The Logic of the Pre-Socratic Philosophy

William Arthur Heidel

IT is not the purpose of this study to show that the Pre-Socratics possessed a system of logic which is now for the first time brought to the notice of the modern world. Indeed, there is nothing to indicate that they had reflected on mental processes in such a way as to call for an organized body of canons regulating the forms of concepts and conclusions. Aristotle attributed the discovery of the art of dialectic to Zeno the Eleatic, and we shall see in the sequel that there was much to justify the opinion. But logic, in the technical sense, is inconceivable without concepts, and from the days of Aristotle it has been universally believed that proper definitions owe their origin to Socrates. A few crude attempts at definition, if such they may be rightly called, are referred to Empedocles and Democritus. But in so far as they were conceived in the spirit of science, they essayed to define things materially by giving, so to speak, the chemical formula for their production. Significant as this very fact is, it shows that even the rudiments of the canons of thought were not the subjects of reflection.

In his Organon Aristotle makes it evident that the demand for a regulative art of scientific discourse was created by the eristic logic-chopping of those who were most deeply influenced by the Eleatic philosophy. Indeed, the case is quite parallel to the rise of the art of rhetoric. Aristotle regarded Empedocles as the originator of that art, as he referred the

(204) beginnings of dialectic to Zeno. But ,the formulation of both arts in well-rounded systems came much later. As men conducted lawsuits before the days of Tisias and Corax, so also were the essential principles of logic operative and effective in practice before Aristotle gave them their abstract formulation.

While it is true, therefore, that the Pre-Socratics had no formal logic, it is equally true, and far more significant, that they either received from their predecessors or themselves developed the conceptions and the presuppositions on which the Aristotelian logic is founded. One of the objects of this study is to institute a search for some of these basic conceptions of Greek thought, almost all of which existed before the days of Socrates, and to consider their origin as well as their logical significance. The other aim here kept in view is to trace the course of thought in which the logical principles, latent in all attempts to construct and verify theories, came into play.

It is impossible, no doubt, to discover a body of thought a which does not ground itself upon presuppositions. They are the warp into which the woof of the system, itself too often consisting of frayed ends of other fabrics, is woven with the delight of a supposed creator. Rarely is the thinker so conscious of his own mental processes that he is aware of what he takes for granted. Ordinarily this retirement to an interior line takes place only when one has been driven back from the advanced position which could no longer be maintained. Emerson has somewhere said: "The foregoing generations beheld God and Nature face to face; we through their eyes. Why should not we also enjoy an original relation to the universe ? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us and not the history of theirs?" The difficulty lies precisely in our faith in immediate insight and revelation,

(205) which are themselves only short-cuts of induction, psychological short circuits, conducted by media we have disregarded. Only a fundamentally critical philosophy pushes its doubt to the limit of demanding the credentials of those conceptions which have come to be regarded as axiomatic.

The need of going back of Aristotle in our quest for the truth is well shown by his attitude toward the first principles of the several sciences. To him they are immediately given — amesoi protaseiV —and hence are ultimate a priori. The historical significance of this fact is already apparent. It means that in his day these first principles, which sum up the outcome of previous inductive movements of thought, were regarded as so conclusively established that the steps by which they had been inferred were allowed to lapse from memory.

No account of the history of thought can hope to satisfy the demands of reason that does not explain the origin of the convictions thus embodied in principles. The only acceptable explanation would be in terms of will and interest. To give such an account would, however, require the knowledge of secular pursuits and ambitions no longer obtainable. It might be fruitful of results if w e could discover even the theoretical interests of the age before Thales; but we know that in modern times the direction of interest characteristic of the purely practical pursuits manifests its reformative influences in speculation a century or more after it has begun to shape the course of common life. Hence we might misinterpret the historical data if they were obtainable. But general considerations, which we need not now rehearse, as well as indications contained in the later history of thought, hereinafter sketched, point to the primacy of the practical as yielding the direction of interest that determines the course it shall take.

