you ask?’ ‘Let me introduce some of my fellow countrymen, who love philosophy. They have heard that Antiphon remembers a conversation between Socrates, Parmenides, and Zeno. He heard an account of it from Pythodorus, Zeno’s friend.’ ‘That is quite true.’ ‘Can they hear the conversation?’ ‘Nothing could be easier. He studied the account carefully when he was young. But his interests now lie elsewhere. Like his grandfather, he has given up philosophy for horses.’

'We went to look for him, and found him giving instructions to a worker in brass about a bridle. When he had done with him, and had learned from his brothers the purpose of our visit, he saluted me as an old acquaintance, and we asked him to repeat the dialogue. At first, he complained of the trouble, but he soon consented. He told us that Pythodorus had described to him the appearance of Parmenides and Zeno; they had come to Athens at the great Panathenaea, the former being at the time about sixty-five years old, aged but well-favoured—Zeno, who was said to have been beloved of Parmenides in the days of his youth, about forty, and very good-looking:—that they lodged with Pythodorus at the Ceramicus outside the wall, whither Socrates, then a very young man, came to see them: Zeno was reading one of his theses, which he had nearly finished, when Pythodorus entered with Parmenides and Aristoteles, who was afterwards one of the Thirty. When the recitation was completed, Socrates requested that the first thesis of the treatise might be read again.'

'We went to look for him and found him giving a brass worker instructions about a bridle. When he had finished and learned from his brothers why we had come, he greeted me as an old acquaintance. We asked him to repeat the dialogue. At first, he complained about the trouble, but he soon agreed. He told us that Pythodorus had described Parmenides and Zeno to him. They had come to Athens for the great Panathenaea. Parmenides was about sixty-five at the time, old but still handsome. Zeno was about forty and very good-looking. He was said to have been loved by Parmenides when he was young. They were staying with Pythodorus in the Ceramicus outside the city wall. Socrates, who was then very young, came there to see them. Zeno was reading one of his theses and had nearly finished when Pythodorus entered with Parmenides and Aristoteles. Aristoteles later became one of the Thirty. When Zeno finished reading, Socrates asked him to read the first thesis of the treatise again.'

'You mean, Zeno,' said Socrates, 'to argue that being, if it is many, must be both like and unlike, which is a contradiction; and each division of your argument is intended to elicit a similar absurdity, which may be supposed to follow from the assumption that being is many.' 'Such is my meaning.' 'I see,' said Socrates, turning to Parmenides, 'that Zeno is your second self in his writings too; you prove admirably that the all is one: he gives proofs no less convincing that the many are nought. To deceive the world by saying the same thing in entirely different forms, is a strain of art beyond most of us.' 'Yes, Socrates,' said Zeno; 'but though you are as keen as a Spartan hound, you do not quite catch the motive of the piece, which was only intended to protect Parmenides against ridicule by showing that the hypothesis of the existence of the many involved greater absurdities than the hypothesis of the one. The book was a youthful composition of mine, which was stolen from me, and therefore I had no choice about the publication.' 'I quite believe you,' said Socrates; 'but will you answer me a question? I should like to know, whether you would assume an idea of likeness in the abstract, which is the contradictory of unlikeness in the abstract, by participation in either or both of which things are like or unlike or partly both. For the same things may very well partake of like and unlike in the concrete, though like and unlike in the abstract are irreconcilable. Nor does there appear to me to be any absurdity in maintaining that the same things may partake of the one and many, though I should be indeed surprised to hear that the absolute one is also many. For example, I, being many, that is to say, having many parts or members, am yet also one, and partake of the one, being one of seven who are here present (compare Philebus). This is not an absurdity, but a truism. But I should be amazed if there were a similar entanglement in the nature of the ideas themselves, nor can I believe that one and many, like and unlike, rest and motion, in the abstract, are capable either of admixture or of separation.'

'You mean, Zeno,' said Socrates, 'to argue that if being is many, it must be both like and unlike. That is a contradiction. Each part of your argument is meant to bring out a similar absurdity. Each absurdity may be thought to follow from the assumption that being is many.' 'That is what I mean.' 'I see,' said Socrates, turning to Parmenides, 'that Zeno is your second self in his writing too. You prove admirably that the whole is one. He gives equally convincing proofs that the many are nothing. To fool the world by saying the same thing in entirely different ways takes more skill than most of us possess.' 'Yes, Socrates,' said Zeno, 'but although you are as keen as a Spartan hound, you have not quite caught the purpose of my work. It was meant only to protect Parmenides from ridicule. It showed that the hypothesis that the many exist leads to greater absurdities than the hypothesis that the one exists. I wrote the book in my youth, and it was stolen from me. So I had no choice about its publication.' 'I quite believe you,' said Socrates. 'But will you answer a question? I would like to know whether you would accept an idea of likeness in itself, which is the opposite of unlikeness in itself. By participating in either or both, things are like, unlike, or partly both. The same things may very well share in both likeness and unlikeness, although likeness and unlikeness themselves cannot be reconciled. 'Nor does it seem absurd to me that the same things may share in both the one and the many. But I would indeed be surprised to hear that the one itself is also many. For example, I am many because I have many parts or limbs. Yet I am also one and share in the one, since I am one of seven people here (compare Philebus). That is not absurd. It is obviously true. 'But I would be amazed if the ideas themselves were tangled together in the same way. Nor can I believe that the ideas of one and many, like and unlike, and rest and motion can be mixed or separated.'

Pythodorus said that in his opinion Parmenides and Zeno were not very well pleased at the questions which were raised; nevertheless, they looked at one another and smiled in seeming delight and admiration of Socrates. 'Tell me,' said Parmenides, 'do you think that the abstract ideas of likeness, unity, and the rest, exist apart from individuals which partake of them? and is this your own distinction?' 'I think that there are such ideas.' 'And would you make abstract ideas of the just, the beautiful, the good?' 'Yes,' he said. 'And of human beings like ourselves, of water, fire, and the like?' 'I am not certain.' 'And would you be undecided also about ideas of which the mention will, perhaps, appear laughable: of hair, mud, filth, and other things which are base and vile?' 'No, Parmenides; visible things like these are, as I believe, only what they appear to be: though I am sometimes disposed to imagine that there is nothing without an idea; but I repress any such notion, from a fear of falling into an abyss of nonsense.' 'You are young, Socrates, and therefore naturally regard the opinions of men; the time will come when philosophy will have a firmer hold of you, and you will not despise even the meanest things. But tell me, is your meaning that things become like by partaking of likeness, great by partaking of greatness, just and beautiful by partaking of justice and beauty, and so of other ideas?' 'Yes, that is my meaning.' 'And do you suppose the individual to partake of the whole, or of the part?' 'Why not of the whole?' said Socrates. 'Because,' said Parmenides, 'in that case the whole, which is one, will become many.' 'Nay,' said Socrates, 'the whole may be like the day, which is one and in many places: in this way the ideas may be one and also many.' 'In the same sort of way,' said Parmenides, 'as a sail, which is one, may be a cover to many—that is your meaning?' 'Yes.' 'And would you say that each man is covered by the whole sail, or by a part only?' 'By a part.' 'Then the ideas have parts, and the objects partake of a part of them only?' 'That seems to follow.' 'And would you like to say that the ideas are really divisible and yet remain one?' 'Certainly not.' 'Would you venture to affirm that great objects have a portion only of greatness transferred to them; or that small or equal objects are small or equal because they are only portions of smallness or equality?' 'Impossible.' 'But how can individuals participate in ideas, except in the ways which I have mentioned?' 'That is not an easy question to answer.' 'I should imagine the conception of ideas to arise as follows: you see great objects pervaded by a common form or idea of greatness, which you abstract.' 'That is quite true.' 'And supposing you embrace in one view the idea of greatness thus gained and the individuals which it comprises, a further idea of greatness arises, which makes both great; and this may go on to infinity.' Socrates replies that the ideas may be thoughts in the mind only; in this case, the consequence would no longer follow. 'But must not the thought be of something which is the same in all and is the idea? And if the world partakes in the ideas, and the ideas are thoughts, must not all things think? Or can thought be without thought?' 'I acknowledge the unmeaningness of this,' says Socrates, 'and would rather have recourse to the explanation that the ideas are types in nature, and that other things partake of them by becoming like them.' 'But to become like them is to be comprehended in the same idea; and the likeness of the idea and the individuals implies another idea of likeness, and another without end.' 'Quite true.' 'The theory, then, of participation by likeness has to be given up. You have hardly yet, Socrates, found out the real difficulty of maintaining abstract ideas.' 'What difficulty?' 'The greatest of all perhaps is this: an opponent will argue that the ideas are not within the range of human knowledge; and you cannot disprove the assertion without a long and laborious demonstration, which he may be unable or unwilling to follow. In the first place, neither you nor any one who maintains the existence of absolute ideas will affirm that they are subjective.' 'That would be a contradiction.' 'True; and therefore any relation in these ideas is a relation which concerns themselves only; and the objects which are named after them, are relative to one another only, and have nothing to do with the ideas themselves.' 'How do you mean?' said Socrates. 'I may illustrate my meaning in this way: one of us has a slave; and the idea of a slave in the abstract is relative to the idea of a master in the abstract; this correspondence of ideas, however, has nothing to do with the particular relation of our slave to us.—Do you see my meaning?' 'Perfectly.' 'And absolute knowledge in the same way corresponds to absolute truth and being, and particular knowledge to particular truth and being.' Clearly.' 'And there is a subjective knowledge which is of subjective truth, having many kinds, general and particular. But the ideas themselves are not subjective, and therefore are not within our ken.' 'They are not.' 'Then the beautiful and the good in their own nature are unknown to us?' 'It would seem so.' 'There is a worse consequence yet.' 'What is that?' 'I think we must admit that absolute knowledge is the most exact knowledge, which we must therefore attribute to God. But then see what follows: God, having this exact knowledge, can have no knowledge of human things, as we have divided the two spheres, and forbidden any passing from one to the other:—the gods have knowledge and authority in their world only, as we have in ours.' 'Yet, surely, to deprive God of knowledge is monstrous.'—'These are some of the difficulties which are involved in the assumption of absolute ideas; the learner will find them nearly impossible to understand, and the teacher who has to impart them will require superhuman ability; there will always be a suspicion, either that they have no existence, or are beyond human knowledge.' 'There I agree with you,' said Socrates. 'Yet if these difficulties induce you to give up universal ideas, what becomes of the mind? and where are the reasoning and reflecting powers? philosophy is at an end.' 'I certainly do not see my way.' 'I think,' said Parmenides, 'that this arises out of your attempting to define abstractions, such as the good and the beautiful and the just, before you have had sufficient previous training; I noticed your deficiency when you were talking with Aristoteles, the day before yesterday. Your enthusiasm is a wonderful gift; but I fear that unless you discipline yourself by dialectic while you are young, truth will elude your grasp.' 'And what kind of discipline would you recommend?' 'The training which you heard Zeno practising; at the same time, I admire your saying to him that you did not care to consider the difficulty in reference to visible objects, but only in relation to ideas.' 'Yes; because I think that in visible objects you may easily show any number of inconsistent consequences.' 'Yes; and you should consider, not only the consequences which follow from a given hypothesis, but the consequences also which follow from the denial of the hypothesis. For example, what follows from the assumption of the existence of the many, and the counter-argument of what follows from the denial of the existence of the many: and similarly of likeness and unlikeness, motion, rest, generation, corruption, being and not being. And the consequences must include consequences to the things supposed and to other things, in themselves and in relation to one another, to individuals whom you select, to the many, and to the all; these must be drawn out both on the affirmative and on the negative hypothesis,—that is, if you are to train yourself perfectly to the intelligence of the truth.' 'What you are suggesting seems to be a tremendous process, and one of which I do not quite understand the nature,' said Socrates; 'will you give me an example?' 'You must not impose such a task on a man of my years,' said Parmenides. 'Then will you, Zeno?' 'Let us rather,' said Zeno, with a smile, 'ask Parmenides, for the undertaking is a serious one, as he truly says; nor could I urge him to make the attempt, except in a select audience of persons who will understand him.' The whole party joined in the request.

Pythodorus said that he thought Parmenides and Zeno were not very pleased by the questions raised. Nevertheless, they looked at each other and smiled, apparently delighted and impressed by Socrates. 'Tell me,' said Parmenides, 'do you think that the abstract ideas of likeness, unity, and the rest exist separately from the individual things that share in them? And is this distinction your own?' 'I think there are such ideas.' 'And would you also say there are abstract ideas of justice, beauty, and goodness?' 'Yes,' he said. 'And of human beings like ourselves, of water, fire, and the like?' 'I am not certain.' 'And would you also be uncertain about ideas that may sound ridiculous to mention, such as hair, mud, filth, and other low and vile things?' 'No, Parmenides. I believe visible things like these are only what they appear to be. Though I am sometimes inclined to imagine that nothing exists without an idea, I put the thought aside. I fear falling into an abyss of nonsense.' 'You are young, Socrates, so naturally you care about what people think. The time will come when philosophy has a firmer hold on you, and you will not despise even the lowest things. But tell me, is this what you mean? Things become alike by sharing in likeness, great by sharing in greatness, just and beautiful by sharing in justice and beauty, and so on with the other ideas?' 'Yes, that is what I mean.' 'And do you suppose that an individual thing shares in the whole idea, or only in part of it?' 'Why not the whole?' said Socrates. 'Because,' said Parmenides, 'in that case the whole, which is one, will become many.' 'No,' said Socrates, 'the whole may be like the day, which is one and exists in many places. In this way, the ideas may be both one and many.' 'Do you mean,' said Parmenides, 'that it is like a single sail covering many people?' 'Yes.' 'And would you say that each person is covered by the whole sail, or only by part of it?' 'By a part.' 'Then the ideas have parts, and things share only in a part of them?' 'That seems to follow.' 'And would you want to say that the ideas can really be divided and yet remain one?' 'Certainly not.' 'Would you dare to claim that great things receive only a portion of greatness? Or that small or equal things are small or equal because they are only portions of smallness or equality?' 'Impossible.' 'But how can individual things share in ideas, except in the ways I have mentioned?' 'That is not an easy question to answer.' 'I imagine that the idea of greatness arises like this. You see great things and recognize a common form or idea of greatness present in them. You then draw that idea from them.' 'That is quite true.' 'Now suppose you look at the idea of greatness you have gained and the individual things it includes together. A further idea of greatness then arises, making both the idea and the things great. And this may go on forever.' Socrates replies that ideas may exist only as thoughts in the mind. In that case, this consequence would no longer follow. 'But must the thought not be about something that is the same in all the things and is the idea? And if the world shares in the ideas, and the ideas are thoughts, must not all things think? Or can there be thought without thinking?' 'I admit that this makes no sense,' says Socrates. 'I would rather turn to the explanation that ideas are patterns in nature, and other things share in them by becoming like them.' 'But to become like the ideas is to be included in the same idea. And the likeness between an idea and individual things implies another idea of likeness, and then another, without end.' 'Quite true.' 'Then the theory that things share in ideas by being like them must be abandoned. Socrates, you have hardly yet discovered the real difficulty of maintaining that abstract ideas exist.' 'What difficulty?' 'Perhaps the greatest difficulty is this. An opponent will argue that ideas are beyond human knowledge. You cannot disprove this claim without a long and demanding demonstration, which your opponent may be unable or unwilling to follow. First, neither you nor anyone else who maintains that absolute ideas exist will say that they are subjective.' 'That would be a contradiction.' 'True. So any relation between these ideas concerns only the ideas themselves. And the things named after them are related only to one another and have nothing to do with the ideas themselves.' 'What do you mean?' said Socrates. 'I can explain it this way. One of us has a slave. The abstract idea of a slave is related to the abstract idea of a master. But this relation between the ideas has nothing to do with the particular relation between our slave and us. Do you see what I mean?' 'Perfectly.' 'In the same way, absolute knowledge corresponds to absolute truth and being, and particular knowledge to particular truth and being.' 'Clearly.' 'And there is a subjective knowledge of subjective truth, with many kinds, both general and particular. But the ideas themselves are not subjective, so they are beyond our knowledge.' 'They are.' 'Then we do not know beauty and goodness as they are in themselves?' 'It would seem so.' 'There is an even worse consequence.' 'What is that?' 'I think we must admit that absolute knowledge is the most exact knowledge, so we must attribute it to God. But consider what follows. God has this exact knowledge, yet he can have no knowledge of human things. We have divided the two spheres and forbidden any crossing from one to the other. The gods have knowledge and authority only in their world, just as we do in ours.' 'Yet surely it is monstrous to deny God knowledge.' 'These are some of the difficulties involved in assuming that absolute ideas exist. A learner will find them nearly impossible to understand. A teacher trying to explain them will need superhuman ability. There will always be a suspicion that the ideas either do not exist or are beyond human knowledge.' 'I agree with you there,' said Socrates. 'Yet if these difficulties lead you to give up universal ideas, what becomes of the mind? What becomes of our powers of reasoning and reflection? Philosophy comes to an end.' 'I certainly do not see a way forward.' 'I think,' said Parmenides, 'that this is because you are trying to define abstractions, such as goodness, beauty, and justice, before you have had enough training. I noticed your lack of training when you were talking with Aristoteles the day before yesterday. Your enthusiasm is a wonderful gift. But I fear that truth will escape you unless you discipline yourself through dialectic while you are young.' 'And what kind of discipline would you recommend?' 'The training you heard Zeno practicing. At the same time, I admire what you said to him. You said you did not care to consider the difficulty in relation to visible objects, but only in relation to ideas.' 'Yes, because I think you can easily show any number of inconsistent consequences in visible objects.' 'Yes. And you should consider not only the consequences of a given hypothesis, but also the consequences of denying it. For example, consider what follows if the many exist, and then what follows if the many do not exist. Do the same for likeness and unlikeness, motion, rest, coming into being, destruction, being and not being. 'You must consider the consequences for the things assumed and for other things. Consider them in themselves and in relation to one another. Consider the consequences for individuals you select, for the many, and for the all. You must work out these consequences both if the hypothesis is true and if it is not. You must do this if you are to train yourself fully to understand the truth.' 'What you suggest seems like a tremendous task, and I do not quite understand what it involves,' said Socrates. 'Will you give me an example?' 'You must not impose such a task on a man of my age,' said Parmenides. 'Then will you, Zeno?' 'Let us ask Parmenides instead,' said Zeno with a smile. 'As he rightly says, the undertaking is a serious one. I could not urge him to attempt it except before a select audience who will understand him.' The whole party joined in the request.

