Now the real bases on which the Eleatics and their successors built their airy fabric of abstractions seem to me to be two.

I. The abstraction is in every case nearer us than the parent concrete; for all ideas, once formed, have their abode and their being in the mind which conceived them. And this connexion is continuous and increasing, whereas the sensations to which they owe their existence are only observed occasionally and accidentally. The idea, e.g. implied in the common noun 'man,' or the abstraction 'motion,' is more inseparable from our mental being than are its physical correlatives—a given individual, or a body in actual motion. Hence, the idea claims an existence more complete and perfect in itself, and more indissolubly connected with our intellect, than the passing sensation from which it is derived.

II. The abstraction is not only nearer to us, but it is infinitely more enduring, than the concrete whence it is derived. No idea came more home to the Eleatic than the mere relative transitory nature of all the physical elements of human knowledge. Not only are all phenomena diverse, fluctuating, and perishable, but we ourselves are similarly liable to change, growth, decay, and death. In the noumena, or the universe of mental abstractions, on the other hand, all is stationary, permanent, and eternal. The phenomenon, a white object, e.g. co-exists only with my perception of it, or its perception by others similarly constituted. The abstraction, or noumenon whiteness, is independent not only of that or any other particular sensation, but even of my existence, and the existence of all other beings endued with the same faculties as myself. This mode of reasoning could easily be applied to all other phenomena, with their correlated noumena; and thus we can understand how the absolute became to the subtle thinkers of Elea, as afterwards to Plato and his school, a self-existing and independent power possessing an inherent and autocratic jurisdiction, and capable of giving laws to all subordinate, i.e. physical, sensations and conceptions of whatever kind; so that, in the view of an Eleatic thinker, absolute likeness, for instance, might be conceived and defined as independent of all relations and particular instances, and would exist absolutely and eternally, though every object in the universe were dissimilar from all the rest.

We hence perceive that abstract thought, independently of its necessity in language, is a protest against the temporary and changeable nature of all terrene experience. To use the expression of Spinoza, it is the contemplation of the universe, sub specie æternitatis;' it seizes those elements in human thought and experience which seem perennial, and relegates all the rest to an

inferior position. That, under these circumstances, the diversity and manifoldness of the outer world of human experience could be melted down into a homogeneous, indifferentiated One or single Ens, can hardly surprise us. Nor can it seem wonderful that thought, with its absolute jurisdiction over the whole sum of existence, should be conceived as identical with it.

This brief survey of the growth of metaphysical abstractions will, I hope, enable you to appreciate the arguments of Zenon, as well as the connexion of Eleatic speculation with that of succeeding thinkers. Zenon's efforts were directed to the defence of the single Ens of Parmenides, and to the denial of many discontinuous beings (or Entia). You must, therefore, bear in mind that we are now moving in a world of abstractions, in which all existences and qualities are conceived and spoken of as unrelated to the phenomenal world, and as possessing a real noumenal existence of their own.

Truth or absolute existence is one, immutable, unconditioned, indiscerptible. Such was the first article in the creed of the Eleatic. Those who denied this axiom, did not do so on the ground of the multiplicity or variety of phenomenal objects. This was a fact accepted equally by the two parties-a fact of which every sensation was held to be a sufficient and incontrovertible proof. The contest was purely metaphysical and supersensual. 'You,' we may imagine Zenon's opponents saying, 'affirm that absolute existence consists of a single Ens, or that it is One. We, on the other hand, say that there are just as many abstract beings as there are separate concrete phenomena. The whiteness of snow, e.g. is one thing; of marble, another; of a flower, a third; and so on, for every single object. The region of the absolute consists, in fact, of the ideal semblances or images of our physical perceptions, and there are just as many beings (or Entia) as there are sensible phenomena.'

To this Zenon or Parmenides would have replied: 'Not so. Absolute being is only one. You are confounding two different things-abstractions related to phenomenal objects, and abstractions which are not so related. You think, i.e. of whiteness as a quality of a specific object. To me it is a pure idea-thing in itself—noumenon, or whatever else you choose to call it. I have not that faculty, which you seem to possess, of considering these abstractions as different discrete existences. I cannot thus break up the mental continuity I am conscious of possessing-or, rather, which is my sole veritable being into an indefinite number of parts and fractions. Absolute whiteness is to me a single, indivisible, unchangeable Ens; and to separate the whiteness of one object

from the whiteness of another, or to try to discriminate between the attribute I observed yesterday or a year ago, and the similar or rather identical attribute which I am now conscious of observing, seems to me nothing less than a denial of my personal identity, and plunges all my mental being into inextricable confusion. Besides, I require fixity in absolute knowledge or existence, on its own account. Truth, to be demonstrative and reliable, must, I conceive, be immoveable and eternal, not relatively merely, but absolutely. Fluctuating or changeable truth is to me no truth at all. That which is now true is so fully, finally, incontrovertibly; the bare possibility of increase or diminution implies change and imperfection. Similarly, truth must be absolutely one. Introduce number, divisibility, into its being, and in the very act you introduce the elements of divergency and dissolution.'

Such, I take it, were the main grounds of dispute between Zenon and his opponents, expressed, however, in terms more familiar to ourselves. He denied the principle of manifoldness in absolute existence, as well as the reality of motion, space, time, or whatever other entity or phenomenon that is necessarily conceived or expressed under a discrete, discontinuous aspect.

Let us take a few specimens of Zenon's subtle ratiocination which will show more clearly than any lengthened disquisition the nature and tendency of his thought.

