And therefore if the one is the same with itself, ply parts and multitude. Once more, can one be the one is not one with itself; and therefore one older or younger than itself or other? or of the and not one. And therefore one is neither other same age with itself or other? That would imply than other, nor the same with itself. Neither will likeness and unlikeness, equality and inequality.
the one be like or unlike itself or other; for like-Therefore one cannot be in time, because that ness is sameness of affections, and the one and which is in time is ever becoming older and the same are different. And one having any af-younger than itself, (for older and younger are fection which is other than being one would be relative terms, and he who becomes older be-more than one. The one, then, cannot have the comes younger,) and is also of the same age with same affection with and therefore cannot be like itself. None of which, or any other expressions of itself or other; nor can the one have any other time, whether past, future, or present, can be affection than its own, that is, be unlike itself or affirmed of one. One neither is, has been, nor any other, for this would imply that it was more will be, nor becomes, nor has, nor will become.
than one. The one, then, is neither like nor un-And, as these are the only modes of being, one is like itself or other. This being the case, neither not, and is not one. But to that which is not, there can the one be equal or unequal to itself or other.
is no attribute or relative, neither name nor word For equality implies sameness of measure, as nor idea nor science nor perception nor opinion inequality implies a greater or less number of appertaining. One, then, is neither named, nor measures. But the one, not having sameness, uttered, nor known, nor perceived, nor imagined.
cannot have sameness of measure; nor a greater But can all this be true? ‘I think not.’
or less number of measures, for that would im-1.b. Let us, however, commence the inquiry 27
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again. We have to work out all the consequences we have two things which separately are called which follow on the assumption that the one is.
either, and together both. And both are two and If one is, one partakes of being, which is not the either of two is severally one, and if one be added same with one; the words ‘being’ and ‘one’
to any of the pairs, the sum is three; and two is have different meanings. Observe the conse-an even number, three an odd; and two units exist quence: In the one of being or the being of one twice, and therefore there are twice two; and are two parts, being and one, which form one three units exist thrice, and therefore there are whole. And each of the two parts is also a whole, thrice three, and taken together they give twice and involves the other, and may be further sub-three and thrice two: we have even numbers divided into one and being, and is therefore not multiplied into even, and odd into even, and even one but two; and thus one is never one, and in into odd numbers. But if one is, and both odd this way the one, if it is, becomes many and infi-and even numbers are implied in one, must not nite. Again, let us conceive of a one which by an every number exist? And number is infinite, and effort of abstraction we separate from being: will therefore existence must be infinite, for all and this abstract one be one or many? You say one every number partakes of being; therefore be-only; let us see. In the first place, the being of ing has the greatest number of parts, and every one is other than one; and one and being, if dif-part, however great or however small, is equally ferent, are so because they both partake of the one. But can one be in many places and yet be a nature of other, which is therefore neither one whole? If not a whole it must be divided into parts nor being; and whether we take being and other, and represented by a number corresponding to or being and one, or one and other, in any case the number of the parts. And if so, we were wrong 28
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in saying that being has the greatest number of garded as a sum of parts is in itself; and is, there-parts; for being is coequal and coextensive with fore, both in itself and in another. This being the one, and has no more parts than one; and so the case, the one is at once both at rest and in mo-abstract one broken up into parts by being is tion: at rest, because resting in itself; in motion, many and infinite. But the parts are parts of a because it is ever in other. And if there is truth in whole, and the whole is their containing limit, what has preceded, one is the same and not the and the one is therefore limited as well as infi-same with itself and other. For everything in re-nite in number; and that which is a whole has lation to every other thing is either the same with beginning, middle, and end, and a middle is equi-it or other; or if neither the same nor other, then distant from the extremes; and one is therefore in the relation of part to a whole or whole to a of a certain figure, round or straight, or a combi-part. But one cannot be a part or whole in rela-nation of the two, and being a whole includes all tion to one, nor other than one; and is therefore the parts which are the whole, and is therefore the same with one. Yet this sameness is again self-contained. But then, again, the whole is not contradicted by one being in another place from in the parts, whether all or some. Not in all, be-itself which is in the same place; this follows from cause, if in all, also in one; for, if wanting in any one being in itself and in another; one, there-one, how in all?—not in some, because the greater fore, is other than itself. But if anything is other would then be contained in the less. But if not in than anything, will it not be other than other?
all, nor in any, nor in some, either nowhere or in And the not one is other than the one, and the other. And if nowhere, nothing; therefore in other.