Here we have, first of all, an unmistakable attack made by the youthful Socrates on the paradoxes of Zeno. He perfectly understands their drift, and Zeno himself is supposed to admit this. But they appear to him, as he says in the Philebus also, to be rather truisms than paradoxes. For every one must acknowledge the obvious fact, that the body being one has many members, and that, in a thousand ways, the like partakes of the unlike, the many of the one. The real difficulty begins with the relations of ideas in themselves, whether of the one and many, or of any other ideas, to one another and to the mind. But this was a problem which the Eleatic philosophers had never considered; their thoughts had not gone beyond the contradictions of matter, motion, space, and the like.

First, we see the young Socrates clearly attacking Zeno’s paradoxes. Socrates fully understands what they mean, and Zeno himself is presented as admitting this. But, as Socrates also says in the Philebus, the paradoxes seem to him more like obvious truths than paradoxes. Everyone must recognize the obvious fact that the body is one thing but has many parts. Everyone must also recognize that, in countless ways, what is alike shares in what is unlike, and the many share in the one. The real difficulty begins with the relations of ideas themselves to one another and to the mind. This applies to the ideas of the one and the many, or to any other ideas. But the Eleatic philosophers had never considered this problem. Their thinking had not gone beyond the contradictions of matter, motion, space, and similar things.

It was no wonder that Parmenides and Zeno should hear the novel speculations of Socrates with mixed feelings of admiration and displeasure. He was going out of the received circle of disputation into a region in which they could hardly follow him. From the crude idea of Being in the abstract, he was about to proceed to universals or general notions. There is no contradiction in material things partaking of the ideas of one and many; neither is there any contradiction in the ideas of one and many, like and unlike, in themselves. But the contradiction arises when we attempt to conceive ideas in their connexion, or to ascertain their relation to phenomena. Still he affirms the existence of such ideas; and this is the position which is now in turn submitted to the criticisms of Parmenides.

It was no wonder that Parmenides and Zeno heard Socrates’ new ideas with both admiration and displeasure. He was moving beyond the usual bounds of debate into territory where they could hardly follow him. He was about to move from the crude idea of Being in the abstract to universals, or general notions. There is no contradiction in material things sharing in the ideas of one and many. Nor is there any contradiction in the ideas of one and many, or like and unlike, considered in themselves. But contradiction arises when we try to understand how ideas relate to one another or to phenomena. Still, Socrates maintains that such ideas exist. This claim is now, in turn, subjected to Parmenides’ criticism.

To appreciate truly the character of these criticisms, we must remember the place held by Parmenides in the history of Greek philosophy. He is the founder of idealism, and also of dialectic, or, in modern phraseology, of metaphysics and logic (Theaet., Soph.). Like Plato, he is struggling after something wider and deeper than satisfied the contemporary Pythagoreans. And Plato with a true instinct recognizes him as his spiritual father, whom he 'revered and honoured more than all other philosophers together.' He may be supposed to have thought more than he said, or was able to express. And, although he could not, as a matter of fact, have criticized the ideas of Plato without an anachronism, the criticism is appropriately placed in the mouth of the founder of the ideal philosophy.

To understand these criticisms fully, we must remember Parmenides’ place in the history of Greek philosophy. He founded idealism and dialectic, or, in modern terms, metaphysics and logic (Theaet., Soph.). Like Plato, he sought something broader and deeper than what satisfied the Pythagoreans of his time. Plato rightly recognized Parmenides as his spiritual father, whom he 'revered and honoured more than all other philosophers together.' We may suppose that Parmenides thought more than he said or could express. In fact, Parmenides could not have criticized Plato’s ideas without an anachronism. Even so, it is fitting to place the criticism in the mouth of the founder of idealist philosophy.

There was probably a time in the life of Plato when the ethical teaching of Socrates came into conflict with the metaphysical theories of the earlier philosophers, and he sought to supplement the one by the other. The older philosophers were great and awful; and they had the charm of antiquity. Something which found a response in his own mind seemed to have been lost as well as gained in the Socratic dialectic. He felt no incongruity in the veteran Parmenides correcting the youthful Socrates. Two points in his criticism are especially deserving of notice. First of all, Parmenides tries him by the test of consistency. Socrates is willing to assume ideas or principles of the just, the beautiful, the good, and to extend them to man (compare Phaedo); but he is reluctant to admit that there are general ideas of hair, mud, filth, etc. There is an ethical universal or idea, but is there also a universal of physics?—of the meanest things in the world as well as of the greatest? Parmenides rebukes this want of consistency in Socrates, which he attributes to his youth. As he grows older, philosophy will take a firmer hold of him, and then he will despise neither great things nor small, and he will think less of the opinions of mankind (compare Soph.). Here is lightly touched one of the most familiar principles of modern philosophy, that in the meanest operations of nature, as well as in the noblest, in mud and filth, as well as in the sun and stars, great truths are contained. At the same time, we may note also the transition in the mind of Plato, to which Aristotle alludes (Met.), when, as he says, he transferred the Socratic universal of ethics to the whole of nature.

There was probably a time in Plato’s life when Socrates’ ethical teaching conflicted with earlier philosophers’ metaphysical theories. Plato sought to supplement each with the other. The older philosophers were great and awe-inspiring, and their antiquity gave them a special appeal. The Socratic method of questioning seemed to have lost something that Plato himself valued, even as it gained something else. He saw no inconsistency in having the experienced Parmenides correct the young Socrates. Two points in Parmenides’ criticism deserve particular attention. First, Parmenides tests Socrates for consistency. Socrates is willing to assume that there are ideas or principles of the just, the beautiful, and the good. He is also willing to extend this assumption to human beings (compare Phaedo). But he hesitates to admit that there are general ideas of hair, mud, filth, and so on. There is a universal principle or idea in ethics, but is there also one in the physical world? Is there one for the lowest things in the world as well as the greatest? Parmenides rebukes Socrates for this inconsistency, which he attributes to Socrates’ youth. As Socrates grows older, philosophy will take a firmer hold of him. Then he will look down on neither great things nor small ones, and he will care less about others’ opinions (compare Soph.). This passage briefly touches on one of the most familiar principles of modern philosophy. Great truths are found in the lowest processes of nature as well as in the noblest, in mud and filth as well as in the sun and stars. At the same time, we may also notice a change in Plato’s thinking that Aristotle mentions (Met.). Aristotle says that Plato extended the Socratic idea of a universal principle in ethics to all of nature.

The other criticism of Parmenides on Socrates attributes to him a want of practice in dialectic. He has observed this deficiency in him when talking to Aristoteles on a previous occasion. Plato seems to imply that there was something more in the dialectic of Zeno than in the mere interrogation of Socrates. Here, again, he may perhaps be describing the process which his own mind went through when he first became more intimately acquainted, whether at Megara or elsewhere, with the Eleatic and Megarian philosophers. Still, Parmenides does not deny to Socrates the credit of having gone beyond them in seeking to apply the paradoxes of Zeno to ideas; and this is the application which he himself makes of them in the latter part of the dialogue. He then proceeds to explain to him the sort of mental gymnastic which he should practise. He should consider not only what would follow from a given hypothesis, but what would follow from the denial of it, to that which is the subject of the hypothesis, and to all other things. There is no trace in the Memorabilia of Xenophon of any such method being attributed to Socrates; nor is the dialectic here spoken of that 'favourite method' of proceeding by regular divisions, which is described in the Phaedrus and Philebus, and of which examples are given in the Politicus and in the Sophist. It is expressly spoken of as the method which Socrates had heard Zeno practise in the days of his youth (compare Soph.).

Parmenides’ other criticism of Socrates is that he lacks practice in dialectic. Parmenides noticed this weakness when Socrates spoke with Aristoteles on an earlier occasion. Plato seems to suggest that Zeno’s dialectic involved more than Socrates’ method of asking questions. Here again, Plato may perhaps be describing his own mental development. He may have experienced this process when he first became more closely acquainted with the Eleatic and Megarian philosophers, whether at Megara or elsewhere. Still, Parmenides gives Socrates credit for going beyond them by trying to apply Zeno’s paradoxes to ideas. Parmenides himself applies the paradoxes to ideas in the later part of the dialogue. Parmenides then explains the kind of mental exercise Socrates should practise. He should consider what would follow from a given hypothesis, but also what would follow if the hypothesis were denied. He should consider the consequences for both the subject of the hypothesis and all other things. Xenophon’s Memorabilia shows no trace of any such method being attributed to Socrates. Nor is the dialectic discussed here the 'favourite method' of proceeding through regular divisions. That method is described in the Phaedrus and Philebus, and examples appear in the Politicus and the Sophist. The dialectic discussed here is expressly described as the method Socrates had heard Zeno practise when Socrates was young (compare Soph.).

The discussion of Socrates with Parmenides is one of the most remarkable passages in Plato. Few writers have ever been able to anticipate 'the criticism of the morrow' on their favourite notions. But Plato may here be said to anticipate the judgment not only of the morrow, but of all after-ages on the Platonic Ideas. For in some points he touches questions which have not yet received their solution in modern philosophy.

Socrates’ discussion with Parmenides is one of the most remarkable passages in Plato. Few writers have been able to anticipate ‘the criticism of the morrow’ of their favorite ideas. But Plato may be said to anticipate the judgment not only of tomorrow, but of all later ages on the Platonic Ideas. For he raises some questions that modern philosophy has not yet resolved.

The first difficulty which Parmenides raises respecting the Platonic ideas relates to the manner in which individuals are connected with them. Do they participate in the ideas, or do they merely resemble them? Parmenides shows that objections may be urged against either of these modes of conceiving the connection. Things are little by partaking of littleness, great by partaking of greatness, and the like. But they cannot partake of a part of greatness, for that will not make them great, etc.; nor can each object monopolise the whole. The only answer to this is, that 'partaking' is a figure of speech, really corresponding to the processes which a later logic designates by the terms 'abstraction' and 'generalization.' When we have described accurately the methods or forms which the mind employs, we cannot further criticize them; at least we can only criticize them with reference to their fitness as instruments of thought to express facts.

The first difficulty Parmenides raises about the Platonic ideas concerns how individual things are connected to them. Do things participate in the ideas, or do they merely resemble them? Parmenides shows that both ways of understanding the connection are open to objections. Things are small by sharing in smallness, great by sharing in greatness, and so on. But they cannot share in just a part of greatness, because that would not make them great. Nor can each object have the whole of greatness to itself. The only answer is that 'partaking' is a figure of speech. It really corresponds to processes that later logic calls 'abstraction' and 'generalization.' Once we have accurately described the methods or forms the mind uses, we cannot criticize them further. At least, we can only judge how well they serve as tools of thought for expressing facts.

Socrates attempts to support his view of the ideas by the parallel of the day, which is one and in many places; but he is easily driven from his position by a counter illustration of Parmenides, who compares the idea of greatness to a sail. He truly explains to Socrates that he has attained the conception of ideas by a process of generalization. At the same time, he points out a difficulty, which appears to be involved—viz. that the process of generalization will go on to infinity. Socrates meets the supposed difficulty by a flash of light, which is indeed the true answer 'that the ideas are in our minds only.' Neither realism is the truth, nor nominalism is the truth, but conceptualism; and conceptualism or any other psychological theory falls very far short of the infinite subtlety of language and thought.

Socrates tries to support his view of the ideas by comparing an idea to a day, which is one and present in many places. But Parmenides easily drives Socrates from this position with a counterexample. Parmenides compares the idea of greatness to a sail. He rightly explains to Socrates that he arrived at his conception of ideas through a process of generalization. At the same time, Parmenides points out a difficulty that seems to follow: the process of generalization will go on forever. Socrates meets this supposed difficulty with a flash of insight, which is indeed the true answer: 'that the ideas are in our minds only.' Neither realism nor nominalism is the truth, but conceptualism is. Yet conceptualism, like any other psychological theory, falls very far short of capturing the infinite subtlety of language and thought.

But the realism of ancient philosophy will not admit of this answer, which is repelled by Parmenides with another truth or half-truth of later philosophy, 'Every subject or subjective must have an object.' Here is the great though unconscious truth (shall we say?) or error, which underlay the early Greek philosophy. 'Ideas must have a real existence;' they are not mere forms or opinions, which may be changed arbitrarily by individuals. But the early Greek philosopher never clearly saw that true ideas were only universal facts, and that there might be error in universals as well as in particulars.

But the realism of ancient philosophy cannot accept this answer. Parmenides rejects it with another truth, or half-truth, from later philosophy: 'Every subject or subjective thing must have an object.' Here is the great unconscious truth, or should we say error, underlying early Greek philosophy. 'Ideas must have a real existence.' They are not mere forms or opinions that individuals can change at will. But early Greek philosophers never clearly saw that true ideas were only universal facts. Nor did they see that universals, like particulars, could contain errors.