It was said above that the principles of science are the

( 206) result of an inductive movement, and that the inductive movement is directed by an interest. Hence the principles are contained in, or rather are the express definition of, the interest that gave them birth. In other words, there is implied in all induction a process of deduction. Every stream of thought embraces not only the main current, but also an eddy, which here and there re-enters it. And this is one way of explaining the phenomenon which has long engaged the thought of philosophers, namely, the fact of successful anticipations of the discoveries of science or, more generally still, the possibility of synthetic judgments a priori. The solution of the problem is ultimately contained in its statement.[2]

To arrive at a stage of mentality not based on assumptions one would have, no doubt, to go back to its beginnings. Greek thought, even in the time of Thales, was well furnished with them. We cannot pause to catalogue them, but it may further our project if we consider a few of the more important. The precondition of thought as of life is that nature be uniform, or ultimately that the world be rational. This is not even, as it becomes later, a conscious demand; it is the primary ethical postulate which expresses itself in the confidence that it is so. Viewed from a certain angle it may be called the principle of sufficient reason. Closely associated with it is the universal belief of the early philosophers of Greece that everything that comes into being is bound up inseparably with that which has been before; more precisely, that there is no absolute, but only relative, Becoming. Corollaries of this axiom soon appeared in the postulates of the conservation of matter or mass, and the conservation of energy, or more properly for the ancients, of motion.

(207) Logically these principles appear to signify that the subject, while under definition, shall remain just what it is ; and that, in the system constituted of subject, predicate, and copula, the terms shall stay put" while the adjustment of verification is in progress. It is a matter of course that the constants in the great problem should become permanent landmarks.

Other corollaries derive from this same principle of uniformity. Seeing that all that comes to be in some sense already is, there appears the postulate of the unity of the world ; and this unity manifests itself not only in the integrity and homogeneity of the world-ground, but also in the more ideal conception of a universal law to which all special modes of procedure in nature are ancillary. In these we recognize the insistent demand for the organization of predicate and copula. Side by side with these formulae stands the other, which requires an ordered process of becoming and a graduated scale of existences, such as can mediate between the extremes of polarity. Such series meet us on every hand in early Greek thought. The process of rarefaction and condensation in Anaximenes, the odoV auw katw of Heraclitus, the regular succession of the four Empedoclean elements in almost all later systems—these and other examples spontaneously occur to the mind. The significance of this conception, as the representative of an effective copula, will presently be seen. More subtle, perhaps, than any of these principles, though not allowed to go so long unchallenged, is the assumption of a fusiV, that is, the assumption that all nature is instinct with life. The logical interpretation of this postulate would seem to be that the concrete system of things—subject, predicate, copula—constitutes a totality complete in itself and needing no jog from without.

In this survey of the preconceptions of the early Greek philosophers I have employed the terms of the judgment without apology. The justification for this course must come

(208) ultimately, as for any assumption, from the success of its application to the facts. But if " logic " merely formulates 'in a schematic way that which in life is the manipulation of concrete experience, with a view to attaining practical ends, then its forms must apply here as well as anywhere. Logical terminology may therefore be assumed to be welcome to this field where judgments are formed, induction is made from certain facts to defined conceptions, and deductions are derived from principles or premises assumed. Speaking then in these terms we may say that the Pre-Socratics had three logical problems set for them: First, there was a demand for a predicate, or, in other words, for a theory of the world. Secondly, there was the need of ascertaining just what should be regarded as the subject, or, otherwise stated, just what it was that required explanation. Thirdly, there arose the necessity of discovering ways and means by which the theory could be predicated of the world and by which, in turn, the hypothesis erected could be made to account for the concrete experience of life: in terms of logic this problem is that of maintaining an efficient copula. It is not assumed that the sequence thus stated was historically observed without crossing and overlapping; but a survey of the history of the period will show that, in a general way, the logical requirements asserted themselves in this order.

