Philosophical Works of the Late James Frederick Ferrier/Lectures on Greek Philosophy (1888)/Zeno
ZENO.
25. Zeno, like Parmenides, was a native of Elea. If we may believe Plato, he was twenty-five years younger than Parmenides. Both of them are said to have taken an active part in the administration of the affairs of their native city. Zeno was a resolute opponent of tyranny, and is reported by some authorities to have died a martyr in the defence of liberty.
26. Zeno is styled by Aristotle the father and founder of dialectic; and if the evolution of the issues contained in the philosophy of Parmenides entitle a man to this appellation, he deserves it well. Zeno was the author of those subtle and paradoxical puzzles respecting motion, the solution of which has for the most part baffled logicians even down to the present day. These puzzles, which ought not to be regarded as quibbles (although this is the light in which they are usually looked at), are full of deep significance as illustrative of the laws and progress of thinking. They show how thought is absolutely at variance with itself, and thus, by bringing the opposition fairly to the surface, they prepare the way for its ultimate conciliation under the presidency of a higher principle. Some of the paradoxes are expressed in the words, "Achilles can never overtake a tortoise"—"the flying arrow rests." And generally the impossibility of motion is the leading paradox in the philosophy of Zeno. I may touch upon some of these hereafter: meanwhile, I shall make a few remarks on the principle on which he founds, and on the difference between him and Parmenides.
27. The only difference between Parmenides and Zeno seems to be this, that the one of them argued the affirmative and the other the negative side of the same question. Parmenides took the affirmative side, and argued that Being, the one alone, truly existed. Zeno took the opposite side, and argued that not-Being, the many, had no true existence. The dialectical movement of thought, namely, the opposition between the one and the many, Being and not-Being carried to an extreme, this is, of course, in both cases the same. But if we are to make a distinction between the procedure of Parmenides and that of Zeno, the distinction which I have now pointed out to you is the one which we must draw.
28. In what I have as yet said I am not sure that I have quite reached the ultimate foundation on which the Eleatic philosophy rests. At least I am not sure that I have given it sufficient prominence, or distinguished it with sufficient clearness from the collateral considerations that went along with it. I shall now attempt to make these ultimate points clear, because it is only by getting thoroughly to the root of the matter that we can understand either the motive or the character of the Eleatic speculations. To express their principle, then, almost in one word, it is this: that opposite determinations cannot be combined in the same object, that contrary predicates cannot be assigned to the same thing. They hold, for example, that what was one could not be not-one, i.e., many; and that what was many or not-one could not be one. They held that what was universal could not be non-universal, i.e., particular; and that what was particular or non-universal could not be universal. They held that what was intelligible could not be non-intelligible, i.e., sensible; and that what was non-intelligible or sensible could not be intelligible. The same rule was applied to their own ultimate generalisation of Being and not-Being. What was Being could not be not-Being, and what was not-Being could not be Being. What was could not not be, and what was not could not be. To Being, the one, the universal, the intelligible—the predicate not-Being could not be applied; and to not-Being, the particular, the sensible, the many—the predicate of Being could not be applied. In short, the incompatibility of opposite predicates or determinations attaching to the same subject, this is the ultimate foundation, the fundamental position, of the Eleatic philosophy.
29. Now, the question here arises, a question, however, which I shall merely broach without discussing; the question, Are contrary, opposite, or, as I will call them, contradictory determinations incompatible in the same subject? If they are, then I hold that the philosophy of the Eleatics must be accepted with all its consequences. There is no escape from the paradoxes of Zeno if this principle be true. And, certainly, at first sight it appears not only to be true, but to be forced upon us as true by the very necessities of reason. It seems to be a necessary truth of thought that a thing cannot be one and not one, cannot be universal and not universal, cannot be infinite and finite, and, in fine, cannot be and not be: and, accordingly, this principle has been recognised as a necessary truth in most of the schools of philosophy, even by those which abjure the conclusions of Parmenides and Zeno. Reserving this question for subsequent discussion, I may just here remark that this principle, so far from being a necessary truth of reason (however like one it may look), is, on the contrary, a downright contradiction, an absurdity to all reason; and that its opposite, namely, the principle that opposite determinations are not only compatible in the same subject, but are necessary to the constitution of every subject—this is a necessary truth of reason, is, in fact, the law of the universe, the law of the universe of things as well as of the universe of thought, and that its discovery and enunciation rest with Heraclitus.