Socrates makes one more attempt to defend the Platonic Ideas by representing them as paradigms; this is again answered by the 'argumentum ad infinitum.' We may remark, in passing, that the process which is thus described has no real existence. The mind, after having obtained a general idea, does not really go on to form another which includes that, and all the individuals contained under it, and another and another without end. The difficulty belongs in fact to the Megarian age of philosophy, and is due to their illogical logic, and to the general ignorance of the ancients respecting the part played by language in the process of thought. No such perplexity could ever trouble a modern metaphysician, any more than the fallacy of 'calvus' or 'acervus,' or of 'Achilles and the tortoise.' These 'surds' of metaphysics ought to occasion no more difficulty in speculation than a perpetually recurring fraction in arithmetic.

Socrates makes one more attempt to defend the Platonic Ideas by presenting them as models. This is again answered by the 'argumentum ad infinitum.' We may note in passing that the process described here does not actually occur. Once the mind has formed a general idea, it does not go on to form another that includes the first idea and all the individuals it covers. Nor does it continue forming such ideas without end. In fact, the difficulty belongs to the Megarian age of philosophy. It arises from the Megarians' illogical logic and the ancients' general ignorance of the role language plays in thought. Such a puzzle could never trouble a modern metaphysician, any more than the fallacy of 'calvus' or 'acervus,' or of 'Achilles and the tortoise.' These 'surds' of metaphysics should cause no more difficulty in speculation than an endlessly repeating fraction does in arithmetic.

It is otherwise with the objection which follows: How are we to bridge the chasm between human truth and absolute truth, between gods and men? This is the difficulty of philosophy in all ages: How can we get beyond the circle of our own ideas, or how, remaining within them, can we have any criterion of a truth beyond and independent of them? Parmenides draws out this difficulty with great clearness. According to him, there are not only one but two chasms: the first, between individuals and the ideas which have a common name; the second, between the ideas in us and the ideas absolute. The first of these two difficulties mankind, as we may say, a little parodying the language of the Philebus, have long agreed to treat as obsolete; the second remains a difficulty for us as well as for the Greeks of the fourth century before Christ, and is the stumbling-block of Kant's Kritik, and of the Hamiltonian adaptation of Kant, as well as of the Platonic ideas. It has been said that 'you cannot criticize Revelation.' 'Then how do you know what is Revelation, or that there is one at all,' is the immediate rejoinder—'You know nothing of things in themselves.' 'Then how do you know that there are things in themselves?' In some respects, the difficulty pressed harder upon the Greek than upon ourselves. For conceiving of God more under the attribute of knowledge than we do, he was more under the necessity of separating the divine from the human, as two spheres which had no communication with one another.

The next objection is different: How can we bridge the gap between human truth and absolute truth, between gods and humans? This is the difficulty philosophy faces in every age. How can we get beyond the circle of our own ideas? Or, while remaining within that circle, how can we have any standard for judging truth beyond and independent of our ideas? Parmenides explains this difficulty very clearly. According to him, there are two gaps, not just one. The first lies between individual things and the ideas that share their names. The second lies between the ideas in us and the absolute ideas. To borrow and slightly parody the language of the Philebus, we might say that humanity has long agreed to treat the first difficulty as obsolete. The second remains a difficulty for us, just as it was for the Greeks of the fourth century BC. It is a stumbling block for Kant's Kritik and for the Hamiltonian adaptation of Kant, as well as for the Platonic ideas. It has been said that 'you cannot criticize Revelation.' The immediate reply is, 'Then how do you know what Revelation is, or that there is any Revelation at all?' To the claim 'You know nothing of things in themselves,' the reply is, 'Then how do you know that there are things in themselves?' In some respects, the difficulty was more pressing for the Greeks than for us. The Greeks thought of God more in terms of knowledge than we do. They therefore had a greater need to separate the divine from the human, as two spheres with no connection between them.

It is remarkable that Plato, speaking by the mouth of Parmenides, does not treat even this second class of difficulties as hopeless or insoluble. He says only that they cannot be explained without a long and laborious demonstration: 'The teacher will require superhuman ability, and the learner will be hard of understanding.' But an attempt must be made to find an answer to them; for, as Socrates and Parmenides both admit, the denial of abstract ideas is the destruction of the mind. We can easily imagine that among the Greek schools of philosophy in the fourth century before Christ a panic might arise from the denial of universals, similar to that which arose in the last century from Hume's denial of our ideas of cause and effect. Men do not at first recognize that thought, like digestion, will go on much the same, notwithstanding any theories which may be entertained respecting the nature of the process. Parmenides attributes the difficulties in which Socrates is involved to a want of comprehensiveness in his mode of reasoning; he should consider every question on the negative as well as the positive hypothesis, with reference to the consequences which flow from the denial as well as from the assertion of a given statement.

It is remarkable that Plato, speaking through Parmenides, does not treat even this second class of difficulties as hopeless or impossible to solve. He says only that explaining them would require a long and painstaking demonstration: 'The teacher will need superhuman ability, and the learner will find it hard to understand.' But an attempt must be made to answer these difficulties. For both Socrates and Parmenides admit that denying abstract ideas destroys the mind. We can easily imagine a panic among Greek schools of philosophy in the fourth century before Christ over the denial of universals. It might have resembled the panic that arose in the last century over Hume's denial of our ideas of cause and effect. At first, people do not recognize that thought, like digestion, will continue much as before, regardless of theories about how it works. Parmenides blames Socrates' difficulties on a lack of breadth in his reasoning. Socrates should consider every question on both the negative and the positive hypothesis. He should examine the consequences of denying a statement as well as those of asserting it.

The argument which follows is the most singular in Plato. It appears to be an imitation, or parody, of the Zenonian dialectic, just as the speeches in the Phaedrus are an imitation of the style of Lysias, or as the derivations in the Cratylus or the fallacies of the Euthydemus are a parody of some contemporary Sophist. The interlocutor is not supposed, as in most of the other Platonic dialogues, to take a living part in the argument; he is only required to say 'Yes' and 'No' in the right places. A hint has been already given that the paradoxes of Zeno admitted of a higher application. This hint is the thread by which Plato connects the two parts of the dialogue.

The argument that follows is the most unusual in Plato. It seems to imitate or parody Zenonian dialectic. Similarly, the speeches in the Phaedrus imitate Lysias’s style. The word derivations in the Cratylus and the fallacies in the Euthydemus likewise parody some contemporary Sophist. Unlike in most other Platonic dialogues, the interlocutor is not expected to take an active part in the argument. He only has to say 'Yes' and 'No' at the right places. An earlier hint suggested that Zeno’s paradoxes could be applied to higher questions. Plato uses that hint to connect the two parts of the dialogue.

The paradoxes of Parmenides seem trivial to us, because the words to which they relate have become trivial; their true nature as abstract terms is perfectly understood by us, and we are inclined to regard the treatment of them in Plato as a mere straw-splitting, or legerdemain of words. Yet there was a power in them which fascinated the Neoplatonists for centuries afterwards. Something that they found in them, or brought to them—some echo or anticipation of a great truth or error, exercised a wonderful influence over their minds. To do the Parmenides justice, we should imagine similar aporiai raised on themes as sacred to us, as the notions of One or Being were to an ancient Eleatic. 'If God is, what follows? If God is not, what follows?' Or again: If God is or is not the world; or if God is or is not many, or has or has not parts, or is or is not in the world, or in time; or is or is not finite or infinite. Or if the world is or is not; or has or has not a beginning or end; or is or is not infinite, or infinitely divisible. Or again: if God is or is not identical with his laws; or if man is or is not identical with the laws of nature. We can easily see that here are many subjects for thought, and that from these and similar hypotheses questions of great interest might arise. And we also remark, that the conclusions derived from either of the two alternative propositions might be equally impossible and contradictory.

The paradoxes of Parmenides seem trivial to us because the words they concern have become trivial. We fully understand that these words are abstract terms. We are inclined to see Plato’s treatment of them as mere hair-splitting or verbal trickery. Yet these paradoxes had a power that fascinated the Neoplatonists for centuries afterward. Something they found in the paradoxes, or brought to them, had a wonderful influence on their minds. It was some echo or anticipation of a great truth or error. To do the Parmenides justice, we should imagine similar puzzles raised about subjects as sacred to us as the notions of One or Being were to an ancient Eleatic. 'If God is, what follows? If God is not, what follows?' Or again: If God is or is not the world. If God is or is not many, has or does not have parts, or is or is not in the world or in time. If God is or is not finite or infinite. Or if the world is or is not, has or does not have a beginning or end, or is or is not infinite or infinitely divisible. Or again: If God is or is not identical with his laws, or if man is or is not identical with the laws of nature. We can easily see that there are many subjects for thought here. Questions of great interest might arise from these and similar hypotheses. We also notice that the conclusions drawn from either of two opposing propositions might be equally impossible and contradictory.

When we ask what is the object of these paradoxes, some have answered that they are a mere logical puzzle, while others have seen in them an Hegelian propaedeutic of the doctrine of Ideas. The first of these views derives support from the manner in which Parmenides speaks of a similar method being applied to all Ideas. Yet it is hard to suppose that Plato would have furnished so elaborate an example, not of his own but of the Eleatic dialectic, had he intended only to give an illustration of method. The second view has been often overstated by those who, like Hegel himself, have tended to confuse ancient with modern philosophy. We need not deny that Plato, trained in the school of Cratylus and Heracleitus, may have seen that a contradiction in terms is sometimes the best expression of a truth higher than either (compare Soph.). But his ideal theory is not based on antinomies. The correlation of Ideas was the metaphysical difficulty of the age in which he lived; and the Megarian and Cynic philosophy was a 'reductio ad absurdum' of their isolation. To restore them to their natural connexion and to detect the negative element in them is the aim of Plato in the Sophist. But his view of their connexion falls very far short of the Hegelian identity of Being and Not-being. The Being and Not-being of Plato never merge in each other, though he is aware that 'determination is only negation.'

What is the purpose of these paradoxes? Some have said they are merely a logical puzzle. Others have seen them as a Hegelian introduction to the doctrine of Ideas. The first view finds support in Parmenides’ claim that a similar method can be applied to all Ideas. Yet it is hard to believe that Plato intended only to illustrate a method. If he had, why would he have given such an elaborate example of Eleatic dialectic, rather than his own? The second view has often been overstated by those who, like Hegel himself, tend to confuse ancient and modern philosophy. Plato was trained in the school of Cratylus and Heracleitus. We need not deny that he may have seen a contradiction in terms as sometimes best expressing a truth higher than either term (compare Soph.). But his theory of Ideas is not based on antinomies. The relationship among Ideas was the central metaphysical difficulty of Plato’s age. Megarian and Cynic philosophy was a 'reductio ad absurdum' of treating the Ideas as isolated. In the Sophist, Plato aims to restore the Ideas to their natural connection and identify the negative element in them. But his view of their connection falls far short of the Hegelian identity of Being and Not-being. For Plato, Being and Not-being never merge, although he is aware that 'determination is only negation.'

After criticizing the hypotheses of others, it may appear presumptuous to add another guess to the many which have been already offered. May we say, in Platonic language, that we still seem to see vestiges of a track which has not yet been taken? It is quite possible that the obscurity of the Parmenides would not have existed to a contemporary student of philosophy, and, like the similar difficulty in the Philebus, is really due to our ignorance of the mind of the age. There is an obscure Megarian influence on Plato which cannot wholly be cleared up, and is not much illustrated by the doubtful tradition of his retirement to Megara after the death of Socrates. For Megara was within a walk of Athens (Phaedr.), and Plato might have learned the Megarian doctrines without settling there.

After criticizing other people's hypotheses, it may seem presumptuous to add another guess to the many already offered. But, to use Platonic language, may we say that we still seem to see traces of a path not yet taken? A student of philosophy in Plato's time might well have found nothing obscure in the Parmenides. Like the similar difficulty in the Philebus, its obscurity may really be due to our ignorance of how people thought at the time. Plato was influenced by Megarian thought in ways that cannot be fully explained. The uncertain story that he retired to Megara after Socrates' death does little to clarify this influence. Megara was within walking distance of Athens (Phaedr.), so Plato could have learned Megarian doctrines without settling there.

We may begin by remarking that the theses of Parmenides are expressly said to follow the method of Zeno, and that the complex dilemma, though declared to be capable of universal application, is applied in this instance to Zeno's familiar question of the 'one and many.' Here, then, is a double indication of the connexion of the Parmenides with the Eristic school. The old Eleatics had asserted the existence of Being, which they at first regarded as finite, then as infinite, then as neither finite nor infinite, to which some of them had given what Aristotle calls 'a form,' others had ascribed a material nature only. The tendency of their philosophy was to deny to Being all predicates. The Megarians, who succeeded them, like the Cynics, affirmed that no predicate could be asserted of any subject; they also converted the idea of Being into an abstraction of Good, perhaps with the view of preserving a sort of neutrality or indifference between the mind and things. As if they had said, in the language of modern philosophy: 'Being is not only neither finite nor infinite, neither at rest nor in motion, but neither subjective nor objective.'

We may begin by noting that Parmenides' theses are explicitly said to follow Zeno's method. The complex dilemma is said to apply universally, but here it is applied to Zeno's familiar question of the 'one and many.' These are two indications of the connection between the Parmenides and the Eristic school. The early Eleatics asserted the existence of Being. They regarded Being first as finite, then as infinite, and then as neither finite nor infinite. Some gave Being what Aristotle calls 'a form,' while others attributed only a material nature to it. Their philosophy tended to deny that Being had any predicates. The Megarians, who came after the Eleatics, maintained, like the Cynics, that no predicate could be asserted of any subject. They also turned the idea of Being into an abstraction of Good. They did this perhaps to preserve a kind of neutrality or indifference between the mind and things. It was as if they had said, in the language of modern philosophy: 'Being is not only neither finite nor infinite, neither at rest nor in motion, but neither subjective nor objective.'

This is the track along which Plato is leading us. Zeno had attempted to prove the existence of the one by disproving the existence of the many, and Parmenides seems to aim at proving the existence of the subject by showing the contradictions which follow from the assertion of any predicates. Take the simplest of all notions, 'unity'; you cannot even assert being or time of this without involving a contradiction. But is the contradiction also the final conclusion? Probably no more than of Zeno's denial of the many, or of Parmenides' assault upon the Ideas; no more than of the earlier dialogues 'of search.' To us there seems to be no residuum of this long piece of dialectics. But to the mind of Parmenides and Plato, 'Gott-betrunkene Menschen,' there still remained the idea of 'being' or 'good,' which could not be conceived, defined, uttered, but could not be got rid of. Neither of them would have imagined that their disputation ever touched the Divine Being (compare Phil.). The same difficulties about Unity and Being are raised in the Sophist; but there only as preliminary to their final solution.

This is the path Plato is leading us along. Zeno tried to prove that the one exists by disproving the existence of the many. Parmenides seems to have a similar aim. He tries to prove that the subject exists by showing the contradictions that follow from assigning it any predicates. Take the simplest notion of all, 'unity'. You cannot even say that unity exists or is in time without creating a contradiction. But is the contradiction also the final conclusion? Probably not, any more than Zeno's denial of the many was his final conclusion. The same is probably true of Parmenides' attack on the Ideas and of the earlier dialogues 'of search.' To us, nothing seems to remain after this long exercise in dialectic. But for Parmenides and Plato, 'Gott-betrunkene Menschen,' the idea of 'being' or 'good' still remained. It could not be conceived, defined, or put into words, but it could not be dismissed either. Neither would have thought that their argument ever touched the Divine Being (compare Phil.). The same difficulties about Unity and Being arise in the Sophist. But there they serve only as preparation for their final solution.

If this view is correct, the real aim of the hypotheses of Parmenides is to criticize the earlier Eleatic philosophy from the point of view of Zeno or the Megarians. It is the same kind of criticism which Plato has extended to his own doctrine of Ideas. Nor is there any want of poetical consistency in attributing to the 'father Parmenides' the last review of the Eleatic doctrines. The latest phases of all philosophies were fathered upon the founder of the school.

