and with others the assumption, however vaguely understood, seems to have been that the subject, like the predicate, was simple. Thus the essential unity of the world, considered as existence no less than as meaning, is a foregone conclusion. The sense of a division in the subject seems to arise with Empedocles when, reaping the harvest of the Eleatic definition of substance, he parted the world, as subject and as predicate, into four elements.
We may, perhaps, pause a moment to consider the significance of the assumption of four elements which plays so large a part in subsequent philosophies. There is no need of enlarging on the importance of the association of multiple elements with the postulate that nothing is absolutely created and nothing absolutely passes away. These are indeed the pillars that support chemical science, and they further imply the existence of qualities of different rank; but that implication, as we shall see, lay even in the process of rarefaction and condensation introduced by Anaximenes. The four elements concern us here chiefly as testifying to the fact that certain practical interests had summed up the essential characteristics of nature in forms sufficiently significant to have maintained themselves even to our day. In regard to fire, air, and water this is not greatly to be wondered at; it is a somewhat different case with earth. If metallurgy and other pursuits which deal with that which is roughly classed as earth had been highly enough developed to have reacted upon the popular mind, this element could not possibly have been assumed to be so homogeneous. The conception clearly reflects the predominantly agricultural interest of the Greeks in their relation to the earth. This further illustrates the slow progress which deduction makes in the reconstitution of the subject.
It is different, however, with Anaxagoras and the Atomists. Apparently the movement begun by Empedocles soon ran its extreme course. Instead of four elements there is now an infinite number of substances, each differentiated from the other. The meaning of this wide swing of the pendulum is not altogether clear; but it is evident from the system of Anaxagoras that the metals, for example, possessed a significance which they can not have had for Empedocles.
The opposite swing of the pendulum is seen in the later course of the Eleatics. Given a predicate as fixed and unified as they assumed, the subject cannot possibly be conceived in terms of it and hence it is denied outright. In the dialectic of Zeno and Melissus, dealing with the problems of the One and the Many, there is much that suggests the solution offered by the Atomists; but it is probably impossible now to ascertain whether these passages criticise a doctrine already propounded or pointed the way for successors. While the Eleatics asserted the sole reality of the One, Anaxagoras and the Atomists postulated a multiplicity without essential unity. But the human mind seems to be incapable of resting in that decision; it demands that the world shall have not meanings, but a meaning. This demand calls not only for a unified predicate, but also for an effective copula.
3. We have already remarked that the steps by which the predicate was inferred are for the most part unknown. Certain suggestions are contained in the reports 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