30. Reserving for a future opportunity what I have to say on Zeno's subtle paradoxes in disproof of motion, and also his position that opposite predicates or attributes cannot attach to the same subject, I shall now offer a short summary of the Eleatic philosophy. The general scope and substance of the Eleatic philosophy may be summed up under the following heads:—First, the Eleatic philosophers assumed Being, and nothing but Being, as their universal, their truth for all reason; this with them was the τὸ ὂν, or the real. Secondly, they denied or discarded the opposite of this, τὸ ἓτερον or τὸ μὴ ὄν, the not-Being. Thirdly, they denied this on the ground that the same thought or the same thing could not contain or consist of opposite determinations or contrary predicates. Fourthly, the consequence was, that there was no diversity, no plurality, no difference, no life, no generation, and no decay; in short, no change or movement in the universe, according to them; nothing but a dead and unvarying uniformity, a stagnant fixedness, more inanimate than nonentity itself. Being, according to Parmenides, was strictly synonymous with the permanent. Hence his conclusion followed at once: the world of Being is the world of permanence. In the world of permanence there is and can be no change, otherwise the permanent would not be the permanent; therefore, in the world of Being there is and can be no change. Or it may be put in this way, the world of Being excludes not-Being; not-Being is essential to change; therefore, the world of Being excludes change. To understand how not-Being is essential to change you have but to consider that all change is the cessation, or putting oft or not being of one state or determination, and the putting on or being of another state or determination. But in the world of Being there can be no not-Being of any state or determination, because this is the sphere of pure unmixed Being, and not-Being is absolutely excluded from it. And, therefore, inasmuch as not-Being is absolutely excluded from this sphere, and inasmuch as not-Being is essential to constitute change, it follows that all change is necessarily excluded from this sphere. In other words, in the world of Being there is no change, no creation, no becoming; that is, no coming into Being and no going out of Being; there is a mere dead unvarying uniformity. That is the world of reason and of truth according to Parmenides; and it is fairly, indeed inevitably, reached upon his principles, which are, that the world of Being and of not-Being stand towards each other in a relation of irreconcilable antagonism, and that opposite determinations cannot belong to, and may not be predicated of, the same subject
31. Let us now consider shortly the position of Zeno. In the world of change there is no Being. This is the same thesis viewed negatively. Parmenides showed that what is, cannot change; and his ground or fulcrum of proof was, that Being excludes not-Being, and not-Being is essential to change; for instance, the not-Being of solidity is essential to the Being of fluidity. On the other hand, Zeno proves that what changes, cannot be; and his fulcrum is that not-Being excludes Being. To repeat his position: in the world of change there is no Being. The proof is this: if the world of change included Being, it would include the permanent, because Being and the permanent are identical; but the permanent is excluded from the changeable by the very terms of the conception, therefore Being is excluded from the world of change; in other words, in the world of change there is no Being. Such is the negative supplement by means of which Zeno reinforced the positive argument of Parmenides. In the sphere of Being, or the one, the universal, says Parmenides, there can be no not-Being (and consequently no change), because to introduce not-Being here would be to assign opposite determinations to the same subject. And in the sphere of not-Being, the many, the particular, says Zeno, there can be no Being (and consequently nothing but change), because to introduce Being here would, in like manner, be to assign opposite determinations to the same subject. The reasonings of the Eleatics are impregnable if their principle, namely, that contrary determinations cannot belong to the same subject, be conceded.