If this view is correct, the real aim of Parmenides’ hypotheses is to criticize earlier Eleatic philosophy from the perspective of Zeno or the Megarians. This is the same kind of criticism that Plato has applied to his own doctrine of Ideas. Nor is it poetically inconsistent to attribute the final review of Eleatic doctrines to ‘father Parmenides’. The latest phases of all philosophies were attributed to the founder of the school.

Other critics have regarded the final conclusion of the Parmenides either as sceptical or as Heracleitean. In the first case, they assume that Plato means to show the impossibility of any truth. But this is not the spirit of Plato, and could not with propriety be put into the mouth of Parmenides, who, in this very dialogue, is urging Socrates, not to doubt everything, but to discipline his mind with a view to the more precise attainment of truth. The same remark applies to the second of the two theories. Plato everywhere ridicules (perhaps unfairly) his Heracleitean contemporaries: and if he had intended to support an Heracleitean thesis, would hardly have chosen Parmenides, the condemner of the 'undiscerning tribe who say that things both are and are not,' to be the speaker. Nor, thirdly, can we easily persuade ourselves with Zeller that by the 'one' he means the Idea; and that he is seeking to prove indirectly the unity of the Idea in the multiplicity of phenomena.

Other critics have regarded the final conclusion of the Parmenides as either sceptical or Heracleitean. In the first case, they assume that Plato means to show that no truth is possible. But this is not in keeping with Plato’s spirit. Nor would it be appropriate to put such a view in the mouth of Parmenides. In this very dialogue, Parmenides urges Socrates not to doubt everything, but to discipline his mind to reach the truth more precisely. The same objection applies to the second theory. Plato ridicules his Heracleitean contemporaries throughout his work, perhaps unfairly. If he had intended to support a Heracleitean thesis, he would hardly have chosen Parmenides as the speaker. Parmenides condemned the 'undiscerning tribe who say that things both are and are not.' Nor, thirdly, can we easily accept Zeller’s view that by the 'one' Plato means the Idea. On Zeller’s view, Plato is trying to prove indirectly the unity of the Idea in the multiplicity of phenomena.

We may now endeavour to thread the mazes of the labyrinth which Parmenides knew so well, and trembled at the thought of them.

We may now try to find our way through the labyrinth’s mazes. Parmenides knew them well and trembled at the thought of them.

The argument has two divisions: There is the hypothesis that

The argument has two parts: One is the assumption that

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'I cannot refuse,' said Parmenides, 'since, as Zeno remarks, we are alone, though I may say with Ibycus, who in his old age fell in love, I, like the old racehorse, tremble at the prospect of the course which I am to run, and which I know so well. But as I must attempt this laborious game, what shall be the subject? Suppose I take my own hypothesis of the one.' 'By all means,' said Zeno. 'And who will answer me? Shall I propose the youngest? he will be the most likely to say what he thinks, and his answers will give me time to breathe.' 'I am the youngest,' said Aristoteles, 'and at your service; proceed with your questions.'—The result may be summed up as follows:—

'I cannot refuse,' said Parmenides, 'since, as Zeno says, we are alone. Yet I can say, like Ibycus, who fell in love in his old age, that I tremble like an old racehorse. I tremble at the prospect of running a course I know so well. But since I must attempt this demanding game, what shall the subject be? Suppose I take my own hypothesis about the one.' 'By all means,' said Zeno. 'And who will answer me? Shall I choose the youngest? He will be most likely to say what he thinks, and his answers will give me time to breathe.' 'I am the youngest,' said Aristoteles, 'and I am at your service. Go ahead with your questions.' The result can be summed up as follows:

1.a. One is not many, and therefore has no parts, and therefore is not a whole, which is a sum of parts, and therefore has neither beginning, middle, nor end, and is therefore unlimited, and therefore formless, being neither round nor straight, for neither round nor straight can be defined without assuming that they have parts; and therefore is not in place, whether in another which would encircle and touch the one at many points; or in itself, because that which is self-containing is also contained, and therefore not one but two. This being premised, let us consider whether one is capable either of motion or rest. For motion is either change of substance, or motion on an axis, or from one place to another. But the one is incapable of change of substance, which implies that it ceases to be itself, or of motion on an axis, because there would be parts around the axis; and any other motion involves change of place. But existence in place has been already shown to be impossible; and yet more impossible is coming into being in place, which implies partial existence in two places at once, or entire existence neither within nor without the same; and how can this be? And more impossible still is the coming into being either as a whole or parts of that which is neither a whole nor parts. The one, then, is incapable of motion. But neither can the one be in anything, and therefore not in the same, whether itself or some other, and is therefore incapable of rest. Neither is one the same with itself or any other, or other than itself or any other. For if other than itself, then other than one, and therefore not one; and, if the same with other, it would be other, and other than one. Neither can one while remaining one be other than other; for other, and not one, is the other than other. But if not other by virtue of being one, not by virtue of itself; and if not by virtue of itself, not itself other, and if not itself other, not other than anything. Neither will one be the same with itself. For the nature of the same is not that of the one, but a thing which becomes the same with anything does not become one; for example, that which becomes the same with the many becomes many and not one. And therefore if the one is the same with itself, the one is not one with itself; and therefore one and not one. And therefore one is neither other than other, nor the same with itself. Neither will the one be like or unlike itself or other; for likeness is sameness of affections, and the one and the same are different. And one having any affection which is other than being one would be more than one. The one, then, cannot have the same affection with and therefore cannot be like itself or other; nor can the one have any other affection than its own, that is, be unlike itself or any other, for this would imply that it was more than one. The one, then, is neither like nor unlike itself or other. This being the case, neither can the one be equal or unequal to itself or other. For equality implies sameness of measure, as inequality implies a greater or less number of measures. But the one, not having sameness, cannot have sameness of measure; nor a greater or less number of measures, for that would imply parts and multitude. Once more, can one be older or younger than itself or other? or of the same age with itself or other? That would imply likeness and unlikeness, equality and inequality. Therefore one cannot be in time, because that which is in time is ever becoming older and younger than itself, (for older and younger are relative terms, and he who becomes older becomes younger,) and is also of the same age with itself. None of which, or any other expressions of time, whether past, future, or present, can be affirmed of one. One neither is, has been, nor will be, nor becomes, nor has, nor will become. And, as these are the only modes of being, one is not, and is not one. But to that which is not, there is no attribute or relative, neither name nor word nor idea nor science nor perception nor opinion appertaining. One, then, is neither named, nor uttered, nor known, nor perceived, nor imagined. But can all this be true? 'I think not.'

1.a. One is not many, so it has no parts. And because a whole is a sum of parts, one is not a whole. So it has no beginning, middle, or end. It is therefore unlimited and has no shape. It is neither round nor straight, since neither shape can be defined without assuming it has parts. So one is not in a place. It cannot be in something else, which would surround it and touch it at many points. Nor can it be in itself. For what contains itself is also contained, and is therefore not one but two. Given this, let us consider whether one can move or be at rest. Motion is either a change in substance, rotation on an axis, or movement from one place to another. But one cannot change its substance, since that would mean it ceased to be itself. Nor can it rotate on an axis, because there would be parts around the axis. Any other motion involves a change of place. But we have already shown that one cannot exist in a place. It is even more impossible for one to come into being in a place. That would mean existing partly in two places at once, or existing entirely neither inside nor outside the same place. How can this be? And it is still more impossible for something with neither a whole nor parts to come into being as either a whole or parts. One, then, cannot move. But it cannot be in anything either, and therefore cannot be in the same place, whether in itself or in something else. So it cannot be at rest. Nor is one the same as itself or anything else, or different from itself or anything else. For if it were different from itself, it would be different from one, and therefore not one. If it were the same as something else, it would be something else and different from one. Nor can one, while remaining one, be different from something else. For it is by being different, not by being one, that something is different from something else. But if one is not different by virtue of being one, it is not different by virtue of itself. And if it is not different by virtue of itself, it is not itself different. If it is not itself different, it is not different from anything. Nor will one be the same as itself. For the nature of sameness is not the nature of oneness. A thing that becomes the same as something does not thereby become one. For example, what becomes the same as the many becomes many, not one. So if one is the same as itself, it is not one with itself. It is therefore both one and not one. Thus one is neither different from something else nor the same as itself. Nor will one be like or unlike itself or anything else. For likeness means having the same qualities, and one and the same are different. And if one had any quality other than being one, it would be more than one. So one cannot have the same quality as itself or anything else. It therefore cannot be like itself or anything else. Nor can it have any quality other than its own, that is, be unlike itself or anything else. For that would mean it was more than one. One, then, is neither like nor unlike itself or anything else. Since this is so, one cannot be equal or unequal to itself or anything else. For equality means having the same measure, while inequality means having a greater or smaller number of measures. But one has no sameness, so it cannot have the same measure. Nor can it have a greater or smaller number of measures, because that would imply parts and multiplicity. Again, can one be older or younger than itself or anything else? Or can it be the same age as itself or anything else? That would imply likeness and unlikeness, equality and inequality. So one cannot be in time. For anything in time is always becoming both older and younger than itself. Older and younger are relative terms, and whoever becomes older becomes younger. Whatever is in time is also the same age as itself. None of these things can be said of one. Nor can any other expression of time, whether past, future, or present, be applied to it. One neither is, has been, nor will be. It neither becomes, has become, nor will become. And since these are the only ways of being, one does not exist and is not one. But what does not exist has no attribute or relation. No name, word, idea, science, perception, or opinion belongs to it. One, then, is neither named nor spoken of, neither known nor perceived nor imagined. But can all this be true? 'I think not.'

1.b. Let us, however, commence the inquiry again. We have to work out all the consequences which follow on the assumption that the one is. If one is, one partakes of being, which is not the same with one; the words 'being' and 'one' have different meanings. Observe the consequence: In the one of being or the being of one are two parts, being and one, which form one whole. And each of the two parts is also a whole, and involves the other, and may be further subdivided into one and being, and is therefore not one but two; and thus one is never one, and in this way the one, if it is, becomes many and infinite. Again, let us conceive of a one which by an effort of abstraction we separate from being: will this abstract one be one or many? You say one only; let us see. In the first place, the being of one is other than one; and one and being, if different, are so because they both partake of the nature of other, which is therefore neither one nor being; and whether we take being and other, or being and one, or one and other, in any case we have two things which separately are called either, and together both. And both are two and either of two is severally one, and if one be added to any of the pairs, the sum is three; and two is an even number, three an odd; and two units exist twice, and therefore there are twice two; and three units exist thrice, and therefore there are thrice three, and taken together they give twice three and thrice two: we have even numbers multiplied into even, and odd into even, and even into odd numbers. But if one is, and both odd and even numbers are implied in one, must not every number exist? And number is infinite, and therefore existence must be infinite, for all and every number partakes of being; therefore being has the greatest number of parts, and every part, however great or however small, is equally one. But can one be in many places and yet be a whole? If not a whole it must be divided into parts and represented by a number corresponding to the number of the parts. And if so, we were wrong in saying that being has the greatest number of parts; for being is coequal and coextensive with one, and has no more parts than one; and so the abstract one broken up into parts by being is many and infinite. But the parts are parts of a whole, and the whole is their containing limit, and the one is therefore limited as well as infinite in number; and that which is a whole has beginning, middle, and end, and a middle is equidistant from the extremes; and one is therefore of a certain figure, round or straight, or a combination of the two, and being a whole includes all the parts which are the whole, and is therefore self-contained. But then, again, the whole is not in the parts, whether all or some. Not in all, because, if in all, also in one; for, if wanting in any one, how in all?—not in some, because the greater would then be contained in the less. But if not in all, nor in any, nor in some, either nowhere or in other. And if nowhere, nothing; therefore in other. The one as a whole, then, is in another, but regarded as a sum of parts is in itself; and is, therefore, both in itself and in another. This being the case, the one is at once both at rest and in motion: at rest, because resting in itself; in motion, because it is ever in other. And if there is truth in what has preceded, one is the same and not the same with itself and other. For everything in relation to every other thing is either the same with it or other; or if neither the same nor other, then in the relation of part to a whole or whole to a part. But one cannot be a part or whole in relation to one, nor other than one; and is therefore the same with one. Yet this sameness is again contradicted by one being in another place from itself which is in the same place; this follows from one being in itself and in another; one, therefore, is other than itself. But if anything is other than anything, will it not be other than other? And the not one is other than the one, and the one than the not one; therefore one is other than all others. But the same and the other exclude one another, and therefore the other can never be in the same; nor can the other be in anything for ever so short a time, as for that time the other will be in the same. And the other, if never in the same, cannot be either in the one or in the not one. And one is not other than not one, either by reason of other or of itself; and therefore they are not other than one another at all. Neither can the not one partake or be part of one, for in that case it would be one; nor can the not one be number, for that also involves one. And therefore, not being other than the one or related to the one as a whole to parts or parts to a whole, not one is the same as one. Wherefore the one is the same and also not the same with the others and also with itself; and is therefore like and unlike itself and the others, and just as different from the others as they are from the one, neither more nor less. But if neither more nor less, equally different; and therefore the one and the others have the same relations. This may be illustrated by the case of names: when you repeat the same name twice over, you mean the same thing; and when you say that the other is other than the one, or the one other than the other, this very word other (eteron), which is attributed to both, implies sameness. One, then, as being other than others, and other as being other than one, are alike in that they have the relation of otherness; and likeness is similarity of relations. And everything as being other of everything is also like everything. Again, same and other, like and unlike, are opposites: and since in virtue of being other than the others the one is like them, in virtue of being the same it must be unlike. Again, one, as having the same relations, has no difference of relation, and is therefore not unlike, and therefore like; or, as having different relations, is different and unlike. Thus, one, as being the same and not the same with itself and others—for both these reasons and for either of them—is also like and unlike itself and the others. Again, how far can one touch itself and the others? As existing in others, it touches the others; and as existing in itself, touches only itself. But from another point of view, that which touches another must be next in order of place; one, therefore, must be next in order of place to itself, and would therefore be two, and in two places. But one cannot be two, and therefore cannot be in contact with itself. Nor again can one touch the other. Two objects are required to make one contact; three objects make two contacts; and all the objects in the world, if placed in a series, would have as many contacts as there are objects, less one. But if one only exists, and not two, there is no contact. And the others, being other than one, have no part in one, and therefore none in number, and therefore two has no existence, and therefore there is no contact. For all which reasons, one has and has not contact with itself and the others.

