zation, the fruitful germ of a higher development of philosophy."

Plato has succinctly characterized the difference between Parmenides and Zeno by saying, that the master established the existence of The One, and the disciple proved the non-existence of The Many.

When he argued that there was but One thing really existing, all the others being only modifications or appearances of that One, he did not deny that there were many appearances, he only denied that these appearances were real existences. So, in like manner, he denied motion, but not the appearance of motion. Diogenes the Cynic, who, to refute his arguments against motion, rose and walked, entirely mistook the argument; his walking was no more a refutation of Zeno, than Dr. Johnson's kicking a stone was a refutation of Berkeley's denial of matter. Zeno would have answered: Very true; you walk: according to Opinion (rò doğuσróv) you are in motion; but according to Reason you are at rest. What you call motion is but the name given to a series of similar conditions, each of which, separately considered, is rest. Thus, every object filling space equal to its bulk is necessarily at rest in that space; motion from one spot to another is but a name given to the sum-total of all these intermediate spaces in which the object at each moment is at rest. Take the illustration of the circle: a circle is composed of a number of individual points, or straight lines; not one of these lines can individually be called a circle; but all these lines, considered as a totality, have one general name given them, viz. a circle. In the same way, in each individual point of space, the object is at rest; the sum-total of a number of these states of rest is called motion.

The original fallacy is in the supposition that Motion is a thing superadded, whereas, as Zeno clearly saw, it is only a condition. In a falling stone there is not the "stone" and a thing called "motion;" otherwise there would be also another thing called "rest." But both motion and rest are names given to express

conditions of the stone. Even rest is a positive exertion of force. Rest is force resistant, and Motion is force triumphant. It follows that matter is always in motion; which amounts to the same as Zeno's saying, there is no such thing as motion.

The other arguments of Zeno against the possibility of Motion. (and he maintained four, the third of which we have above explained,) are given by Aristotle; but they seem more like the ingenious puzzles of dialectical subtlety than the real arguments of an earnest man. It has, therefore, been asserted, that they were only brought forward to ridicule the unskilfulness of his adversaries. We must not, however, be hasty in rescuing Zeno from his own logical net, into which he may have fallen as easily as others. Greater men than he have been the dupes of their own verbal distinctions.

Here are his two first arguments:

1. Motion is impossible, because before that which is in motion can reach the end, it must reach the middle point; but this middle point then becomes the end, and the same objection applies to it—since to reach it the object in motion must traverse a middle point; and so on ad infinitum, seeing that matter is infinitely divisible. Thus, if a stone be cast four paces, before it can reach the fourth it must reach the second; the second then becomes the end, and the first pace the middle; but before the object can reach the first pace, it must reach the half of the first pace, and before the half it must reach the half of that half; and so on ad infinitum.

2. This is his famous Achilles puzzle. We give both the statement and refutation as we find it in Mill's Logic (ii. 453).

The argument is, let Achilles run ten times as fast as a tortoise, yet, if the tortoise has the start, Achilles will never overtake him; for, suppose them to be at first separated by an interval of a thousand feet; when Achilles has run these thousand feet, the tortoise will have run a hundred, and when Achilles has run those hundred, the tortoise will have got on ten, and so on forever: therefore Achilles may run forever without overtaking the tortoise.

Now the "forever" in the conclusion means, for any length of time that can be supposed; but in the premises, "forever" does not mean any length of time-it means any number of subdivisions of time. It means that we may divide a thousand feet by ten, and that quotient again by ten, and so on as often as we please; that there never need be an end to the subdivisions of the distance, nor, consequently, to those of the time in which it is performed. But an unlimited number of subdivisions may be made of that which is itself limited. The argument proves no other infinity of duration than may be embraced within five minutes. As long as the five minutes are not expired, what remains of them may be divided by ten, and again by ten, as often as we like, which is perfectly compatible with their being only five minutes altogether. It proves, in short, that to pass through this finite space requires a time which is infinitely divisible, but not an infinite time; the confounding of which distinction Hobbes had already seen to be the gist of the fallacy.

Although the credit of seeing the ground of the fallacy is given by Mill to Hobbes, we must also observe that Aristotle had clearly seen it in the same light. His answer to Zeno, which Bayle thinks "pitiable," was, that a foot of space being only potentially infinite, but actually finite, it could be easily traversed in a finite time.

We have no space to follow Zeno in his various arguments against the existence of a multitude of things. His position may be briefly summed up thus:-There is but one Being existing, necessarily indivisible and infinite. To suppose that The One is divisible, is to suppose it finite. If divisible, it must be infinitely divisible. But, suppose two things to exist, then there must necessarily be an interval between those two; something separating and limiting them. What is that something? It is some other thing. But then, if not the same thing, it also must be separated and limited; and so on ad infinitum. Thus only One thing can exist as the substratum for all manifold appearances.

Zeno closes the second great line of independent inquiry, which, opened by Anaximander, and continued by Pythagoras, Xenophanes, and Parmenides, we may characterize as the Mathematical or Absolute system. Its opposition to the Ionian, Physical or Empirical system was radical and constant. But, up to the coming of Zeno, these two systems had been developed almost in parallel lines, so little influence did they exert upon each other. The two systems clashed together on the arrival of Zeno at Athens. The result of the conflict was the creation of a new method-Dialectics. This method created the Sophists and the Skeptics. It also greatly influenced all succeeding schools, and may be said to have constituted one great peculiarity of Socrates and Plato, as will be shown.

We must, however, previously trace the intermediate steps which philosophy took, before the crisis of Sophistry, which ceded the era of Socrates.

SECOND EPOCH.

SPECULATIONS ON THE CREATION OF THE UNIVERSE, AND ON THE ORIGIN OF KNOWLEDGE.

CHAPTER I.

§ I. HERACLITUS.

"LIFE is a comedy to those who think, a tragedy to those who feel." This, Horace Walpole's epigram, may be applied to Democritus and Heraclitus, celebrated throughout antiquity as the laughing and the weeping philosophers:

"One pitied, one condemn'd the woeful times;

One laugh'd at follies, and one wept o'er crimes."

Modern criticism has indeed pronounced both these characteristics to be fabulous; but fables themselves are often only exaggerations of truth, and there must have been something in each of these philosophers which formed the nucleus round which the fables grew. Of Heraclitus it has been well said, “The vulgar notion of him as the crying philosopher must not be wholly discarded, as if it meant nothing, or had no connection with the history of his speculations. The thoughts which came forth in his system are like fragments torn from his own personal being, and not torn from it without such an effort and violence as must needs have drawn a sigh from the sufferer. If Anaximenes discovered that he had within him a power and principle which ruled over all the acts and functions of his bodily frame, Herac