Parmenides by Plato (lightweight ebook reader .TXT) 📕

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,