1. Greek philosophy began its career with induction. We have already stated that the preconceptions with which it approached its task were the result of previous inductions, and indeed the' epic and theogonic poetry of the Greeks abounds in thoughts indicative of the consciousness of all of these problems. Thus Homer is familiar with the notion that all things proceed from water,[3] and that, when the human body decays, it resolves itself into earth and water.[4] Other opinions might be enumerated, but they would add

(209) nothing to the purpose. When men began, in the spirit of philosophy, to theorize about the world, they assumed that it —the subject—was sufficiently known. Its existence was taken for granted, and that which engaged their attention was the problem of its meaning. What predicate—so we may formulate their question—should be given to the subject? It is noticeable that their induction was quite perfunctory. But such is always the case until there are rival theories competing for acceptance, and even then the impulse to gather up evidence derived from a wide field and assured by resort to experiment comes rather with the desire to test a hypothesis than to form it. It is the effort to verify that brings out details and also the negative instances. Hence we are not to blame Thales for rashness in making his generalization that all is Water. We do not know what indications led to this conclusion. Aristotle ventured a guess, but the motives assumed for Thales agree too well with those which weighed with Hippo to admit of ready acceptance.

Anaximander, feeling the need of deduction as a sequel to induction, found his predicate in the Infinite. We cannot now delay to inquire just what he meant by the term; but it is not unlikely that its very vagueness recommended it to a man of genius who caught enthusiastically at the skirts of knowledge. Anaximenes, having pushed verification somewhat farther and eliciting some negative instances, rejected water and the Infinite and inferred that all was air. His arch must have the quality of infinity, but, a copula having been found in the process of rarefaction and condensation, it must occupy a determinate place in the series of typical forms of existence. The logical significance of this thought will engage our attention later.

Meanwhile it may be well to note that thus far wily one predicate has been offered by each philosopher. This is doubtless due to the preconception of the unity and homo-

(210) -geneity of the world, of which we have already made mention. Although at the beginning its significance was little realized, the conception was destined to play a prominent part in Greek thought. It may be regarded from different points of view not necessarily antagonistic. One may say, as indeed has oftentimes been said, that it was due to ignorance. Men did not know the complexity of the world, and hence declared its substance to be simple. Again, it may be armed that the assumption was merely the naive reflex of the ethical postulate that we shall unify our experience and organize it for the realization of our ideals. While increased knowledge has multiplied the so-called chemical elements, physics knows nothing of their differences, and chemistry itself demands their reduction.

The extension and enlarged scope of homogeneity came in two ways: First, it presented itself by way of abstraction from the particular predicates that may be given to things. This was due to the operation of the fundamental assumption that the world must be intelligible. Thus, even in Anaximander, the world-ground takes no account of the diversity of things except in the negative way of providing that the contrariety of experience shall arise from it. We are therefore referred for our predicate to a somewhat behind concrete experience. The Pythagoreans fix upon a single aspect of things as the essential, and find the meaning of the world in mathematical relations. The Eleatics press the conception of homogeneity until it is reduced to identity. Identity means the absence of difference ; hence, spatially considered, it requires the negation of a void and the indivisibility of the world; viewed temporally, it precludes the succession of different states and hence the possibility of change.

We thus reach the acute stage of the problem of the one and the Many. The One is here the predicate, the subject

(211) is the Many. The solution of the difficulty is the task of the copula, and we shall recur to the theme in due time. It may be well, however, at this point to draw attention to the fact that the One is not always identical with the predicate, nor the Many with the subject. In the rhythmic movement of erecting and verifying hypotheses the interest shifts and what was but now the predicate, by taking the place of the premises, comes to be regarded as the given from which the particular is to be derived or deduced. There is thus likewise a shift in the positions of existence and meaning. The subject, or the world, was first assumed as the given means with which to construct the predicate, its meaning; once the hypothesis has been erected, the direction of interest shifts back to the beginning, and in the process of verification or deduction the quondam predicate, now the premises, becomes the given, and the task set for thought is the derivation of fact. For the moment, or until the return to the world is accomplished, the One is the only real, the Manifold remains mere appearance.