one than the not one; therefore one is other than The one as a whole, then, is in another, but reall others. But the same and the other exclude 29
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one another, and therefore the other can never be names: when you repeat the same name twice in the same; nor can the other be in anything for over, you mean the same thing; and when you ever so short a time, as for that time the other say that the other is other than the one, or the will be in the same. And the other, if never in the one other than the other, this very word other same, cannot be either in the one or in the not (eteron), which is attributed to both, implies one. And one is not other than not one, either by sameness. One, then, as being other than others, reason of other or of itself; and therefore they are and other as being other than one, are alike in not other than one another at all. Neither can the that they have the relation of otherness; and like-not one partake or be part of one, for in that case ness is similarity of relations. And everything as it would be one; nor can the not one be number, being other of everything is also like everything.
for that also involves one. And therefore, not be-Again, same and other, like and unlike, are oppo-ing other than the one or related to the one as a sites: and since in virtue of being other than the whole to parts or parts to a whole, not one is the others the one is like them, in virtue of being the same as one. Wherefore the one is the same and same it must be unlike. Again, one, as having the also not the same with the others and also with same relations, has no difference of relation, and itself; and is therefore like and unlike itself and is therefore not unlike, and therefore like; or, as the others, and just as different from the others having different relations, is different and unlike.
as they are from the one, neither more nor less.
Thus, one, as being the same and not the same But if neither more nor less, equally different; and with itself and others—for both these reasons and therefore the one and the others have the same for either of them—is also like and unlike itself relations. This may be illustrated by the case of and the others. Again, how far can one touch it-30
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self and the others? As existing in others, it be greater or less than each other or equal to touches the others; and as existing in itself, one another, they will be greater or less or equal touches only itself. But from another point of view, by reason of equality or greatness or smallness that which touches another must be next in or-inhering in them in addition to their own proper der of place; one, therefore, must be next in or-nature. Let us begin by assuming smallness to der of place to itself, and would therefore be two, be inherent in one: in this case the inherence is and in two places. But one cannot be two, and either in the whole or in a part. If the first, small-therefore cannot be in contact with itself. Nor ness is either coextensive with the whole one, or again can one touch the other. Two objects are contains the whole, and, if coextensive with the required to make one contact; three objects make one, is equal to the one, or if containing the one two contacts; and all the objects in the world, if will be greater than the one. But smallness thus placed in a series, would have as many contacts performs the function of equality or of greatness, as there are objects, less one. But if one only ex-which is impossible. Again, if the inherence be ists, and not two, there is no contact. And the othin a part, the same contradiction follows: smallers, being other than one, have no part in one, ness will be equal to the part or greater than the and therefore none in number, and therefore two part; therefore smallness will not inhere in any-has no existence, and therefore there is no con-thing, and except the idea of smallness there will tact. For all which reasons, one has and has not be nothing small. Neither will greatness; for contact with itself and the others.
greatness will have a greater;—and there will be Once more, Is one equal and unequal to itself no small in relation to which it is great. And there and the others? Suppose one and the others to will be no great or small in objects, but great-31
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ness and smallness will be relative only to each
‘to be’ is the participation of being in present other; therefore the others cannot be greater or time, ‘to have been’ in past, ‘to be about to less than the one; also the one can neither exceed be’ in future time. And as time is ever moving nor be exceeded by the others, and they are there-forward, the one becomes older than itself; and fore equal to one another. And this will be true therefore younger than itself; and is older and also of the one in relation to itself: one will be also younger when in the process of becoming it equal to itself as well as to the others (talla). Yet arrives at the present; and it is always older and one, being in itself, must also be about itself, con-younger, for at any moment the one is, and there-taining and contained, and is therefore greater fore it becomes and is not older and younger than and less than itself. Further, there is nothing be-itself but during an equal time with itself, and is side the one and the others; and as these must be therefore contemporary with itself.
in something, they must therefore be in one an-And what are the relations of the one to the other; and as that in which a thing is is greater others? Is it or does it become older or younger than the thing, the inference is that they are both than they? At any rate the others are more than greater and less than one another, because con-one, and one, being the least of all numbers, must taining and contained in one another. Therefore be prior in time to greater numbers. But on the the one is equal to and greater and less than itself other hand, one must come into being in a man-or other, having also measures or parts or num-ner accordant with its own nature. Now one has bers equal to or greater or less than itself or other.
parts or others, and has therefore a beginning, But does one partake of time? This must be middle, and end, of which the beginning is first acknowledged, if the one partakes of being. For and the end last. And the parts come into exist-32
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ence first; last of all the whole, contemporane-ever become and never have become, for then ously with the end, being therefore younger, they would be. Thus the one and others always while the parts or others are older than the one.
