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Parmenides

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.

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.

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.

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.

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 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.

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.'

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.

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.'

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.

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.

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.

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

The argument has two divisions: There is the hypothesis that

1. One is.

2. One is not.

If one is, it is nothing.

If one is not, it is everything.

But is and is not may be taken in two senses:

Either one is one,

Or, one has being,

from which opposite consequences are deduced,

1. a. If one is one, it is nothing.

1. b. If one has being, it is all things.

To which are appended two subordinate consequences:

1. aa. If one has being, all other things are.

1. bb. If one is one, all other things are not.

The same distinction is then applied to the negative hypothesis:

2. a. If one is not one, it is all things.

2. b. If one has not being, it is nothing.

Involving two parallel consequences respecting the other or remainder:

2. aa. If one is not one, other things are all.

2. bb. If one has not being, other things are not.

…

'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: —

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. 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.

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.

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.

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.

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.