The second form in which the sense of the homogeneity of the world embodies itself is not, like the first, static, but is altogether dynamic. That which makes the whole world kin is neither the presence nor the absence of a quality, but a principle. The law thus revealed is, therefore, not a matter of the predicate, but is the copula itself. Hence we must defer a fuller consideration of it for the present.

2. As has already been said, the inductive movement implies the deductive, and not only as something preceding or accompanying it, but as its inner meaning and ultimate purpose. So too it was with the earliest Greek thinkers. Their object in setting up a predicate was the derivation of the subject from it. In other words their ambition was to discover the arch  from which the genesis of the world proceeds. But deduction is really a much more serious task

(212) than would at first appear to one who is familiar with the Aristotelian machinery of premises and middle terms. The business of deduction is to reveal the subject, and ordinarily the subject quite vanishes from view. Induction is rapid, but deduction lags far behind. It may require but a momentary flash of `insight" on the part of the physical philosopher to discover a principle; if it is really significant, inventors will be engaged for centuries in deducing from it applications to the needs of life by means of contrivances. Thus after ages we come to know more of the subject, which is thereby enriched. The contrivances are the representatives of the copula in practical affairs ; in quasi-theoretical spheres they are the apparatus for experimentation. It has just been remarked that by the application of the principles to life it is enriched ; in other words, it receives new meaning, and new meaning signifies a new predicate. Theory is at times painfully aware of the multitude of new predicates proposed; rarely does it realize that there has been created a new heaven and a new earth. Without the latter, the former would be absurd.

Men take very much for granted and regard almost every achievement as a matter of course. Hence they do not become aware of their changed position except as it reflects itself in new schemes and in a larger outlook. The subject receives only a summary glance to discover what new predicate shall be evolved. Hence, while there is in Greek philosophy a strongly marked deductive movement, the theoretical results to the subject are insignificant. Thales seems, indeed, to have had no means to offer for the derivation of the world, but he evidently had no doubt that it was possible. With him and with others the assumption, however vaguely understood, seems to have been that the subject, UP the predicate, was simple Thus the essential unity of the world, considered as existence no less than as meaning, is a foregone conclusion. The

(213) 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 infinito 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

(214) 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 segrega-

(215) -tion or separation (ekkrinesqai) 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 anti 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;[5]

(216) 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.[6]

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.[7] 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

(217)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.[8] 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

(218) 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.[9]

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

(219) 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.[10]

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 difficulty of securing unity and co-operation in an effective copula is, if that be possible, further aggravated. His grasp of the problem, if we may judge from the relatively small body of documentary evidence, was not so sure as that of Empedocles, though he employed in general the same means for its solution. He too postulates a mixture of all substances, more consciously and definitely indeed than his

(220) predecessor. Believing that only like can act on like,[11] he is led to assume not only an infinite multiplicity of substances, but also their complete mixture, so that everything, however small, contains a portion of every other. Food, for example, however seeming-simple, nourishes the most diverse tissues of the body. Thus we discover in the universal mixture of substances the basis for co-operation and interaction.