are and are becoming and not becoming younger But, again, the one comes into being in each of and also older than one another. And one, par-the parts as much as in the whole, and must be taking of time and also partaking of becoming of the same age with them. Therefore one is at older and younger, admits of all time, present, once older and younger than the parts or others, past, and future—was, is, shall be—was becom-and also contemporaneous with them, for no part ing, is becoming, will become. And there is sci-can be a part which is not one. Is this true of ence of the one, and opinion and name and ex-becoming as well as being? Thus much may be pression, as is already implied in the fact of our affirmed, that the same things which are older inquiry.
or younger cannot become older or younger in a Yet once more, if one be one and many, and greater degree than they were at first by the neither one nor many, and also participant of addition of equal times. But, on the other hand, time, must there not be a time at which one as the one, if older than others, has come into be-being one partakes of being, and a time when ing a longer time than they have. And when equal one as not being one is deprived of being? But time is added to a longer and shorter, the rela-these two contradictory states cannot be experi-tive difference between them is diminished. In enced by the one both together: there must be a this way that which was older becomes younger, time of transition. And the transition is a pro-and that which was younger becomes older, that cess of generation and destruction, into and from is to say, younger and older than at first; and they being and not-being, the one and the others. For 33
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the generation of the one is the destruction of imply a whole to which they belong; otherwise the others, and the generation of the others is each part would be a part of many, and being the destruction of the one. There is also separa-itself one of them, of itself, and if a part of all, of tion and aggregation, assimilation and dissimi-each one of the other parts, which is absurd. For lation, increase, diminution, equalization, a pas-a part, if not a part of one, must be a part of all sage from motion to rest, and from rest to mo-but this one, and if so not a part of each one; and tion in the one and many. But when do all these if not a part of each one, not a part of any one of changes take place? When does motion become many, and so not of one; and if of none, how of rest, or rest motion? The answer to this ques-all? Therefore a part is neither a part of many tion will throw a light upon all the others. Noth-nor of all, but of an absolute and perfect whole ing can be in motion and at rest at the same time; or one. And if the others have parts, they must and therefore the change takes place ‘in a mo-partake of the whole, and must be the whole of ment’—which is a strange expression, and seems which they are the parts. And each part, as the to mean change in no time. Which is true also of word ‘each’ implies, is also an absolute one. And all the other changes, which likewise take place both the whole and the parts partake of one, for in no time.
the whole of which the parts are parts is one, 1.aa. But if one is, what happens to the others, and each part is one part of the whole; and whole which in the first place are not one, yet may par-and parts as participating in one are other than take of one in a certain way? The others are other one, and as being other than one are many and than the one because they have parts, for if they infinite; and however small a fraction you sepa-had no parts they would be simply one, and parts rate from them is many and not one. Yet the fact 34
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of their being parts furnishes the others with a ness, some and other, generation and corruption, limit towards other parts and towards the whole; odd and even. For if they had these they would they are finite and also infinite: finite through partake either of one opposite, and this would participation in the one, infinite in their own be a participation in one; or of two opposites, nature. And as being finite, they are alike; and and this would be a participation in two. Thus if as being infinite, they are alike; but as being both one exists, one is all things, and likewise noth-finite and also infinite, they are in the highest ing, in relation to one and to the others.
degree unlike. And all other opposites might with-2.a. But, again, assume the opposite hypoth-out difficulty be shown to unite in them.
esis, that the one is not, and what is the conse-1.bb. Once more, leaving all this: Is there not quence? In the first place, the proposition, that also an opposite series of consequences which is one is not, is clearly opposed to the proposition, equally true of the others, and may be deduced that not one is not. The subject of any negative from the existence of one? There is. One is dis-proposition implies at once knowledge and dif-tinct from the others, and the others from one; ference. Thus ‘one’ in the proposition—’The one for one and the others are all things, and there is is not,’ must be something known, or the words no third existence besides them. And the whole would be unintelligible; and again this ‘one of one cannot be in others nor parts of it, for it is which is not’ is something different from other separated from others and has no parts, and things. Moreover, this and that, some and other, therefore the others have no unity, nor plurality, may be all attributed or related to the one which nor duality, nor any other number, nor any oppo-is not, and which though non-existent may and sition or distinction, such as likeness and unlike-must have plurality, if the one only is non-exis-35
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tent and nothing else; but if all is not-being there ing of not-being, and being the not-being of notis nothing which can be spoken of. Also the one being; or more truly being partakes of the being which is not differs, and is different in kind from of being and not of the being of not-being, and the others, and therefore unlike them; and they not-being of the being of not-being and not of being other than the one, are unlike the one, the not-being of not-being. And therefore the one which is therefore unlike them. But one, being which is not has being and also not-being. And unlike other, must be like itself; for the unlike-the union of being and not-being involves change ness of one to itself is the destruction of the hy-or motion. But how can not-being, which is no-pothesis; and one cannot be equal to the others; where, move or change, either from one place to for that would suppose being in the one, and the another or in the same place? And whether it is others would be equal to one and like one; both or is not, it would cease to be one if experiencing which are impossible, if one does not exist. The a change of substance. The one which is not, then, one which is not, then, if not equal is unequal to is both in motion and at rest, is altered and unal-the others, and in equality implies great and tered, and becomes and is destroyed, and does small, and equality lies between great and small, not become and is not destroyed.