1.b. Let us begin the inquiry again. We must work out every consequence of assuming that the one exists. If the one exists, it shares in being, which is not the same as the one. The words 'being' and 'one' have different meanings. Notice what follows. In the one that exists, or the being of the one, there are two parts: being and one. Together they form a whole. Each part is also a whole and includes the other. Each can be further divided into one and being, so each is not one but two. Thus the one is never one. In this way, if the one exists, it becomes many and infinite. Now let us imagine that we separate a one from being by an act of abstraction. Will this abstract one be one or many? You say it will be one only. Let us see. First, the being of the one is different from the one. If one and being are different, both must share in the nature of otherness. So otherness is neither one nor being. Whether we consider being and otherness, being and one, or one and otherness, we have two things. We can call each of them either one, and the two together both. Both are two, and each of the two is separately one. If one is added to any pair, the sum is three. Two is an even number, and three is odd. Two units exist twice, so there are twice two. Three units exist three times, so there are three times three. Taken together, they give twice three and three times two. We have even numbers multiplied by even numbers, odd by even, and even by odd. But if the one exists, and it implies both odd and even numbers, must not every number exist? Number is infinite. Therefore, existence must be infinite, since each and every number shares in being. So being has the greatest number of parts, and every part, however large or small, is equally one. But can the one be in many places and still be a whole? If it is not a whole, it must be divided into parts. It must be represented by a number corresponding to the number of its parts. If so, we were wrong to say that being has the greatest number of parts. For being is equal to one and extends as far as one does. It has no more parts than one. So the abstract one, divided into parts by being, is many and infinite. But the parts are parts of a whole, and the whole is the limit that contains them. The one is therefore limited as well as infinite in number. What is whole has a beginning, a middle, and an end. The middle is equally distant from the two ends. So the one has a certain shape, round or straight or a combination of the two. As a whole, it includes all the parts that make up the whole. It is therefore contained within itself. But the whole is not in the parts, whether in all of them or in some. It is not in all the parts because, if it were, it would also be in each one. If it were missing from any one part, how could it be in all? Nor is it in some of the parts, because the greater would then be contained in the less. But if it is not in all, any, or some of the parts, it is either nowhere or in something else. If it were nowhere, it would be nothing. So it is in something else. The one as a whole, then, is in another. But considered as the sum of its parts, it is in itself. It is therefore both in itself and in another. This being so, the one is both at rest and in motion. It is at rest because it rests in itself. It is in motion because it is always in another. If what has come before is true, the one is both the same as and different from itself and the other. For everything in relation to every other thing is either the same as it or different from it. If neither, then one is related to the other as a part to a whole or a whole to a part. But one cannot be a part or a whole in relation to one, nor can it be different from one. It is therefore the same as one. Yet this sameness is contradicted in another way. The one is in a place other than itself, which is in the same place. This follows from the one being both in itself and in another. The one is therefore different from itself. But if anything is different from anything, will it not be different through otherness? What is not one is different from the one, and the one is different from what is not one. Therefore, the one is different from all others. But the same and the other exclude each other. So the other can never be in the same. Nor can the other be in anything for even the shortest time. For during that time, the other would be in the same. And if the other is never in the same, it cannot be in either the one or the not one. So the one is not different from the not one through otherness or through itself. Therefore, they are not different from each other at all. Nor can the not one share in or be part of the one. If it did, it would be one. Nor can the not one be number, since number also involves one. So the not one is not different from the one. Nor is it related to the one as a whole to parts or as parts to a whole. It is therefore the same as the one. Thus the one is both the same as and different from the others and itself. It is therefore both like and unlike itself and the others. The one is just as different from the others as they are from the one, neither more nor less. But if neither is more or less different, they are equally different. So the one and the others have the same relations. Names can illustrate this. When you repeat the same name twice, you mean the same thing. And consider saying that the other is different from the one, or the one from the other. The very word other (eteron), applied to both, implies sameness. The one is different from the others, and the others are different from the one. So they are alike in having the relation of otherness. And likeness is similarity of relations. Everything, then, is also like everything else because it is different from everything else. Again, same and other are opposites, as are like and unlike. Since the one is like the others by being different from them, it must be unlike them by being the same. Again, the one has no difference of relation when its relations are the same. It is therefore not unlike, and so is like. Or, when its relations are different, it is different and unlike. Thus the one is both the same as and different from itself and the others. For both these reasons, and for either one, it is also both like and unlike itself and the others. Again, how far can the one touch itself and the others? Since it exists in the others, it touches the others. And since it exists in itself, it touches only itself. But from another point of view, anything that touches another thing must be next to it in place. The one must therefore be next to itself in place. It would then be two and in two places. But the one cannot be two, so it cannot be in contact with itself. Nor can the one touch the other. Two objects are needed to make one contact. Three objects make two contacts. If all the objects in the world were placed in a series, there would be one fewer contacts than objects. But if only one exists, and not two, there is no contact. The others, being different from one, have no part in one. So they have no part in number. Therefore, two does not exist, and there is no contact. For all these reasons, the one both has and does not have contact with itself and the others.

Once more, Is one equal and unequal to itself and the others? Suppose one and the others to be greater or less than each other or equal to one another, they will be greater or less or equal by reason of equality or greatness or smallness inhering in them in addition to their own proper nature. Let us begin by assuming smallness to be inherent in one: in this case the inherence is either in the whole or in a part. If the first, smallness is either coextensive with the whole one, or contains the whole, and, if coextensive with the one, is equal to the one, or if containing the one will be greater than the one. But smallness thus performs the function of equality or of greatness, which is impossible. Again, if the inherence be in a part, the same contradiction follows: smallness will be equal to the part or greater than the part; therefore smallness will not inhere in anything, and except the idea of smallness there will be nothing small. Neither will greatness; for greatness will have a greater;—and there will be no small in relation to which it is great. And there will be no great or small in objects, but greatness and smallness will be relative only to each other; therefore the others cannot be greater or less than the one; also the one can neither exceed nor be exceeded by the others, and they are therefore equal to one another. And this will be true also of the one in relation to itself: one will be equal to itself as well as to the others (talla). Yet one, being in itself, must also be about itself, containing and contained, and is therefore greater and less than itself. Further, there is nothing beside the one and the others; and as these must be in something, they must therefore be in one another; and as that in which a thing is is greater than the thing, the inference is that they are both greater and less than one another, because containing and contained in one another. Therefore the one is equal to and greater and less than itself or other, having also measures or parts or numbers equal to or greater or less than itself or other.

Once more, is the one equal and unequal to itself and to the others? Suppose the one and the others are greater or smaller than each other, or equal to each other. They will be so because equality, greatness, or smallness is present in them, in addition to their own proper nature. Let us begin by assuming that smallness is present in the one. In that case, smallness is present either in the whole or in a part. If it is present in the whole, smallness either extends exactly as far as the whole one or contains it. If smallness extends exactly as far as the one, it is equal to the one. If it contains the one, it is greater than the one. But smallness is thereby doing the work of equality or greatness, which is impossible. Again, if smallness is present in a part, the same contradiction follows. Smallness will be equal to or greater than the part. Therefore, smallness will not be present in anything, and nothing will be small except the idea of smallness. Greatness will not be present in anything either. For greatness will have something greater than it, and there will be nothing small in relation to which it is great. There will be nothing great or small in objects. Greatness and smallness will relate only to each other. Therefore, the others cannot be greater or smaller than the one. The one can neither exceed nor be exceeded by the others, so they are equal to each other. The same will be true of the one in relation to itself. The one will be equal to itself as well as to the others (talla). Yet the one, being in itself, must also surround itself, containing itself and being contained by itself. It is therefore greater and smaller than itself. Further, there is nothing besides the one and the others. Since these must be in something, they must be in each other. What contains a thing is greater than the thing it contains. So the one and the others are both greater and smaller than each other, because each contains and is contained by the other. Therefore, the one is equal to, greater than, and smaller than itself or the others. It also has measures, parts, or numbers equal to, greater than, or smaller than itself or the others.

But does one partake of time? This must be acknowledged, if the one partakes of being. For 'to be' is the participation of being in present time, 'to have been' in past, 'to be about to be' in future time. And as time is ever moving forward, the one becomes older than itself; and therefore younger than itself; and is older and also younger when in the process of becoming it arrives at the present; and it is always older and younger, for at any moment the one is, and therefore it becomes and is not older and younger than itself but during an equal time with itself, and is therefore contemporary with itself.

But does the one participate in time? We must acknowledge that it does, if the one participates in being. For 'to be' is to participate in being in the present. 'To have been' is to participate in being in the past. And 'to be about to be' is to participate in being in the future. As time always moves forward, the one becomes older than itself, and therefore younger than itself. And when, in the process of becoming, it arrives at the present, it is older and younger than itself. It is always older and younger, because the one exists at every moment. Therefore, it becomes and is older and younger, not than itself, but for an equal amount of time with itself. It is therefore contemporary with itself.

And what are the relations of the one to the others? Is it or does it become older or younger than they? At any rate the others are more than one, and one, being the least of all numbers, must be prior in time to greater numbers. But on the other hand, one must come into being in a manner accordant with its own nature. Now one has parts or others, and has therefore a beginning, middle, and end, of which the beginning is first and the end last. And the parts come into existence first; last of all the whole, contemporaneously with the end, being therefore younger, while the parts or others are older than the one. But, again, the one comes into being in each of the parts as much as in the whole, and must be of the same age with them. Therefore one is at once older and younger than the parts or others, and also contemporaneous with them, for no part can be a part which is not one. Is this true of becoming as well as being? Thus much may be affirmed, that the same things which are older or younger cannot become older or younger in a greater degree than they were at first by the addition of equal times. But, on the other hand, the one, if older than others, has come into being a longer time than they have. And when equal time is added to a longer and shorter, the relative difference between them is diminished. In this way that which was older becomes younger, and that which was younger becomes older, that is to say, younger and older than at first; and they ever become and never have become, for then they would be. Thus the one and others always are and are becoming and not becoming younger and also older than one another. And one, partaking of time and also partaking of becoming older and younger, admits of all time, present, past, and future—was, is, shall be—was becoming, is becoming, will become. And there is science of the one, and opinion and name and expression, as is already implied in the fact of our inquiry.

What is the relation of the one to the others? Is it, or does it become, older or younger than they are? In any case, the others are more than one. And one, being the smallest of all numbers, must come before greater numbers in time. But on the other hand, the one must come into being in a way that accords with its own nature. Now the one has parts, or others, and therefore has a beginning, middle, and end. The beginning comes first and the end last. The parts come into existence first. The whole comes last, at the same time as the end. The whole is therefore younger, while the parts, or others, are older than the one. But again, the one comes into being in each of the parts as much as in the whole. It must therefore be the same age as the parts. So the one is at once older and younger than the parts, or others, and also the same age as them. For nothing can be a part unless it is one. Is this true of becoming as well as being? We can say this much: things that are older or younger cannot become still older or younger when equal time is added to their ages. But on the other hand, if the one is older than the others, it has existed longer than they have. And when equal time is added to a longer and a shorter time, the relative difference between them decreases. In this way, what was older becomes younger, and what was younger becomes older. That is, each becomes younger or older than at first. And they are always becoming so, but have never become so, for then they would be so. Thus the one and the others always are, and are becoming and not becoming, younger and also older than one another. The one partakes of time and also of becoming older and younger. It therefore admits of all time, present, past, and future. It was, is, and will be. It was becoming, is becoming, and will become. And there is knowledge of the one, as well as opinion, a name, and an expression for it. This is already implied by the fact that we are examining it.

Yet once more, if one be one and many, and neither one nor many, and also participant of time, must there not be a time at which one as being one partakes of being, and a time when one as not being one is deprived of being? But these two contradictory states cannot be experienced by the one both together: there must be a time of transition. And the transition is a process of generation and destruction, into and from being and not-being, the one and the others. For the generation of the one is the destruction of the others, and the generation of the others is the destruction of the one. There is also separation and aggregation, assimilation and dissimilation, increase, diminution, equalization, a passage from motion to rest, and from rest to motion in the one and many. But when do all these changes take place? When does motion become rest, or rest motion? The answer to this question will throw a light upon all the others. Nothing can be in motion and at rest at the same time; and therefore the change takes place 'in a moment'—which is a strange expression, and seems to mean change in no time. Which is true also of all the other changes, which likewise take place in no time.

Once again, suppose the one is both one and many, and neither one nor many, and also participates in time. Must there not be a time when the one, being one, shares in being? And must there not be a time when the one, not being one, is deprived of being? But the one cannot experience these two contradictory states at the same time. There must be a time of transition. This transition is a process of coming into being and passing away. It moves between being and not-being, and between the one and the others. For when the one comes into being, the others are destroyed. And when the others come into being, the one is destroyed. There is also separation and gathering, becoming alike and becoming unlike, increase, decrease, and becoming equal. The one and the many also pass from motion to rest and from rest to motion. But when do all these changes take place? When does motion become rest, or rest become motion? The answer to this question will shed light on all the others. Nothing can be in motion and at rest at the same time. So the change takes place 'in a moment'. This is a strange expression, and it seems to mean that the change takes place in no time. The same is true of all the other changes, which likewise take place in no time.

1.aa. But if one is, what happens to the others, which in the first place are not one, yet may partake of one in a certain way? The others are other than the one because they have parts, for if they had no parts they would be simply one, and parts imply a whole to which they belong; otherwise each part would be a part of many, and being itself one of them, of itself, and if a part of all, of each one of the other parts, which is absurd. For a part, if not a part of one, must be a part of all but this one, and if so not a part of each one; and if not a part of each one, not a part of any one of many, and so not of one; and if of none, how of all? Therefore a part is neither a part of many nor of all, but of an absolute and perfect whole or one. And if the others have parts, they must partake of the whole, and must be the whole of which they are the parts. And each part, as the word 'each' implies, is also an absolute one. And both the whole and the parts partake of one, for the whole of which the parts are parts is one, and each part is one part of the whole; and whole and parts as participating in one are other than one, and as being other than one are many and infinite; and however small a fraction you separate from them is many and not one. Yet the fact of their being parts furnishes the others with a limit towards other parts and towards the whole; they are finite and also infinite: finite through participation in the one, infinite in their own nature. And as being finite, they are alike; and as being infinite, they are alike; but as being both finite and also infinite, they are in the highest degree unlike. And all other opposites might without difficulty be shown to unite in them.

1.aa. But if one exists, what happens to the others? The others are not one, though they may share in one in a certain way. They are other than the one because they have parts. If they had no parts, they would simply be one. And parts imply a whole to which they belong. Otherwise, each part would be part of many things. Since it is itself one of those things, it would be part of itself. And if it were part of all of them, it would be part of each other part. That is absurd. For if a part is not part of one thing, it must be part of all but that one. If so, it is not part of each one. And if it is not part of each one, it is not part of any one of the many. So it is not part of one. And if it is part of none, how can it be part of all? Therefore, a part is neither part of many nor part of all, but of an absolute and complete whole or one. And if the others have parts, they must share in the whole. They must also be the whole of which they are the parts. And each part, as the word 'each' implies, is also an absolute one. Both the whole and the parts share in one. For the whole of which the parts are parts is one, and each part is one part of the whole. By sharing in one, the whole and the parts are other than one. And because they are other than one, they are many and infinite. However small a fraction you separate from them, it is many and not one. Yet being parts gives the others a limit in relation to other parts and to the whole. They are finite and also infinite. They are finite because they share in the one, and infinite in their own nature. As finite things, they are alike. And as infinite things, they are alike. But because they are both finite and infinite, they are unlike in the highest degree. It could easily be shown that all other opposites also unite in them.

1.bb. Once more, leaving all this: Is there not also an opposite series of consequences which is equally true of the others, and may be deduced from the existence of one? There is. One is distinct from the others, and the others from one; for one and the others are all things, and there is no third existence besides them. And the whole of one cannot be in others nor parts of it, for it is separated from others and has no parts, and therefore the others have no unity, nor plurality, nor duality, nor any other number, nor any opposition or distinction, such as likeness and unlikeness, some and other, generation and corruption, odd and even. For if they had these they would partake either of one opposite, and this would be a participation in one; or of two opposites, and this would be a participation in two. Thus if one exists, one is all things, and likewise nothing, in relation to one and to the others.

1.bb. Let us set all this aside once more. Is there not also an opposite set of conclusions about the others, equally true, that follows from the existence of one? There is. One is distinct from the others, and the others are distinct from one. Together, one and the others make up everything. There is no third thing besides them. Neither the whole of one nor any part of it can be in the others. For one is separate from the others and has no parts. Therefore, the others have no unity, plurality, duality, or any other number. Nor do they have any oppositions or distinctions, such as likeness and unlikeness, some and other, coming into being and passing away, odd and even. For if they had these, they would share in either one opposite or two opposites. Sharing in one opposite would mean sharing in one. Sharing in two opposites would mean sharing in two. Thus, if one exists, it is all things and also nothing, both in relation to itself and to the others.