Anaxagoras, therefore, like Empedocles, feels the need of bridging the chasm which he has assumed to exist between his distinct substances. Their failure is alike great, and is due to the presuppositions they inherited from the Eleatic conception of a severe homogeneity which implies an absolute difference from everything else. The embarrassment of Anaxagoras increases with the introduction of the . This agency was conceived with a view to explaining the formation of the world; that is, with a view to mediating between the myriad substances in their essential aloofness and effecting the harmonious concord of concrete things. While, even on the basis of a universal mixture, the function of the Nous? was foredoomed to failure, its task was made more difficult still by the definition given to its nature. According to Anaxagoras it was the sole exception to the composite character of things; it is absolutely pure and simple in nature[12]. By its definition, then, it is prevented from accomplishing the work it was contrived to do; and hence we cannot be surprised at the lamentations raised by Plato and Aristotle about the failure of Anaxagoras to employ the

(221) agency he had introduced. To be sure, the Nous is no more a deus ex machina than were the ideas of Plato or the God of Aristotle. They all labored under the same restrictions. The Atomists followed with the same recognition of the Many, in the infinitely various kinds of atoms; but it was tempered by the assumption of an essential homogeneity. One atom is distinguished from another by characteristics due to its spatial relations. Mass and weight are proportional to size. Aristotle reports that, though things and atoms have differences, it is not in virtue of their differences, but in virtue of their essential identity, that they interact.[13] There is thus introduced a distinction which runs nearly, but not quite, parallel to that between primary and secondary qualities.[14] Primary qualities are those of size, shape, and perhaps[15] position; all others are secondary. On the other hand, that which is common to all atoms is their corporeity, which does indeed define itself with reference to the primary (spatial) qualities, but not alike in all. The atoms of which the world is constituted are alike in essential nature, but they differ most widely in position.

It is the void that breaks up the unity of the world atomizes it, if we may use the expression. It is the basis of all discontinuity. Atoms and void are thus polar extremes reciprocally exclusive. The atoms in their utter isolation in space are incapable of producing a world. In order to bridge the chasm between atom and atom, recourse is had to motion eternal, omnipresent, and necessary. This it is that annihilates distances. In the course of their motion atoms collide, and in their impact one upon the other the

(222) Atomists find the precise mode of co-operation by which the world is formed.[16] To this agency are due what Lucretius happily called "generating motions."

The problem, however, so insistently pursued the philosophers of this time that the Atomists did not content themselves with this solution, satisfactory as modern science has pretended to consider it. They followed the lead of Empedocles and Anaxagoras in postulating a widespread, if not absolutely universal, mixture. Having on principle excluded "essential" differences among the atoms, the impossibility of finally distinguishing essential and non-essential had its revenge. Important as the device of mixture was to Empedocles and Anaxagoras, just so unmeaning ought it to have been in the Atomic philosophy, provided that the hypothesis could accomplish what was claimed for it. It is not necessary to reassert that the assumption of "individua," utterly alienated one from the other by avoid, rendered the problem of the copula insoluble for the Atomists.

Diogenes of Apollonia is commonly treated contemptuously as a mere reactionary who harked back to Anaximenes and had no significance of his own. The best that can be said of such an attitude is that it regards philosophical theories as accidental utterances of individuals, naturally well or ill endowed, who happen to express conclusions with which men in after times agree or disagree. A philosophical tenet is an atom, set somewhere in a vacuum, utterly out of relation to everything else. But it is impossible to see how, on this theory, any system of thought should possess any significance for anybody, or how there should be any progress even, or retardation.

Viewed entirely from without, the doctrine of Diogenes would seem to be substantially a recrudescence of that of

(223) Anaximenes. Air is once more the element or out of which all proceeds and into which all returns. Again the process of transformation is seen in rarefaction and condensation; and the attributes of substance are those which were common to the early hylozoists. But there is present a keen sense of a problem unknown to Anaximenes. What the early philosopher asserted in the innocence of the youth of thought, the later physiologist reiterates with emphasis because he believes that the words are words of life.

