of Aristotle, but it is safe to say that they are generally guesses well or ill founded. The summary inductive mediation has left few traces; and the process of verification, in the course of which hypotheses were rejected and modified, can be followed only here and there in the records. Almost our only source of information is the dialectic of systems. Fortunately for our present purpose we do not need to know the precise form which a question assumed to the minds of the several philosophers; the efforts which they made to meet the imperious demands of logic here speak for themselves.
At first there was no scheme for the mediation of the predicate back to the subject. Indeed there seems not to have existed in the mind of Thales a sense of its need. Anaximander raised the question, but the process of segregation or separation (ἐκκρίνεσθαι) which he propounded was so vaguely conceived that it has created more problems than it solved. Anaximenes first proposed a scheme that has borne fruits. He said that things are produced from air by rarefaction and condensation. This process offers not only a principle of difference, but also a regulative conception, the evaluation of which engaged the thought of almost all the later Pre-Socratics. It implies that extension and mass constitute the essential characters of substance, and, fully apprehended, contains in germ the whole materialistic philosophy from Parmenides at one extreme to Democritus and Anaxagoras at the other. The difficulties inherent in the view were unknown to Anaximenes; for, having a unitary predicate, he assumed also a homogeneous subject.
The logical position of Heraclitus is similar to that of Anaximenes. He likewise posits a simple predicate and further signalizes its functional character by naming it Fire. Without venturing upon debatable ground we may say that it was the restless activity of the element that caused him to single it out as best expressing the meaning of things. Its rhythmic libration typified to him the principle of change in existence and of existence in change. It is the "ever-living" copula, devouring subject and predicate alike and re-creating them functionally as co-ordinate expressions of itself. That which alone is, the abiding, is not the physical composition of a thing, but the law of reciprocity by which it maintains a balance. This he calls variously by the names of Harmony, Logos, Necessity, Justice. In this system of functional co-ordinates nothing escapes the accounting on 'Change;91 all things are in continuous flux, only the nodes of the rhythm remaining constant. It is not surprising therefore that Heraclitus has been the subject of so much speculation and comment in modern times; for the functional character of all distinctions in his system marks the affinity of his doctrines for those of modern psychology and logic.92
The Pythagoreans, having by abstraction obtained a predicate, acknowledged the existence of the subject, but did not feel the need of a copula in the theoretical sphere, except as it concerned the inner relation of the predicate. To them the world was number, but number itself was pluralistic, or let us rather say dualistic. The odd and the even, the generic constituents of number, had somehow to be brought together. The bond was found in Unity, or, again, in Harmony. When they inquired how numbers constituted the world, their answer was in general only a nugatory exercise of an unbridled fancy.93 Such and such a number was Justice, such another, Man. It was only in the wholly practical sphere of experiment that they reached a conclusion worth recording. Its significance they themselves did not perceive. Here, by the application of mathematical measurements to sounds, they discovered how to produce tones of a given pitch, and thus successfully demonstrated the efficiency of their copula.
The Eleatics followed the same general course of abstraction; but with them the sense of the unity of the world effaced its rich diversity. Xenophanes does not appear to have pressed the conception so far as to deny all change within the world. Parmenides, however, bated no jot of the legitimate consequences of his logical position, interpreting, as he did, the predicate, originally conceived as meaning, in terms of existence. That which is simply is. Thus there is left only a one-time predicate, now converted into a subject of which only itself, as a brute fact, can be predicated. Stated logically, Parmenides is capable only of uttering identical propositions: A=A. The fallacious character of the report of the senses and the impossibility of Becoming followed as a matter of course. Where the logical copula is a mere sign of equation there can be neither induction nor deduction. We are caught in a theoretical cul-de-sac.
We are not now concerned to know in what light the demand for a treatise on the world of Opinion may have appeared to Parmenides himself. The avenues by which men reach conclusions which are capable of simplification and syllogistic statement are too various to admit of plausible conjecture in the absence of specific evidence. But it is clear that his resort to the expedient reflected a consciousness of the state of deadlock. In that part of his philosophical poem he dealt with many questions of detail in a rather more practical spirit. Following the lead of Heraclitus and the Pythagoreans he was more successful here than in the field of metaphysics. Thus we see once more that the wounds of theory are healed by practice. But, as usual, even though the metaphysician does receive the answer to his doubts by falling into a severely practical pit and extricating himself by steps which he fashions with his hands, his mental habit is not thereby reconstructed. The fixed predicate of the Eleatics was bequeathed to the Platonic-Aristotelian formal logic, and induction and deduction remained for centuries in theory a race between the hedgehog and the hare.94 The true significance of the destructive criticism brought to bear by Zeno and Melissus on the concepts of unity, plurality, continuity, extension, time, and motion is simply this: that when by a shift of the attention a predicate becomes subject or meaning fossilizes as existence, the terms of the logical process lose their functional reference and grow to be unmeaning and self-contradictory.
We have already remarked that Empedocles, Anaxagoras, and the Atomists sought to solve the problem of the One and the Many, of the subject and the predicate, by shattering the unitary predicate and thus leaving the field to plurality in both spheres. But obviously they were merely postponing the real question. Thought, as well as action, demands a unity somewhere. Hence the absorbing task of these philosophers is to disclose or contrive such a bond of unity. The form which their quest assumed was the search for a basis for physical interaction.95
Empedocles clearly believed that he was solving the difficulty in one form when he instituted the rhythmic libration between unity under the sway of Love and multiplicity under the domination of Hate. But even he was not satisfied with that. While Love brought all the elements together into a sphere and thus produced a unity, it was a unity constituted of a mixture of elements possessing inalienable characters not only different but actually antagonistic. On the other hand, Hate did indeed separate the confused particles, but it effected a sort of unity in that, by segregating the particles of the several elements from the others, it brought like and like together. In so far Aristotle was clearly right in attributing to Love the power to separate as well as to unite. Moreover, it would seem that there never was a moment in which both agencies were not conceived to be operative, to however small an extent.
Empedocles asserted, however, that a world could arise only in the intervals between the extremes of victory in the contest between Love and Hate, when, so to speak, the battle was drawn and there was a general mêlée of the combatants. It may be questioned, perhaps, whether he distinctly stated that in our world everything possessed its portion of each of the elements; but so indispensable did he consider this mixture that its function of providing a physical unity is unmistakable. A further evidence of his insistent demand for unity—the copula—is found in his doctrine that only like can act on like; and the scheme of pores and effluvia which he contrived bears eloquent testimony to the earnest consideration he gave to this matter. For he conceived that all interaction took place by means of them.
Empedocles, then, may be said to have annulled the decree of divorce he had issued for the elements at the beginning. But the solution here too is found, not in the theoretical, but in the practical, sphere; for he never retracts his assertion that the elements are distinct and antagonistic. But even so his problem is defined rather than solved; for after the elements have been brought within microscopic distance of each other in the mixture, since like can act only on like, the narrow space that separates them is still an impassable gulf.96
Anaxagoras endowed his infinitely numerous substances with the same characters of fixity and contrariety that mark the four elements of Empedocles. For him, therefore, the