and therefore the one which is not partakes of 2.b. Once more, let us ask the question, If one equality. Further, the one which is not has being; is not, what happens in regard to one? The ex-for that which is true is, and it is true that the pression ‘is not’ implies negation of being:—do one is not. And so the one which is not, if remit-we mean by this to say that a thing, which is ting aught of the being of non-existence, would not, in a certain sense is? or do we mean abso-become existent. For not being implies the be-lutely to deny being of it? The latter. Then the 36
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one which is not can neither be nor become nor the fractions. For in passing from the greater to perish nor experience change of substance or the less it must reach an intermediate point, place. Neither can rest, or motion, or greatness, which is equality. Moreover, each particle al-or smallness, or equality, or unlikeness, or like-though having a limit in relation to itself and to ness either to itself or other, or attribute or rela-other particles, yet it has neither beginning, tion, or now or hereafter or formerly, or knowl-middle, nor end; for there is always a beginning edge or opinion or perception or name or any-before the beginning, and a middle within the thing else be asserted of that which is not.
middle, and an end beyond he end, because the 2.aa. Once more, if one is not, what becomes of infinitesimal division is never arrested by the one.
the others? If we speak of them they must be, Thus all being is one at a distance, and broken and their very name implies difference, and dif-up when near, and like at a distance and unlike ference implies relation, not to the one, which is when near; and also the particles which compose not, but to one another. And they are others of being seem to be like and unlike, in rest and each other not as units but as infinities, the least motion, in generation and corruption, in contact of which is also infinity, and capable of infinitesi-and separation, if one is not.
mal division. And they will have no unity or num-2.bb. Once more, let us inquire, If the one is ber, but only a semblance of unity and number; not, and the others of the one are, what follows?
and the least of them will appear large and mani-In the first place, the others will not be the one, fold in comparison with the infinitesimal fractions nor the many, for in that case the one would be into which it may be divided. Further, each par-contained in them; neither will they appear to ticle will have the appearance of being equal with be one or many; because they have no commun-37
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ion or participation in that which is not, nor sem-in character with the Zenonian dialectic. Secondly, blance of that which is not. If one is not, the oth-We may note, that the conclusion is really in-ers neither are, nor appear to be one or many, volved in the premises. For one is conceived as like or unlike, in contact or separation. In short, one, in a sense which excludes all predicates.
if one is not, nothing is.
When the meaning of one has been reduced to a The result of all which is, that whether one is point, there is no use in saying that it has nei-or is not, one and the others, in relation to them-ther parts nor magnitude. Thirdly, The concep-selves and to one another, are and are not, and tion of the same is, first of all, identified with the appear to be and appear not to be, in all manner one; and then by a further analysis distinguished of ways.
from, and even opposed to it. Fourthly, We may I. On the first hypothesis we may remark: first, detect notions, which have reappeared in mod-That one is one is an identical proposition, from ern philosophy, e.g. the bare abstraction of unde-which we might expect that no further conse-fined unity, answering to the Hegelian ‘Seyn,’
quences could be deduced. The train of conse-or the identity of contradictions ‘that which is quences which follows, is inferred by altering the older is also younger,’ etc., or the Kantian con-predicate into ‘not many. ’ Yet, perhaps, if a ception of an a priori synthetical proposition ‘one strict Eristic had been present, oios aner ei kai i s . ’
nun paren, he might have affirmed that the not II. In the first series of propositions the word many presented a different aspect of the con-
‘is’ is really the copula; in the second, the verb ception from the one, and was therefore not iden-of existence. As in the first series, the negative tical with it. Such a subtlety would be very much consequence followed from one being affirmed 38
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to be equivalent to the not many; so here the arises out of the imperfection of language, and affirmative consequence is deduced from one should therefore be no longer regarded as a dif-being equivalent to the many.
