Plato and the Other Companions of Sokrates, 3rd ed. Volume 1

In studying the writings of Plato and Aristotle, we must recollect that they found all these theories pre-existent or contemporaneous. We are not to imagine that they were the first who turned an enquiring eye on Nature. So far is this from being the case that Aristotle is, as it were, oppressed both by the multitude and by the discordance of his predecessors, whom he cites, with a sort of indulgent consciousness of superiority, as “the ancients” (οἱ ἀρχαῖοι).9 The dialectic activity, inaugurated by Sokrates and Zeno, lowered the estimation of these cosmical theories in more ways than one: first, by the new topics of man and society, which Sokrates put in the foreground for discussion, and treated as the only topics worthy of discussion: next, by the great acuteness which each of them displayed in the employment of the negative weapons, and in bringing to view the weak part of an opponent’s case. When we look at the number of these early theories, and the great need which all of them had to be sifted and scrutinised, we shall recognise the value of negative procedure under such circumstances, whether the negationist had or had not any better affirmative theory of his own. Sokrates, moreover, not only turned the subject-matter of discussion from physics to ethics, but also brought into conscious review the method of philosophising: which was afterwards still farther considered and illustrated by Plato.

General and abstract terms and their meaning, stood out as the capital problems of philosophical research, and as the governing agents of the human mind during the process: in Plato and Aristotle, and the Dialectics of their age, we find the meaning or concept corresponding to these terms invested with an objective character, and represented as a cause or beginning; by which, or out of which, real concrete things were produced. Logical, metaphysical, ethical, entities, whose existence consists in being named and reasoned about, are presented to us (by Plato) as the real antecedents and producers of the sensible Kosmos and its contents, or (by Aristotle) as coeternal with the Kosmos, but as its underlying constituents — the ἀρχαὶ, primordia or ultimata — into which it was the purpose and duty of the philosopher to resolve sensible things. The men of words and debate, the dialecticians or metaphysical speculators of the period since Zeno and Sokrates, who took little notice of the facts of Nature, stand contrasted in the language of Aristotle with the antecedent physical philosophers who meddled less with debate and more with facts. The contrast is taken in his mind between Plato and Demokritus.10

Both by Stoics and by Epikureans, during the third and second centuries B.C., Demokritus, Empedokles, Anaxagoras, and Herakleitus were studied along with Plato and Aristotle — by some, even more. Lucretius mentions and criticises all the four, though he never names Plato or Aristotle. Cicero greatly admires the style of Demokritus, whose works were arranged in tetralogies by Thrasyllus, as those of Plato were.11

In considering the early theorists above enumerated, there is great difficulty in finding any positive characteristic applicable to all of them. But a negative characteristic may be found, and has already been indicated by Aristotle. “The earlier philosophers (says he) had no part in dialectics: Dialectical force did not yet exist.”12 And the period upon which we are now entering is distinguished mainly by the introduction and increasing preponderance of this new element — Dialectic — first made conspicuously manifest in the Eleatic Zeno and Sokrates; two memorable persons, very different from each other, but having this property in common.

It is Zeno who stands announced, on the authority of Aristotle, as the inventor of dialectic: that is, as the first person of whose skill in the art of cross-examination and refutation conspicuous illustrative specimens were preserved. He was among the first who composed written dialogues on controversial matters of philosophy.13 Both he, and his contemporary the Samian Melissus, took up the defence of the Parmenidean doctrine. It is remarkable that both one and the other were eminent as political men in their native cities. Zeno is even said to have perished miserably, in generous but fruitless attempts to preserve Elea from being enslaved by the despot Nearchus.

We know the reasonings of Zeno and Melissus only through scanty fragments, and those fragments transmitted by opponents. But it is plain that both of them, especially Zeno, pressed their adversaries with grave difficulties, which it was more easy to deride than to elucidate. Both took their departure from the ground occupied by Parmenides. They agreed with him in recognising the phenomenal, apparent, or relative world, the world of sense and experience, as a subject of knowledge, though of uncertain and imperfect knowledge. Each of them gave, as Parmenides had done, certain affirmative opinions, or at least probable conjectures, for the purpose of explaining it.14 But beyond this world of appearances, there lay the real, absolute, ontological, ultra-phenomenal, or Noumenal world, which Parmenides represented as Ens unum continuum, and which his opponents contended to be plural and discontinuous. These opponents deduced absurd and ridiculous consequences from the theory of the One. Herein both Zeno and Melissus defended Parmenides. Zeno, the better dialectician of the two, retorted upon the advocates of absolute plurality and discontinuousness, showing that their doctrine led to consequences not less absurd and contradictory than the Ens unum of Parmenides. He advanced many distinct arguments; some of them antinomies, deducing from the same premisses both the affirmative and the negative of the same conclusion.15

If things in themselves were many (he said) they must be both infinitely small and infinitely great. Infinitely small, because the many things must consist in a number of units, each essentially indivisible: but that which is indivisible has no magnitude, or is infinitely small if indeed it can be said to have any existence whatever:16 Infinitely great, because each of the many things, if assumed to exist, must have magnitude. Having magnitude, each thing has parts which also have magnitude: these parts are, by the hypothesis, essentially discontinuous, but this implies that they are kept apart from each other by other intervening parts — and these intervening parts must be again kept apart by others. Each body will thus contain in itself an infinite number of parts, each having magnitude. In other words, it will be infinitely great.17

Again — If things in themselves were many, they would be both finite and infinite in number. Finite, because they are as many as they are, neither more nor less: and every number is a finite number. Infinite, because being essentially separate, discontinuous, units, each must be kept apart from the rest by an intervening unit; and this again by something else intervening. Suppose a multitude A, B, C, D, &c. A and B would be continuous unless they were kept apart by some intervening unit Z. But A and Z would then be continuous unless they were kept apart by something else — Y: and so on ad infinitum: otherwise the essential discontinuousness could not be maintained.18

By these two arguments,19 drawn from the hypothesis which affirmed perpetual divisibility and denied any Continuum, Zeno showed that such Entia multa discontinua would have contradictory attributes: they would be both infinitely great and infinitely small — they would be both finite and infinite in number. This he advanced as a reductio ad absurdum against the hypothesis.