2.a. But, again, assume the opposite hypothesis, that the one is not, and what is the consequence? In the first place, the proposition, that one is not, is clearly opposed to the proposition, that not one is not. The subject of any negative proposition implies at once knowledge and difference. Thus 'one' in the proposition—'The one is not,' must be something known, or the words would be unintelligible; and again this 'one which is not' is something different from other things. Moreover, this and that, some and other, may be all attributed or related to the one which is not, and which though non-existent may and must have plurality, if the one only is non-existent and nothing else; but if all is not-being there is nothing which can be spoken of. Also the one which is not differs, and is different in kind from the others, and therefore unlike them; and they being other than the one, are unlike the one, which is therefore unlike them. But one, being unlike other, must be like itself; for the unlikeness of one to itself is the destruction of the hypothesis; and one cannot be equal to the others; for that would suppose being in the one, and the others would be equal to one and like one; both which are impossible, if one does not exist. The one which is not, then, if not equal is unequal to the others, and in equality implies great and small, and equality lies between great and small, and therefore the one which is not partakes of equality. Further, the one which is not has being; for that which is true is, and it is true that the one is not. And so the one which is not, if remitting aught of the being of non-existence, would become existent. For not being implies the being of not-being, and being the not-being of not-being; or more truly being partakes of the being of being and not of the being of not-being, and not-being of the being of not-being and not of the not-being of not-being. And therefore the one which is not has being and also not-being. And the union of being and not-being involves change or motion. But how can not-being, which is nowhere, move or change, either from one place to another or in the same place? And whether it is or is not, it would cease to be one if experiencing a change of substance. The one which is not, then, is both in motion and at rest, is altered and unaltered, and becomes and is destroyed, and does not become and is not destroyed.

2.a. But suppose instead that the one does not exist. What follows? First, the proposition that the one does not exist clearly opposes the proposition that not one does not exist. The subject of any negative proposition implies both knowledge and difference. Thus, in the proposition “The one does not exist,” “the one” must be something known. Otherwise, the words would make no sense. Also, this “one which does not exist” is different from other things. Moreover, this and that, some and other, may all be attributed or related to the one that does not exist. Though nonexistent, the one may and must have plurality, if only the one is nonexistent and nothing else is. But if everything is non-being, there is nothing to speak of. Also, the one that does not exist differs from the others and is different in kind from them. It is therefore unlike them. And since the others are other than the one, they are unlike the one. The one is therefore unlike them. But the one, being unlike what is other, must be like itself. If it were unlike itself, the hypothesis would be destroyed. Nor can the one be equal to the others. That would mean that the one has being. It would also mean that the others are equal and like the one. Both are impossible if the one does not exist. The one that does not exist, then, is not equal to the others and is therefore unequal to them. Inequality implies great and small, and equality lies between great and small. Therefore, the one that does not exist partakes of equality. Further, the one that does not exist has being. For what is true is, and it is true that the one does not exist. So if the one that does not exist lost any of the being of non-existence, it would come to exist. For not-being implies the being of not-being, and being implies the not-being of not-being. Or, more exactly, being partakes of the being of being, not of the being of not-being. And not-being partakes of the being of not-being, not of the not-being of not-being. Therefore, the one that does not exist has both being and not-being. And the union of being and not-being involves change or motion. But how can not-being, which is nowhere, move or change, either from one place to another or in the same place? And whether the one exists or not, it would cease to be one if its substance changed. The one that does not exist, then, is both in motion and at rest. It is both altered and unaltered. It both comes to be and is destroyed, and does not come to be and is not destroyed.

2.b. Once more, let us ask the question, If one is not, what happens in regard to one? The expression 'is not' implies negation of being:—do we mean by this to say that a thing, which is not, in a certain sense is? or do we mean absolutely to deny being of it? The latter. Then the one which is not can neither be nor become nor perish nor experience change of substance or place. Neither can rest, or motion, or greatness, or smallness, or equality, or unlikeness, or likeness either to itself or other, or attribute or relation, or now or hereafter or formerly, or knowledge or opinion or perception or name or anything else be asserted of that which is not.

2.b. Once again, let us ask: If one is not, what follows for one? The expression 'is not' denies being. Does it mean that a thing that is not nevertheless exists in some sense? Or does it completely deny that the thing exists? The latter. Then the one that is not can neither exist nor come into being nor perish. It cannot undergo a change in substance or place. Nor can anything be asserted of what is not. It cannot be said to rest or move, or to be great, small, or equal. It cannot be said to be like or unlike itself or anything else. It cannot be said to have any attribute or relation, or to exist now, later, or formerly. Nor can knowledge, opinion, perception, a name, or anything else be attributed to it.

2.aa. Once more, if one is not, what becomes of the others? If we speak of them they must be, and their very name implies difference, and difference implies relation, not to the one, which is not, but to one another. And they are others of each other not as units but as infinities, the least of which is also infinity, and capable of infinitesimal division. And they will have no unity or number, but only a semblance of unity and number; and the least of them will appear large and manifold in comparison with the infinitesimal fractions into which it may be divided. Further, each particle will have the appearance of being equal with the fractions. For in passing from the greater to the less it must reach an intermediate point, which is equality. Moreover, each particle although having a limit in relation to itself and to other particles, yet it has neither beginning, middle, nor end; for there is always a beginning before the beginning, and a middle within the middle, and an end beyond the end, because the infinitesimal division is never arrested by the one. Thus all being is one at a distance, and broken up when near, and like at a distance and unlike when near; and also the particles which compose being seem to be like and unlike, in rest and motion, in generation and corruption, in contact and separation, if one is not.

2.aa. Once again, if the one does not exist, what happens to the others? If we speak of the others, they must exist. Their very name implies difference, and difference implies a relationship. This relationship is not to the one, which does not exist, but to one another. They are others in relation to one another, not as units but as infinities. Even the smallest is infinite and can be divided into infinitesimal parts. They will have no unity or number, but only the appearance of unity and number. Even the smallest will appear large and made up of many parts. That is because it can be divided into infinitesimal fractions. Further, each particle will appear equal to the fractions. For as it passes from greater to smaller, it must reach an intermediate point, where it is equal. Moreover, each particle has a limit in relation to itself and to other particles. Yet it has no beginning, middle, or end. For there is always a beginning before the beginning, a middle within the middle, and an end beyond the end. This is because the one never stops the infinitesimal division. Thus all being appears as one at a distance and broken up when near. It appears alike at a distance and unlike when near. Also, if the one does not exist, the particles that make up being seem both alike and unlike. They seem both at rest and in motion, coming into being and passing away, in contact and separate.

2.bb. Once more, let us inquire, If the one is not, and the others of the one are, what follows? In the first place, the others will not be the one, nor the many, for in that case the one would be contained in them; neither will they appear to be one or many; because they have no communion or participation in that which is not, nor semblance of that which is not. If one is not, the others neither are, nor appear to be one or many, like or unlike, in contact or separation. In short, if one is not, nothing is.

2.bb. Let us ask again: If the one does not exist, but the others of the one do, what follows? First, the others will be neither one nor many, because either would mean that the one was contained in them. Nor will they appear to be one or many. This is because they have no connection with or share in what does not exist, or any appearance of it. If the one does not exist, the others neither are nor appear to be one or many, alike or different, touching or separate. In short, if the one does not exist, nothing exists.

The result of all which is, that whether one is or is not, one and the others, in relation to themselves and to one another, are and are not, and appear to be and appear not to be, in all manner of ways.

The conclusion is that whether the one exists or not, both the one and the others exist and do not exist. They also appear to exist and appear not to exist. This is true in every way, both in relation to themselves and to one another.

I. On the first hypothesis we may remark: first, That one is one is an identical proposition, from which we might expect that no further consequences could be deduced. The train of consequences which follows, is inferred by altering the predicate into 'not many.' Yet, perhaps, if a strict Eristic had been present, oios aner ei kai nun paren, he might have affirmed that the not many presented a different aspect of the conception from the one, and was therefore not identical with it. Such a subtlety would be very much in character with the Zenonian dialectic. Secondly, We may note, that the conclusion is really involved in the premises. For one is conceived as one, in a sense which excludes all predicates. When the meaning of one has been reduced to a point, there is no use in saying that it has neither parts nor magnitude. Thirdly, The conception of the same is, first of all, identified with the one; and then by a further analysis distinguished from, and even opposed to it. Fourthly, We may detect notions, which have reappeared in modern philosophy, e.g. the bare abstraction of undefined unity, answering to the Hegelian 'Seyn,' or the identity of contradictions 'that which is older is also younger,' etc., or the Kantian conception of an a priori synthetical proposition 'one is.'

I. On the first hypothesis, we may note four points. First, the statement that one is one is an identity. We might therefore expect that no further conclusions could be drawn from it. The chain of conclusions that follows comes from changing the predicate to 'not many.' Yet perhaps a strict Eristic, oios aner ei kai nun paren, might have objected. He might have argued that 'not many' presented a different aspect of the concept from 'one.' It was therefore not identical with 'one.' Such subtlety would be very much in keeping with Zenonian dialectic. Second, we may note that the conclusion is already contained in the premises. For one is understood as one in a sense that excludes all predicates. Once the meaning of one has been reduced to a point, there is no use saying that it has neither parts nor magnitude. Third, the concept of the same is first identified with the one. Then, through further analysis, it is distinguished from the one and even opposed to it. Fourth, we may detect ideas that have reappeared in modern philosophy. Examples include the bare abstraction of undefined unity, corresponding to the Hegelian 'Seyn,' and the identity of contradictions, as in 'that which is older is also younger.' Another example is the Kantian concept of an a priori synthetic proposition, as in 'one is.'

II. In the first series of propositions the word 'is' is really the copula; in the second, the verb of existence. As in the first series, the negative consequence followed from one being affirmed to be equivalent to the not many; so here the affirmative consequence is deduced from one being equivalent to the many.

II. In the first series of propositions, 'is' really serves as a copula. In the second series, it expresses existence. In the first series, the negative consequence followed from stating that one was equivalent to the not many. Likewise, here the affirmative consequence is drawn from one being equivalent to the many.

In the former case, nothing could be predicated of the one, but now everything—multitude, relation, place, time, transition. One is regarded in all the aspects of one, and with a reference to all the consequences which flow, either from the combination or the separation of them. The notion of transition involves the singular extra-temporal conception of 'suddenness.' This idea of 'suddenness' is based upon the contradiction which is involved in supposing that anything can be in two places at once. It is a mere fiction; and we may observe that similar antinomies have led modern philosophers to deny the reality of time and space. It is not the infinitesimal of time, but the negative of time. By the help of this invention the conception of change, which sorely exercised the minds of early thinkers, seems to be, but is not really at all explained. The difficulty arises out of the imperfection of language, and should therefore be no longer regarded as a difficulty at all. The only way of meeting it, if it exists, is to acknowledge that this rather puzzling double conception is necessary to the expression of the phenomena of motion or change, and that this and similar double notions, instead of being anomalies, are among the higher and more potent instruments of human thought.

In the former case, nothing could be said of the one. But now everything can be said of it: multitude, relation, place, time, and transition. The one is considered in every aspect of its oneness. It is also considered in relation to all the consequences that follow from combining or separating those aspects. The idea of transition involves the unusual conception of 'suddenness' as something outside time. This idea of 'suddenness' rests on the contradiction involved in supposing that anything can be in two places at once. It is a mere fiction. We may note that similar contradictions have led modern philosophers to deny the reality of time and space. 'Suddenness' is not an infinitesimally small amount of time. It is the absence of time. This invention seems to explain change, a concept that greatly troubled early thinkers. But it does not really explain change at all. The difficulty arises from the imperfections of language, so it should no longer be regarded as a difficulty. If the difficulty does exist, the only way to address it is to acknowledge this puzzling double conception. It is necessary for describing the phenomena of motion or change. We must also acknowledge that this and similar double concepts are not anomalies. They are among the higher and more powerful instruments of human thought.

The processes by which Parmenides obtains his remarkable results may be summed up as follows: (1) Compound or correlative ideas which involve each other, such as, being and not-being, one and many, are conceived sometimes in a state of composition, and sometimes of division: (2) The division or distinction is sometimes heightened into total opposition, e.g. between one and same, one and other: or (3) The idea, which has been already divided, is regarded, like a number, as capable of further infinite subdivision: (4) The argument often proceeds 'a dicto secundum quid ad dictum simpliciter' and conversely: (5) The analogy of opposites is misused by him; he argues indiscriminately sometimes from what is like, sometimes from what is unlike in them: (6) The idea of being or not-being is identified with existence or non-existence in place or time: (7) The same ideas are regarded sometimes as in process of transition, sometimes as alternatives or opposites: (8) There are no degrees or kinds of sameness, likeness, difference, nor any adequate conception of motion or change: (9) One, being, time, like space in Zeno's puzzle of Achilles and the tortoise, are regarded sometimes as continuous and sometimes as discrete: (10) In some parts of the argument the abstraction is so rarefied as to become not only fallacious, but almost unintelligible, e.g. in the contradiction which is elicited out of the relative terms older and younger: (11) The relation between two terms is regarded under contradictory aspects, as for example when the existence of the one and the non-existence of the one are equally assumed to involve the existence of the many: (12) Words are used through long chains of argument, sometimes loosely, sometimes with the precision of numbers or of geometrical figures.

The methods Parmenides uses to reach his remarkable conclusions may be summed up as follows: (1) Compound or related ideas that involve each other are sometimes treated as combined and sometimes as separate. Examples include being and not-being, and one and many. (2) The division or distinction is sometimes treated as a total opposition. This happens, for example, with one and same, and one and other. (3) An idea that has already been divided is treated as capable of further infinite subdivision, like a number. (4) The argument often moves from a qualified statement to an unqualified one, and vice versa. (5) Parmenides misuses the analogy between opposites. He argues indiscriminately, sometimes from what is alike in them and sometimes from what is unlike. (6) The idea of being or not-being is identified with existence or non-existence in space or time. (7) The same ideas are sometimes treated as being in transition and sometimes as alternatives or opposites. (8) There are no degrees or kinds of sameness, likeness, or difference, and no adequate conception of motion or change. (9) One, being, and time are sometimes treated as continuous and sometimes as separate units. Space is treated in the same way in Zeno's puzzle of Achilles and the tortoise. (10) In some parts of the argument, the abstraction becomes so refined that it is not only fallacious but almost unintelligible. One example is the contradiction drawn from the relative terms older and younger. (11) The relation between two terms is viewed in contradictory ways. For example, both the existence and the non-existence of the one are assumed to imply the existence of the many. (12) Words are used throughout long chains of argument, sometimes loosely and sometimes with the precision of numbers or geometric figures.

The argument is a very curious piece of work, unique in literature. It seems to be an exposition or rather a 'reductio ad absurdum' of the Megarian philosophy, but we are too imperfectly acquainted with this last to speak with confidence about it. It would be safer to say that it is an indication of the sceptical, hyperlogical fancies which prevailed among the contemporaries of Socrates. It throws an indistinct light upon Aristotle, and makes us aware of the debt which the world owes to him or his school. It also bears a resemblance to some modern speculations, in which an attempt is made to narrow language in such a manner that number and figure may be made a calculus of thought. It exaggerates one side of logic and forgets the rest. It has the appearance of a mathematical process; the inventor of it delights, as mathematicians do, in eliciting or discovering an unexpected result. It also helps to guard us against some fallacies by showing the consequences which flow from them.

The argument is a very curious piece of work, unique in literature. It seems to explain Megarian philosophy, or rather to be a 'reductio ad absurdum' of it. But we know too little about Megarian philosophy to speak confidently about this. It would be safer to say that the argument reflects the skeptical, overly logical ideas common among Socrates' contemporaries. It sheds some faint light on Aristotle and makes us aware of the debt the world owes him or his school. It also resembles some modern theories that attempt to restrict language so that number and shape can become a calculus of thought. The argument exaggerates one side of logic and forgets the rest. It looks like a mathematical process. Its inventor delights, as mathematicians do, in drawing out or discovering an unexpected result. It also helps guard us against some errors in reasoning by showing their consequences.

