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 nonexistence 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 at 152: (11) The relation between two terms is regarded under contradictory aspects, as for example when the existence of the one and the nonexistence 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