Thus setting himself against the opponents of Parmenides, who affirmed that existence consisted of entia plura discreta, and defending the central doctrine of the Eleatics that absolute existence was Ens unum continuum, he thus reasons: If existing things were many, they must be both infinitely great and infinitely small. Infinitely small, because the many is necessarily composed of a number of units, each one essentially indivisible. But the indivisible has no magnitude, or is infinitely small-if, indeed, it can be said even to exist. Infinitely great, because each of the many things, if assumed to exist, must have magnitude; and each has parts which also have magnitude. These parts are by the hypothesis essentially discrete; but this implies that they are kept apart from each other by other intervening parts, which must again be kept asunder by others. Hence each will contain an infinity of parts, every one possessing magnitude; in other words, it will be infinitely great. In a similar manner he shows that if existence consists of many discretes, they will be both finite and infinite. In short, each thing in this universe of manifoldness will be at once both like and unlike, both one and any, both moving and resting-a congeries of contradictions the

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very conception of which is suicidal and impossible. The antagonism between the one and the many, by which either becomes destructive of the other, is thus shown. A grain of millet dropped on the floor makes no noise, but a bushel does make a noise, and yet there is a distinct ratio between one and the other. Hence if one grain makes no sound, neither in like circumstances can ten thousand grains do so. Pursuing his argument against all ideas compounded of discrete parts, he proves that space has no existence; for, as he argues, assuming that space exists, the supposition necessitates another space in which it exists, and this again another, and so on ad infinitum. He also shows that motion is impossible. For on the theory, which he is combating, of absolute discreteness, every line or distance is divisible into an infinite number of parts; hence a body, in passing through the whole length of the line, would have to pass through an infinite number of infinite distances— a thing clearly impossible. Founded upon the same ratiocination is his celebrated argument of Achilles and the tortoise, which, as Mill remarks, has been too hard for the ingenuity or patience of many philosophers; and, among others, of Dr. Thomas Brown, who considered the sophism as insoluble as a sound argument, though leading to a palpable falsehood; not seeing that such an admission would be a reductio ad absurdum of the reasoning faculty itself.' The argument is this: Let Achilles run ten times as fast as the tortoise, yet if the tortoise has the start Achilles will never overtake him. For assume them to be at first separated by an interval of a thousand feet; when Achilles has run these thousand feet, the tortoise will have got on a hundred; when Achilles has run these hundred, the tortoise will have run ten; and so on, for ever. Here, as in the preceding example, the fallacy lies in assuming that what is ideally infinitely divisible is really infinite.2 Having thus annihilated space as a discrete existence, Zenon shows that motion and time are similarly impossible. An arrow propelled from a bow, while in apparent motion is nevertheless at rest. For the time that elapses while it pursues its course, consists of an infinite number of successive instants; during each of these moments the arrow occupies a certain space and is at rest. Zenon has other arguments bearing on the impossibility of absolute discrete existences, but we need not pursue them further. They are all distinguished by the same characteristics, and are resolvable by similar methods. But we must not suppose that Zenon himself

1 Logic, vol. ii. p. 389. Comp. Grote, Plato, i. p. 101.

2 Mr. Mill offers a solution which he considers more precise and satis

factory in his Logic, vol. ii. p. 380.

was entrapped in these dialectical snares. They were, as I have said, prepared for the enemies of Parmenides and the Eleatic Ens; for thinkers who affirmed that the noumena of the metaphysical world were as various and discrete as the phenomena of the material world. Grant Zenon the conclusiveness of his ratiocination, and there would be in his estimation only one escape from the dilemma, i.e. the absolute indivisible being of his master, Parmenides.

It has often been said that Zenon's reasoning is irrefragable once his premisses are conceded. But the concession of hypothetical premisses presupposes, in all serious argumentation, that there is no subterfuge or sleight of hand in the dialectical procedure. No assumption can make valid an argument on the face of it selfcontradictory, or that establishes with equal facility the affirmative as well as the negative of a given proposition, and thus reduces human reason to an absurdity; and Zenon's reasoning is open to more than one objection on that score. A Skeptical opponent might, e.g. reply to him: The Ens of Parmenides will obviously not endure the test of phenomenal existence. The plura discreta of his opponents, as you have proved, will not abide the criterion of the ideal world, even accepting your own account of the latter. What then remains? An antagonism irreconcilable by dialectic between the ideal and phenomenal world. In other words, an intellectual deadlock, a condition of unavoidable nescience or absolute suspense.' Nor, with every desire to insist on the ontological and supersensual character of Zenon's reasonings, is his Skeptical adversary likely to forget their real basis. His arguments as to the conditions of the absolute are derived-as, indeed, they must be--from the phenomenal world. The fall of the millet, whether a single grain or 10,000, is clearly that of phenomenal and sensible millet, and the impossibility of hearing the fall of a single grain is a defect of ordinary human senses. The space and time with which he conjures so adroitly are the entities of the name and properties with which our common experience has made us familiar. Achilles and the tortoise, with their attributes, are conceived as inhabitants of our sublunary world. The arrows propelled from the bow are the well-known instruments of our physical experience. Even the word 'infinite' is a term belonging to terrestrial and sensible conceptions, and denotes in reality not so much a positive quality, pertaining to any existence outside of us, as the limitation of our own powers. The Skeptic might, therefore, fairly demand by what right Zenon-or, for that matter, any other idealist-transfers to a supersensuous world the attri