ficulty at all. The only way of meeting it, if it In the former case, nothing could be predicated exists, is to acknowledge that this rather puzzling of the one, but now everything—multitude, rela-double conception is necessary to the expression tion, place, time, transition. One is regarded in of the phenomena of motion or change, and that all the aspects of one, and with a reference to all this and similar double notions, instead of being the consequences which flow, either from the anomalies, are among the higher and more po-combination or the separation of them. The notent instruments of human thought.
tion of transition involves the singular extra-tem-The processes by which Parmenides obtains his poral conception of ‘suddenness.’ This idea of remarkable results may be summed up as follows:
‘suddenness’ is based upon the contradiction (1) Compound or correlative ideas which involve which is involved in supposing that anything can each other, such as, being and not-being, one and be in two places at once. It is a mere fiction; and many, are conceived sometimes in a state of com-we may observe that similar antinomies have led position, and sometimes of division: (2) The divi-modern philosophers to deny the reality of time sion or distinction is sometimes heightened into and space. It is not the infinitesimal of time, but total opposition, e.g. between one and same, one the negative of time. By the help of this inven-and other: or (3) The idea, which has been al-tion the conception of change, which sorely exer-ready divided, is regarded, like a number, as ca-cised the minds of early thinkers, seems to be, pable of further infinite subdivision: (4) The ar-but is not really at all explained. The difficulty gument often proceeds ‘a dicto secundum quid 39
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ad dictum simpliciter’ and conversely: (5) The involve the existence of the many: (12) Words are analogy of opposites is misused by him; he argues used through long chains of argument, sometimes indiscriminately sometimes from what is like, some-loosely, sometimes with the precision of numbers times from what is unlike in them: (6) The idea of or of geometrical figures.
being or not-being is identified with existence or The argument is a very curious piece of work, non-existence in place or time: (7) The same ideas unique in literature. It seems to be an exposition are regarded sometimes as in process of transition, or rather a ‘reductio ad absurdum’ of the sometimes as alternatives or opposites: (8) There Megarian philosophy, but we are too imperfectly are no degrees or kinds of sameness, likeness, dif-acquainted with this last to speak with confidence ference, nor any adequate conception of motion or about it. It would be safer to say that it is an change: (9) One, being, time, like space in Zeno’s indication of the sceptical, hyperlogical fancies puzzle of Achilles and the tortoise, are regarded which prevailed among the contemporaries of sometimes as continuous and sometimes as dis-Socrates. It throws an indistinct light upon crete: (10) In ome parts of the argument the ab-Aristotle, and makes us aware of the debt which straction is so rarefied as to become not only falla-the world owes to him or his school. It also bears cious, but almost unintelligible, e.g. in the contra-a resemblance to some modern speculations, in diction which is elicited out of the relative terms which an attempt is made to narrow language in older and younger: (11) The relation between two such a manner that number and figure may be terms is regarded under contradictory aspects, as made a calculus of thought. It exaggerates one for example when the existence of the one and the side of logic and forgets the rest. It has the ap-non-existence of the one are equally assumed to pearance of a mathematical process; the inven-40
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tor of it delights, as mathematicians do, in elicit-that determination is negation, but must get ing or discovering an unexpected result. It also through negation into affirmation. Whether this helps to guard us against some fallacies by show-process is real, or in any way an assistance to ing the consequences which flow from them.
thought, or, like some other logical forms, a mere In the Parmenides we seem to breathe the spirit figure of speech transferred from the sphere of of the Megarian philosophy, though we cannot mathematics, may be doubted. That Plato and compare the two in detail. But Plato also goes the most subtle philosopher of the nineteenth beyond his Megarian contemporaries; he has split century should have lighted upon the same no-their straws over again, and admitted more than tion, is a singular coincidence of ancient and they would have desired. He is indulging the modern thought.
analytical tendencies of his age, which can di-IV. The one and the many or others are reduced vide but not combine. And he does not stop to to their strictest arithmetical meaning. That one inquire whether the distinctions which he makes is three or three one, is a proposition which has, are shadowy and fallacious, but ‘whither the perhaps, given rise to more controversy in the argument blows’ he follows.
world than any other. But no one has ever meant III. The negative series of propositions contains to say that three and one are to be taken in the the first conception of the negation of a nega-same sense. Whereas the one and many of the tion. Two minus signs in arithmetic or algebra Parmenides have precisely the same meaning; make a plus. Two negatives destroy each other.
there is no notion of one personality or substance This abstruse notion is the foundation of the having many attributes or qualities. The truth Hegelian logic. The mind must not only admit seems to be rather the opposite of that which 41
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Socrates imp