Parmenides

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.

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. 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.

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. 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. 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. 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.

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.

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.'

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.