The motive for recurring to the earlier system is supplied by the imperious demand for a copula which had so much distressed Empedocles, Anaxagoras, and the Atomists. And here we are not left to conjecture, but are able to refer to the ipsissima verba of our philosopher. After a brief prologue, in which he stated that one's starting-point must be beyond dispute, he immediately[17] turned to his theme in these words:[18] "In my opinion, to put the whole matter in a nutshell, all things are derived by alteration from the same substance, and indeed all are one and the same. And this is altogether evident. For if the things that now exist in the world-earth and water and air and fire and whatsoever else appears to exist in this world—if, I say, any one of these were different from the other, different that is to say in its proper peculiar nature, and did not rather, being one and the same, change and alter in many ways, then in nowise would things be able to mix with one another, nor would help or harm come to one from the other, nor would any plant spring from the earth, nor any other living thing come into being, if things were not so constituted as to be one and the same."

These words contain a singularly interesting expression

(224) of the need of restoring the integrity of the process which had been lost in the effort to solve the problem of the One and the Many without abandoning the point of view won by the Eleatics. Aristotle and Theophrastus paraphrase and sum up the passage above quoted by saying[19] that interaction is impossible except on the assumption that all the world is one and the same. Hence it is manifest, as was said above, that the return of Diogenes to the monistic system of Anaximenes had for its conscious motive the avoidance of the dualism that had sprung up in the interval and had rendered futile the multiplied efforts to secure an effective copula.

We should note, however, that in the attempt thus made to undo the work of several generations Diogenes retained the principle which had wrought the mischief. We have before remarked that the germ of the Atomic philosophy was contained in the process of rarefaction and condensation. Hence, in accepting it along with the remainder of Anaximenes's theory, the fatal assumption was reinstated. It is the story of human systems in epitome. The superstructure is overthrown, and with the débris a new edifice is built upon the old foundations.

In the entire course of philosophical thought from Thales onward the suggestion of an opposition between the subject and the predicate had appeared. It has often been said that it was expressed by the search for a arch, or a true nature, in contrast with the world as practically accepted. There is a certain truth in this view; for the effort to attain a predicate which does not merely repeat the subject does imply that, there is an opposition. But the efforts made to return from the predicate to the subject, in a deductive movement, shows that the difference was not believed to be absolute. This is true, however, only of those fields of speculation that lie next to the highways of practical life, which lead

(225) equally in both directions, or, let us rather say, which unite while they mark separation. In the sphere of abstract ideas the sense of embarrassment was deep and constantly growing deeper. The reconstruction, accomplished on lower levels, did not attain unto those heights. Men doubted conclusions, but did not think to demand the credentials of their common presuppositions.

Side by side with the later philosophers whom we have mentioned there walked men whom we are wont to call the Sophists. They were the journalists and pamphleteers of those days, men who, without dealing profoundly with any special problem, familiarized themselves with the generalizations of workers in special fields and combined these ideas for the entertainment of the public. They were neither philosophers nor physicists, but, like some men whom we might cite from our own times, endeavored to popularize the teachings of both. Naturally they seized upon the most sweeping generalizations and the preconceptions which disclosed themselves in manifold forms. Just as naturally they had no eyes with which to detect the significance of the besetting problems at which, in matters more concrete, the masters were toiling. Hence the contradictions, revealed in the analysis we have just given of the philosophy of the age, stood out in utter nakedness.

The result was inevitable. The inability to discover a unitary predicate, more still, the failure to attain a working copula, led directly to the denial of the possibility of predication. There was no truth. Granted that it existed, it could not be known. Even if known, it could not be communicated. In these incisive words of Gorgias the conclusion of the ineffectual effort to establish a logic of science is clearly stated. But the statement. is happily only the half-truth, which is almost a complete falsehood. It takes no account of the indications, everywhere present, of a needed

(226) reconstruction. Least of all does it catch the meaning of such a demand.

The Sophists did not, however, merely repeat in abstract from the teachings of the philosophers. It matters not whether they originated the movement or not; at all events they were pioneers in the field of moral philosophy. Here it was that they chiefly drew the inferences from the distinction between fnsei and nomw. Nothing could have been more effective in disengaging the firmly rooted moral prepossessions and rendering them amenable to philosophy. Just here, at last, we catch a hint of the significance of the logical process. In a striking passage in Plato's Protagoras,[20] which one is fain to regard as an essentially true reproduction of a discourse by that great man, Justice and Reverence are accorded true validity. On inquiring to what characteristic this honorable distinction is due, we find that it does not reside in themselves; it is due to the assumption that a state must exist.