In the Parmenides we seem to breathe the spirit of the Megarian philosophy, though we cannot compare the two in detail. But Plato also goes beyond his Megarian contemporaries; he has split their straws over again, and admitted more than they would have desired. He is indulging the analytical tendencies of his age, which can divide but not combine. And he does not stop to inquire whether the distinctions which he makes are shadowy and fallacious, but 'whither the argument blows' he follows.

In the Parmenides, we seem to sense the spirit of Megarian philosophy, though we cannot compare the two in detail. But Plato also goes beyond his Megarian contemporaries. He has split their hairs even further and admitted more than they would have wanted. He indulges his age’s tendency toward analysis, which can divide but not combine. He does not stop to ask whether his distinctions are vague and misleading. Instead, he follows 'whither the argument blows'.

III. The negative series of propositions contains the first conception of the negation of a negation. Two minus signs in arithmetic or algebra make a plus. Two negatives destroy each other. This abstruse notion is the foundation of the Hegelian logic. The mind must not only admit that determination is negation, but must get through negation into affirmation. Whether this process is real, or in any way an assistance to thought, or, like some other logical forms, a mere figure of speech transferred from the sphere of mathematics, may be doubted. That Plato and the most subtle philosopher of the nineteenth century should have lighted upon the same notion, is a singular coincidence of ancient and modern thought.

III. The negative series of propositions contains the first idea of the negation of a negation. Two minus signs in arithmetic or algebra make a plus. Two negatives cancel each other out. This difficult idea is the foundation of Hegelian logic. The mind must not only accept that determination is negation. It must also move through negation to affirmation. We may doubt whether this process is real or helps thought in any way. It may, like some other logical forms, be merely a figure of speech borrowed from mathematics. Plato and the most subtle philosopher of the nineteenth century arrived at the same idea. This is a striking coincidence between ancient and modern thought.

IV. The one and the many or others are reduced to their strictest arithmetical meaning. That one is three or three one, is a proposition which has, perhaps, given rise to more controversy in the world than any other. But no one has ever meant to say that three and one are to be taken in the same sense. Whereas the one and many of the Parmenides have precisely the same meaning; there is no notion of one personality or substance having many attributes or qualities. The truth seems to be rather the opposite of that which Socrates implies: There is no contradiction in the concrete, but in the abstract; and the more abstract the idea, the more palpable will be the contradiction. For just as nothing can persuade us that the number one is the number three, so neither can we be persuaded that any abstract idea is identical with its opposite, although they may both inhere together in some external object, or some more comprehensive conception. Ideas, persons, things may be one in one sense and many in another, and may have various degrees of unity and plurality. But in whatever sense and in whatever degree they are one they cease to be many; and in whatever degree or sense they are many they cease to be one.

IV. The one and the many, or others, are reduced to their strictest numerical meaning. The proposition that one is three, or three is one, has perhaps caused more controversy than any other. But no one has ever meant that three and one should be understood in the same sense. In Parmenides, however, the one and the many have precisely the same meaning. There is no idea of one person or substance having many attributes or qualities. The truth seems to be the opposite of what Socrates implies. Contradiction lies not in the concrete but in the abstract. And the more abstract an idea is, the more obvious the contradiction will be. Nothing can persuade us that the number one is the number three. Likewise, nothing can persuade us that any abstract idea is identical to its opposite. Yet both may exist together in some external object or in a broader conception. Ideas, persons, and things may be one in one sense and many in another. They may also have different degrees of unity and plurality. But in whatever sense and to whatever degree they are one, they cease to be many. And in whatever sense and to whatever degree they are many, they cease to be one.

Two points remain to be considered: 1st, the connexion between the first and second parts of the dialogue; 2ndly, the relation of the Parmenides to the other dialogues.

Two points remain to be considered: first, the connection between the first and second parts of the dialogue. Second, the relationship between the Parmenides and the other dialogues.

I. In both divisions of the dialogue the principal speaker is the same, and the method pursued by him is also the same, being a criticism on received opinions: first, on the doctrine of Ideas; secondly, of Being. From the Platonic Ideas we naturally proceed to the Eleatic One or Being which is the foundation of them. They are the same philosophy in two forms, and the simpler form is the truer and deeper. For the Platonic Ideas are mere numerical differences, and the moment we attempt to distinguish between them, their transcendental character is lost; ideas of justice, temperance, and good, are really distinguishable only with reference to their application in the world. If we once ask how they are related to individuals or to the ideas of the divine mind, they are again merged in the aboriginal notion of Being. No one can answer the questions which Parmenides asks of Socrates. And yet these questions are asked with the express acknowledgment that the denial of ideas will be the destruction of the human mind. The true answer to the difficulty here thrown out is the establishment of a rational psychology; and this is a work which is commenced in the Sophist. Plato, in urging the difficulty of his own doctrine of Ideas, is far from denying that some doctrine of Ideas is necessary, and for this he is paving the way.

I. In both parts of the dialogue, the same person is the main speaker. He also uses the same method in both parts, criticizing accepted opinions. First, he examines the doctrine of Ideas. Then he examines the doctrine of Being. From the Platonic Ideas, we naturally move to the Eleatic One or Being, which is their foundation. These are two forms of the same philosophy. The simpler form is truer and deeper. For the Platonic Ideas are merely different in number. The moment we try to distinguish them, they lose their transcendental character. Ideas of justice, temperance, and good can really be distinguished only by how they apply to the world. If we ask how they relate to individuals or to ideas in the divine mind, they merge again into the original notion of Being. No one can answer the questions Parmenides asks Socrates. Yet these questions are asked with the explicit acknowledgment that denying Ideas would destroy the human mind. The true answer to the difficulty raised here is to establish a rational psychology. This work begins in the Sophist. Plato presses the difficulty in his own doctrine of Ideas. But he is far from denying that some doctrine of Ideas is necessary. He is paving the way for such a doctrine.

In a similar spirit he criticizes the Eleatic doctrine of Being, not intending to deny Ontology, but showing that the old Eleatic notion, and the very name 'Being,' is unable to maintain itself against the subtleties of the Megarians. He did not mean to say that Being or Substance had no existence, but he is preparing for the development of his later view, that ideas were capable of relation. The fact that contradictory consequences follow from the existence or non-existence of one or many, does not prove that they have or have not existence, but rather that some different mode of conceiving them is required. Parmenides may still have thought that 'Being was,' just as Kant would have asserted the existence of 'things in themselves,' while denying the transcendental use of the Categories.

In the same spirit, he criticizes the Eleatic doctrine of Being. He does not mean to deny Ontology. Rather, he shows that the old Eleatic idea, and even the name 'Being,' cannot withstand the subtle arguments of the Megarians. He did not mean that Being or Substance did not exist. Instead, he is preparing to develop his later view that ideas could have relations with one another. Contradictory consequences follow whether one or many exist or do not exist. But this does not prove that one or many exist or do not exist. Rather, it suggests that we need a different way of thinking about them. Parmenides may still have thought that 'Being was.' Similarly, Kant would have asserted the existence of 'things in themselves,' while denying the transcendental use of the Categories.

Several lesser links also connect the first and second parts of the dialogue: (1) The thesis is the same as that which Zeno has been already discussing: (2) Parmenides has intimated in the first part, that the method of Zeno should, as Socrates desired, be extended to Ideas: (3) The difficulty of participating in greatness, smallness, equality is urged against the Ideas as well as against the One.

Several smaller links also connect the first and second parts of the dialogue: (1) The thesis is the same one Zeno has already been discussing. (2) In the first part, Parmenides suggested that Zeno’s method should be extended to Ideas, as Socrates wanted. (3) The difficulty of participating in greatness, smallness, and equality is raised against the Ideas as well as the One.

II. The Parmenides is not only a criticism of the Eleatic notion of Being, but also of the methods of reasoning then in existence, and in this point of view, as well as in the other, may be regarded as an introduction to the Sophist. Long ago, in the Euthydemus, the vulgar application of the 'both and neither' Eristic had been subjected to a similar criticism, which there takes the form of banter and irony, here of illustration.

II. The Parmenides criticizes not only the Eleatic idea of Being, but also the methods of reasoning used at the time. In both respects, it may be seen as an introduction to the Sophist. Much earlier, in the Euthydemus, the crude use of 'both and neither' Eristic had received similar criticism. There the criticism takes the form of banter and irony. Here it takes the form of illustration.

The attack upon the Ideas is resumed in the Philebus, and is followed by a return to a more rational philosophy. The perplexity of the One and Many is there confined to the region of Ideas, and replaced by a theory of classification; the Good arranged in classes is also contrasted with the barren abstraction of the Megarians. The war is carried on against the Eristics in all the later dialogues, sometimes with a playful irony, at other times with a sort of contempt. But there is no lengthened refutation of them. The Parmenides belongs to that stage of the dialogues of Plato in which he is partially under their influence, using them as a sort of 'critics or diviners' of the truth of his own, and of the Eleatic theories. In the Theaetetus a similar negative dialectic is employed in the attempt to define science, which after every effort remains undefined still. The same question is revived from the objective side in the Sophist: Being and Not-being are no longer exhibited in opposition, but are now reconciled; and the true nature of Not-being is discovered and made the basis of the correlation of ideas. Some links are probably missing which might have been supplied if we had trustworthy accounts of Plato's oral teaching.

The attack on the Ideas resumes in the Philebus, followed by a return to a more rational philosophy. There, the puzzle of the One and Many is confined to the realm of Ideas and replaced by a theory of classification. The Good, arranged in classes, is also contrasted with the barren abstraction of the Megarians. The fight against the Eristics continues in all the later dialogues, sometimes with playful irony and sometimes with a kind of contempt. But there is no lengthy refutation of the Eristics. The Parmenides belongs to a stage of Plato's dialogues when he is partly under the Eristics' influence. He uses them as a kind of 'critics or diviners' of the truth of his own theories and the Eleatic theories. In the Theaetetus, a similar negative dialectic is used in an attempt to define science. But despite every effort, science remains undefined. The same question is raised again from the objective side in the Sophist. Being and Not-being are no longer presented as opposites, but are now reconciled. The true nature of Not-being is discovered and made the basis for the correlation of ideas. Some links are probably missing. We might have had them if we had reliable accounts of Plato's oral teaching.

To sum up: the Parmenides of Plato is a critique, first, of the Platonic Ideas, and secondly, of the Eleatic doctrine of Being. Neither are absolutely denied. But certain difficulties and consequences are shown in the assumption of either, which prove that the Platonic as well as the Eleatic doctrine must be remodelled. The negation and contradiction which are involved in the conception of the One and Many are preliminary to their final adjustment. The Platonic Ideas are tested by the interrogative method of Socrates; the Eleatic One or Being is tried by the severer and perhaps impossible method of hypothetical consequences, negative and affirmative. In the latter we have an example of the Zenonian or Megarian dialectic, which proceeded, not 'by assailing premises, but conclusions'; this is worked out and improved by Plato. When primary abstractions are used in every conceivable sense, any or every conclusion may be deduced from them. The words 'one,' 'other,' 'being,' 'like,' 'same,' 'whole,' and their opposites, have slightly different meanings, as they are applied to objects of thought or objects of sense—to number, time, place, and to the higher ideas of the reason;—and out of their different meanings this 'feast' of contradictions 'has been provided.'

In short, Plato’s Parmenides critiques first the Platonic Ideas and then the Eleatic doctrine of Being. It does not completely reject either doctrine. But it shows that assuming either doctrine leads to difficulties and consequences. These show that both doctrines must be revised. The negations and contradictions involved in the idea of the One and the Many come before their final reconciliation. The Platonic Ideas are tested by Socrates’ method of questioning. The Eleatic One, or Being, is tested by a stricter and perhaps impossible method. This method examines the positive and negative consequences of a hypothesis. It is an example of the Zenonian or Megarian dialectic, which proceeded not “by assailing premises, but conclusions.” Plato develops and improves this dialectic. When basic abstractions are used in every conceivable sense, any or every conclusion can be drawn from them. The words “one,” “other,” “being,” “like,” “same,” “whole,” and their opposites have slightly different meanings in different contexts. They are applied to objects of thought or of the senses, to number, time, and place, and to the higher ideas of reason. These different meanings have provided this “feast” of contradictions.

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The Parmenides of Plato belongs to a stage of philosophy which has passed away. At first we read it with a purely antiquarian or historical interest; and with difficulty throw ourselves back into a state of the human mind in which Unity and Being occupied the attention of philosophers. We admire the precision of the language, in which, as in some curious puzzle, each word is exactly fitted into every other, and long trains of argument are carried out with a sort of geometrical accuracy. We doubt whether any abstract notion could stand the searching cross-examination of Parmenides; and may at last perhaps arrive at the conclusion that Plato has been using an imaginary method to work out an unmeaning conclusion. But the truth is, that he is carrying on a process which is not either useless or unnecessary in any age of philosophy. We fail to understand him, because we do not realize that the questions which he is discussing could have had any value or importance. We suppose them to be like the speculations of some of the Schoolmen, which end in nothing. But in truth he is trying to get rid of the stumbling-blocks of thought which beset his contemporaries. Seeing that the Megarians and Cynics were making knowledge impossible, he takes their 'catch-words' and analyzes them from every conceivable point of view. He is criticizing the simplest and most general of our ideas, in which, as they are the most comprehensive, the danger of error is the most serious; for, if they remain unexamined, as in a mathematical demonstration, all that flows from them is affected, and the error pervades knowledge far and wide. In the beginning of philosophy this correction of human ideas was even more necessary than in our own times, because they were more bound up with words; and words when once presented to the mind exercised a greater power over thought. There is a natural realism which says, 'Can there be a word devoid of meaning, or an idea which is an idea of nothing?' In modern times mankind have often given too great importance to a word or idea. The philosophy of the ancients was still more in slavery to them, because they had not the experience of error, which would have placed them above the illusion.

Plato's Parmenides belongs to a stage of philosophy that has passed. At first, we read it purely for its historical interest. We struggle to put ourselves in a state of mind in which Unity and Being occupied philosophers' attention. We admire the precision of the language. As in a curious puzzle, every word fits exactly with every other, and long chains of argument follow with something like geometrical accuracy. We doubt whether any abstract idea could withstand Parmenides' searching examination. Perhaps we finally conclude that Plato has used an imaginary method to reach a meaningless conclusion. But in truth, Plato is carrying out a process that is neither useless nor unnecessary in any age of philosophy. We fail to understand him because we cannot see how his questions could have had any value or importance. We suppose his questions are like the speculations of some of the Schoolmen, which lead nowhere. But Plato is really trying to clear away the obstacles to thought that troubled his contemporaries. He sees that the Megarians and Cynics are making knowledge impossible. So he takes their 'catch-words' and analyzes them from every conceivable point of view. Plato is examining our simplest and most general ideas. Because these ideas cover the most ground, the danger of error is most serious. For if they remain unexamined, everything that follows from them is affected, as in a mathematical demonstration. The error then spreads throughout knowledge. In the early days of philosophy, correcting human ideas was even more necessary than it is today. Ideas were more closely tied to words, and words, once presented to the mind, had greater power over thought. There is a natural tendency to treat words and ideas as real things. It asks, 'Can there be a word with no meaning, or an idea that is an idea of nothing?' In modern times, people have often given too much importance to a word or idea. Ancient philosophy was even more enslaved by words and ideas. The ancients had not yet had the experience of error that would have freed them from the illusion.

