Parmenides

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.

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.

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.'

…

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.

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.

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.

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.

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.