Here, then, in a word, is the upshot of the logical movement. Logical predicates are essentially hypothetical, deriving their validity from the interest that moves men to affirm them. When they lose this hypothetical character, as terms within a volitional system, and set up as entities at large, they cease to function and forfeit their right to exist.


  1. This study may be regarded as in some sense a development of pp. 7-l0 of The Necessary and the Contingent in the Aristotelian System published in 1898 by The University of Chicago Press. While quite independent in treatment, the two papers supplement each other.
  2. The best special illustration of this truth with which I am acquainted is presented for the science of chemistry in an article by F. WALD, "Die Genesis der stöchiometrischen Grundgesetze," in Zeitschrift far physikalische Chemie, Vol. XVIII (1895), pp. 337 ff.
  3. E 701, 246.
  4. H 99.
  5. In allusion to fr. 90 (DIELS). DIELS find, in fr. 108 (fr. 18, BYWATER),  oti sofon esti pantwn kecwrismenon the thought that God is the Absolute, comparing the vovs of Anaxagoras and the cwristh idea of Plato and the ousia cwristh of Aristotle. He assumes that sofon = logoV and concedes great significance to the fragment. But this interpretation is utterly incompatible WILLI eveything else that we know of Heraclitus, and should be admitted only if it were the only one admissible. ZELLER discusses the fragment at length, Vol. 1, p. 629, 1. If Diels's interpretation be accepted, the exposition above given of Heraclitus's logical position must be abandoned.
  6. It has been, and in some quarters is still, the fashion to say that Heraclitus is the originator of the doctrine of relativity; but Zeller is quite right in denying the charge. No doubt his teachings lent themselves readily to such a development, but he did not so express himself. According to him the contrarieties coexist in the process.
  7. Cf. RITTER-PRELLER, §65c.
  8. This, in a word, is the burden of my study of The Necessary and the Contingent in the Aristotelian System.
  9. I have in preparation a study of the problem of physical interaction in PreSocratic philosophy which deals with this question in all its phases.
  10. This statement is, of course, figurative, since Empedocles denied the existence of a void.
  11. I cannot now undertake a defense of this statement, which runs counter to certain ancient reports, but must reserve a full discussion for my account of physical interaction.
  12. The motive for making this assumption was clearly the desire to make of the Nous the prime mover in the world while exempting it from reaction on the part of the world. which would have been unavoidable if its nature had contained parts of other things. It is the same problem of "touching without being touched in return" that led Aristotle t" a Similar definition of God and of the rational soul. Tile same difficulty besets the absolutely "simple" soul of Plato's Phaedo and the causality of the Ideas.
  13. ARISTOTLE, De Generatione et Corruptione, 323b 10 f.
  14. We have seen that this distinction was latent in Anaximenes's process of rarefaction and condensation. For other matters see CHAIGNET, Histoire de la Psychologie, Vol. 1, p. 111, whose account, however, need, to he corrected in some particulars.
  15. I say "perhaps" because ancient reports differ as to the precise relation of position and arrangement to the distinction between qualities, primary and secondary.
  16. This is only another instance of what Mr. VENN (Empirical Logic, p. 56) has wittily alluded to as "screwing up the cause and the effect into close juxtaposition."
  17. Simplicius says euqus meta to prooimion, see DIELS, Die Fragmente der Vorsokra, tiker (Berlin, 1903), p. 347, 1. 18.
  18. Fr. 2, DIELS.
  19. See DIELS, Fragmente tier Vorsokratiker, p. 343, 1. 2; p. 314, 1. 27.
  20. 320 C f.

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