The method of the Parmenides may be compared with the process of purgation, which Bacon sought to introduce into philosophy. Plato is warning us against two sorts of 'Idols of the Den': first, his own Ideas, which he himself having created is unable to connect in any way with the external world; secondly, against two idols in particular, 'Unity' and 'Being,' which had grown up in the pre-Socratic philosophy, and were still standing in the way of all progress and development of thought. He does not say with Bacon, 'Let us make truth by experiment,' or 'From these vague and inexact notions let us turn to facts.' The time has not yet arrived for a purely inductive philosophy. The instruments of thought must first be forged, that they may be used hereafter by modern inquirers. How, while mankind were disputing about universals, could they classify phenomena? How could they investigate causes, when they had not as yet learned to distinguish between a cause and an end? How could they make any progress in the sciences without first arranging them? These are the deficiencies which Plato is seeking to supply in an age when knowledge was a shadow of a name only. In the earlier dialogues the Socratic conception of universals is illustrated by his genius; in the Phaedrus the nature of division is explained; in the Republic the law of contradiction and the unity of knowledge are asserted; in the later dialogues he is constantly engaged both with the theory and practice of classification. These were the 'new weapons,' as he terms them in the Philebus, which he was preparing for the use of some who, in after ages, would be found ready enough to disown their obligations to the great master, or rather, perhaps, would be incapable of understanding them.

The method of the Parmenides may be compared to the process of clearing away errors that Bacon sought to introduce into philosophy. Plato warns us against two kinds of 'Idols of the Den.' The first is his own Ideas. He created them himself, yet cannot connect them in any way to the external world. The second consists of two idols in particular, 'Unity' and 'Being.' These had emerged in pre-Socratic philosophy and still stood in the way of all progress and development of thought. Plato does not say, as Bacon does, 'Let us make truth by experiment,' or 'From these vague and inexact notions let us turn to facts.' The time has not yet come for a purely inductive philosophy. The tools of thought must first be forged so that modern inquirers can use them later. While people were debating universals, how could they classify phenomena? How could they investigate causes when they had not yet learned to distinguish between a cause and an end? How could they make any progress in the sciences without first putting them in order? Plato is trying to fill these gaps in an age when knowledge was only the shadow of a name. In the earlier dialogues, Plato uses his genius to illustrate Socrates' conception of universals. In the Phaedrus, he explains the nature of division. In the Republic, he asserts the law of contradiction and the unity of knowledge. In the later dialogues, he is constantly concerned with both the theory and practice of classification. These were the 'new weapons,' as he calls them in the Philebus. He was preparing them for the use of people in later ages. Some of those people would prove ready enough to deny what they owed the great master. Or perhaps they would be incapable of understanding it.

Numberless fallacies, as we are often truly told, have originated in a confusion of the 'copula,' and the 'verb of existence.' Would not the distinction which Plato by the mouth of Parmenides makes between 'One is one' and 'One has being' have saved us from this and many similar confusions? We see again that a long period in the history of philosophy was a barren tract, not uncultivated, but unfruitful, because there was no inquiry into the relation of language and thought, and the metaphysical imagination was incapable of supplying the missing link between words and things. The famous dispute between Nominalists and Realists would never have been heard of, if, instead of transferring the Platonic Ideas into a crude Latin phraseology, the spirit of Plato had been truly understood and appreciated. Upon the term substance at least two celebrated theological controversies appear to hinge, which would not have existed, or at least not in their present form, if we had 'interrogated' the word substance, as Plato has the notions of Unity and Being. These weeds of philosophy have struck their roots deep into the soil, and are always tending to reappear, sometimes in new-fangled forms; while similar words, such as development, evolution, law, and the like, are constantly put in the place of facts, even by writers who profess to base truth entirely upon fact. In an unmetaphysical age there is probably more metaphysics in the common sense (i.e. more a priori assumption) than in any other, because there is more complete unconsciousness that we are resting on our own ideas, while we please ourselves with the conviction that we are resting on facts. We do not consider how much metaphysics are required to place us above metaphysics, or how difficult it is to prevent the forms of expression which are ready made for our use from outrunning actual observation and experiment.

As we are often rightly told, countless fallacies have arisen from confusing the 'copula' with the 'verb of existence.' Plato, speaking through Parmenides, distinguishes between 'One is one' and 'One has being.' Would this distinction not have saved us from this and many similar confusions? We see again that a long period in the history of philosophy was barren. It was not uncultivated, but it produced no fruit. This was because no one examined the relationship between language and thought. The metaphysical imagination could not supply the missing link between words and things. The famous dispute between Nominalists and Realists would never have arisen if Plato's spirit had been truly understood and appreciated. Instead, his Ideas were transferred into crude Latin terms. At least two famous theological controversies seem to depend on the term substance. These controversies would not have existed, or at least not in their present form, if we had 'interrogated' the word substance. Plato questioned the notions of Unity and Being in this way. These weeds of philosophy have put down deep roots, and they keep tending to reappear, sometimes in new forms. Meanwhile, words such as development, evolution, and law are constantly put in place of facts. Even writers who claim to base truth entirely on fact do this. In an age that rejects metaphysics, there is probably more metaphysics in common sense than in any other age. That is, common sense probably contains more a priori assumptions. This is because we are more completely unaware that we are relying on our own ideas. Instead, we take comfort in the belief that we are relying on facts. We do not consider how much metaphysics is needed to put us above metaphysics. Nor do we consider how difficult it is to keep ready-made forms of expression from outrunning actual observation and experiment.

In the last century the educated world were astonished to find that the whole fabric of their ideas was falling to pieces, because Hume amused himself by analyzing the word 'cause' into uniform sequence. Then arose a philosophy which, equally regardless of the history of the mind, sought to save mankind from scepticism by assigning to our notions of 'cause and effect,' 'substance and accident,' 'whole and part,' a necessary place in human thought. Without them we could have no experience, and therefore they were supposed to be prior to experience—to be incrusted on the 'I'; although in the phraseology of Kant there could be no transcendental use of them, or, in other words, they were only applicable within the range of our knowledge. But into the origin of these ideas, which he obtains partly by an analysis of the proposition, partly by development of the 'ego,' he never inquires—they seem to him to have a necessary existence; nor does he attempt to analyse the various senses in which the word 'cause' or 'substance' may be employed.

In the last century, the educated world was astonished to find its whole system of ideas falling apart. This was because Hume amused himself by analyzing the word 'cause' as a uniform sequence. Then a philosophy arose that was equally indifferent to the history of the mind. It sought to save mankind from scepticism by giving our notions of 'cause and effect,' 'substance and accident,' and 'whole and part' a necessary place in human thought. Without these notions, we could have no experience. They were therefore supposed to come before experience, to be fixed in the 'I'. Yet, in Kant’s terminology, they could have no transcendental use. In other words, they applied only within the range of our knowledge. Kant arrives at these ideas partly by analyzing the proposition and partly by developing the 'ego'. But he never asks where the ideas come from. To him, they seem to exist of necessity. Nor does he try to analyze the various senses in which the word 'cause' or 'substance' may be used.

The philosophy of Berkeley could never have had any meaning, even to himself, if he had first analyzed from every point of view the conception of 'matter.' This poor forgotten word (which was 'a very good word' to describe the simplest generalization of external objects) is now superseded in the vocabulary of physical philosophers by 'force,' which seems to be accepted without any rigid examination of its meaning, as if the general idea of 'force' in our minds furnished an explanation of the infinite variety of forces which exist in the universe. A similar ambiguity occurs in the use of the favourite word 'law,' which is sometimes regarded as a mere abstraction, and then elevated into a real power or entity, almost taking the place of God. Theology, again, is full of undefined terms which have distracted the human mind for ages. Mankind have reasoned from them, but not to them; they have drawn out the conclusions without proving the premises; they have asserted the premises without examining the terms. The passions of religious parties have been roused to the utmost about words of which they could have given no explanation, and which had really no distinct meaning. One sort of them, faith, grace, justification, have been the symbols of one class of disputes; as the words substance, nature, person, of another, revelation, inspiration, and the like, of a third. All of them have been the subject of endless reasonings and inferences; but a spell has hung over the minds of theologians or philosophers which has prevented them from examining the words themselves. Either the effort to rise above and beyond their own first ideas was too great for them, or there might, perhaps, have seemed to be an irreverence in doing so. About the Divine Being Himself, in whom all true theological ideas live and move, men have spoken and reasoned much, and have fancied that they instinctively know Him. But they hardly suspect that under the name of God even Christians have included two characters or natures as much opposed as the good and evil principle of the Persians.

Berkeley’s philosophy could never have meant anything, even to him, if he had first examined the idea of 'matter' from every angle. This poor, forgotten term was 'a very good word' for the simplest generalization about external objects. Physical philosophers have now replaced it with 'force.' They seem to accept this term without closely examining its meaning. They proceed as if our general idea of 'force' explained the infinite variety of forces in the universe. A similar ambiguity appears in the use of the favorite word 'law.' Sometimes it is treated as a mere abstraction. Then it is elevated into a real power or entity, almost taking the place of God. Theology, too, is full of undefined terms that have troubled the human mind for ages. People have reasoned from these terms, but not toward them. They have drawn conclusions without proving their premises. They have asserted their premises without examining the terms in them. Religious groups have been stirred to the greatest passion over words they could not explain and that had no clear meaning. One set of words, faith, grace, justification, has stood for one class of disputes. Substance, nature, person have stood for another, and revelation, inspiration, and similar words for a third. All these terms have been the subject of endless arguments and inferences. But a spell has hung over the minds of theologians and philosophers, preventing them from examining the words themselves. Either the effort to move beyond their own initial ideas was too great, or perhaps doing so seemed irreverent. People have spoken and reasoned much about the Divine Being himself, in whom all true theological ideas live and move. They have imagined that they know him instinctively. But they hardly suspect that even Christians have included under the name of God two characters or natures. These are as opposed to each other as the good and evil principles of the Persians.

To have the true use of words we must compare them with things; in using them we acknowledge that they seldom give a perfect representation of our meaning. In like manner when we interrogate our ideas we find that we are not using them always in the sense which we supposed. And Plato, while he criticizes the inconsistency of his own doctrine of universals and draws out the endless consequences which flow from the assertion either that 'Being is' or that 'Being is not,' by no means intends to deny the existence of universals or the unity under which they are comprehended. There is nothing further from his thoughts than scepticism. But before proceeding he must examine the foundations which he and others have been laying; there is nothing true which is not from some point of view untrue, nothing absolute which is not also relative (compare Republic).

To use words correctly, we must compare them with things. When we use words, we acknowledge that they seldom express our meaning perfectly. Similarly, when we examine our ideas, we find that we do not always use them in the sense we thought. Plato criticizes the inconsistencies in his own doctrine of universals. He also works out the endless consequences of asserting either that 'Being is' or that 'Being is not.' But he does not mean to deny the existence of universals or the unity that includes them. Nothing is further from his mind than skepticism. Before going on, however, he must examine the foundations that he and others have been laying. Nothing is true that is not also untrue from some point of view. Nothing is absolute that is not also relative (compare Republic).

And so, in modern times, because we are called upon to analyze our ideas and to come to a distinct understanding about the meaning of words; because we know that the powers of language are very unequal to the subtlety of nature or of mind, we do not therefore renounce the use of them; but we replace them in their old connexion, having first tested their meaning and quality, and having corrected the error which is involved in them; or rather always remembering to make allowance for the adulteration or alloy which they contain. We cannot call a new metaphysical world into existence any more than we can frame a new universal language; in thought as in speech, we are dependent on the past. We know that the words 'cause' and 'effect' are very far from representing to us the continuity or the complexity of nature or the different modes or degrees in which phenomena are connected. Yet we accept them as the best expression which we have of the correlation of forces or objects. We see that the term 'law' is a mere abstraction, under which laws of matter and of mind, the law of nature and the law of the land are included, and some of these uses of the word are confusing, because they introduce into one sphere of thought associations which belong to another; for example, order or sequence is apt to be confounded with external compulsion and the internal workings of the mind with their material antecedents. Yet none of them can be dispensed with; we can only be on our guard against the error or confusion which arises out of them. Thus in the use of the word 'substance' we are far from supposing that there is any mysterious substratum apart from the objects which we see, and we acknowledge that the negative notion is very likely to become a positive one. Still we retain the word as a convenient generalization, though not without a double sense, substance, and essence, derived from the two-fold translation of the Greek ousia.

Today, we are called upon to analyze our ideas and understand clearly what words mean. We know that language is far less subtle than nature or the mind. Yet we do not stop using words. Instead, we test their meanings and qualities, correct the errors they involve, and return them to their familiar contexts. Or rather, we always remember to allow for the impurities mixed into them. We cannot create a new metaphysical world any more than we can invent a new universal language. In thought, as in speech, we depend on the past. We know that the words 'cause' and 'effect' fall far short of representing nature's continuity and complexity. They also fall short of representing the different ways and degrees in which phenomena are connected. Yet we accept them as our best way of expressing the relationships between forces or objects. We see that the term 'law' is only an abstraction. It covers laws of matter and mind, the law of nature, and the law of the land. Some of these uses are confusing because they bring associations from one area of thought into another. For example, order or sequence can be confused with external compulsion. The inner workings of the mind can also be confused with the material events that precede them. Yet we cannot do without any of these uses. We can only guard against the error or confusion they cause. Similarly, when we use the word 'substance', we do not suppose that some mysterious underlying reality exists apart from the objects we see. We also recognize that this negative idea is very likely to become a positive one. Still, we keep the word as a convenient generalization. It does, however, have two meanings, substance and essence, because the Greek ousia has been translated in two ways.

So the human mind makes the reflection that God is not a person like ourselves—is not a cause like the material causes in nature, nor even an intelligent cause like a human agent—nor an individual, for He is universal; and that every possible conception which we can form of Him is limited by the human faculties. We cannot by any effort of thought or exertion of faith be in and out of our own minds at the same instant. How can we conceive Him under the forms of time and space, who is out of time and space? How get rid of such forms and see Him as He is? How can we imagine His relation to the world or to ourselves? Innumerable contradictions follow from either of the two alternatives, that God is or that He is not. Yet we are far from saying that we know nothing of Him, because all that we know is subject to the conditions of human thought. To the old belief in Him we return, but with corrections. He is a person, but not like ourselves; a mind, but not a human mind; a cause, but not a material cause, nor yet a maker or artificer. The words which we use are imperfect expressions of His true nature; but we do not therefore lose faith in what is best and highest in ourselves and in the world.

The human mind therefore reflects that God is not a person like us. He is not a cause like the material causes in nature, or even an intelligent cause like a human agent. Nor is he an individual, for he is universal. Every idea we can form of him is limited by our human faculties. No effort of thought or faith can put us both inside and outside our own minds at the same moment. How can we conceive of God in terms of time and space, when he is outside both? How can we escape those terms and see him as he is? How can we imagine his relationship to the world or to ourselves? Countless contradictions follow from either possibility, that God is or that he is not. Yet we are far from saying that we know nothing of him because all we know is subject to the conditions of human thought. We return to our old belief in him, but with corrections. He is a person, but not like us. He is a mind, but not a human mind. He is a cause, but not a material cause, nor a maker or craftsman. The words we use are imperfect expressions of his true nature. But we do not therefore lose faith in what is best and highest in ourselves and in the world.

'A little philosophy takes us away from God; a great deal brings us back to Him.' When we begin to reflect, our first thoughts respecting Him and ourselves are apt to be sceptical. For we can analyze our religious as well as our other ideas; we can trace their history; we can criticize their perversion; we see that they are relative to the human mind and to one another. But when we have carried our criticism to the furthest point, they still remain, a necessity of our moral nature, better known and understood by us, and less liable to be shaken, because we are more aware of their necessary imperfection. They come to us with 'better opinion, better confirmation,' not merely as the inspirations either of ourselves or of another, but deeply rooted in history and in the human mind.

'A little philosophy takes us away from God, but a great deal brings us back to him.' When we begin to reflect on God and ourselves, our first thoughts are likely to be skeptical. We can analyze our religious ideas just as we can analyze our other ideas. We can trace their history and criticize how they have been distorted. We see that they depend on the human mind and on one another. But even when we have taken our criticism as far as it can go, these ideas remain. They are a necessity of our moral nature. We know and understand them better, and they are less easily shaken because we are more aware of their necessary imperfection. They come to us with 'better opinion, better confirmation.' They are not merely our own inspirations or those of another person. They are deeply rooted in history and in the human mind.