A Study in the Logic of Early Greek Philosophy


Lloyd, Alfred H. “A Study in the Logic of the Early Greek Philosophy: Pluralism: Empedocles and Democritus.” The Philosophical Review 10, no. 3 (1901): 261. https://doi.org/10.2307/2176262


THAT any study of pluralism is a study, not merely in the history of philosophy or apart from historical setting in technical metaphysics, but also in a field which is bounded only by human experience, seems to me to go quite without saying, and yet I would have it understood that at least between the lines of what follows this general point of view is in my mind. but also to any recognition, open or implicit, of a number of cases of anything, or stages in any process, or points in any argument, or classes in society, or parts of the self; and the conclusions which follow should be applied mutatis mutandis to all these several pluralisms, and to as many others as anybody, perhaps any good pluralist, might care to enumerate. The doctrines of Empedocles and Democritus or Leucippus? which are to be discussed specifically are only the figures on these pages through which I would demonstrate a universal proposition. And this besides: They are selected in grateful recognition of the rich field for study which even the early Greek philosophers have given to modern thinkers.


Among the early Greeks, pluralism was an inevitable conclusion from the peculiar monism of the Eleatics. Eleaticism had reduced the physical account of the world, so far as this could retain monistic form, to the merest bubble that was at the very point of bursting even with the Eleatics themselves and of precipitating physical pluralism. Whether one considers the empty unity of Being, which because empty a negative term, observe was virtually or intensively plural, or recognizes that Being by its very abstraction once for all took unity away from physical things, the case is clear that physical pluralism was bound to succeed Eleaticism. Perhaps the Eleatic Melissos felt this, when he said, defending Eleaticism by assuming pluralism : " If we should assert . . . that things are many, we should still be bound to say that each thing is such as the Eleatics declared the One tube"; but, even if he did not, his statement is most significant, and


Empedocles and Democritus, teaching in their different ways that things were many, and more or less directly that each was the One, were living witnesses to its truth. Empedocles’s pluralism was cruder than Democritus's, being a finite pluralism. That of Democritus was infinite. Thus, Empedocles recognized only a fixed number of elements, earth, air, fire, and water. And what I wish to examine particularly is thinner logic of the projection of a finite pluralism to infinity, or historically the movement of thought from Empedocles to Democritus. Presumably, for example, a finite pluralism and whether there be only four elements recognized or seventy is of no moment has its own peculiar conception of change, while an infinite pluralism, a genuine atomism, if the negative really has any motive, really stands for anything, must have a different conception, but what the difference is, and exactly why it is, need tube determined.


So, to begin in a very simple way, a world of finite elements is bound to lack unity, to be a world of gaps. Only a world of unity, however, can satisfy thought, even the thought of a finite pluralist; and what the thinker fails to recognize directly is sure to force itself upon his indirect recognition, for thought always conserves its universe. For a finite pluralist, then, something besides the elements is logically necessary, something to compensate for the finiteness, or conserve the required unity, or fill the offensive gaps, and in response to this need, force is introduced into the order of things. But why force instead of another element or other elements? Merely because other elements cannot possibly satisfy the demands of thought. Other elements, that are simply elements, mere passive substances, cannot possibly give the required unity to the plural world. Only something active in its nature, that is to say, something external to the elements and qualitatively other than they and calculated to take them out of themselves, can ever fill the want, and such a thing is what is known as a force.


But, secondly, force so conceived, so derived, is of course arbitrary;’ it is arbitrary just because it is external or 'other,' or just because it has to make the elements reach beyond themselves, or to impose its own special nature upon them. Accordingly, again, for the sake of the conservation of reality, for the sake of the unity that thought has to insist upon, the admitted force cannot be single; it must at least be double; there must be two arbitrary but opposing or counteracting and so conserving forces. A single arbitrary force would be at once annihilative and creative. For a finite pluralism, in short, material, or substantial existence and causation as the source of change are bound to be separate functions or separate realities; they cannot be mutually inclusive; they cannot be identical. And then the force upon which the causation depends must be at least double, say on the one hand integrating or organizing or attractive, and on the other disintegrating or differentiating or repulsive; the two of course producing a rhythm by tending to act, not together, but in turn. Thus Empedocles, in addition to his four elements, recognized the two opposite forces of love and hate, which, rising and falling, or 'passing in' and 'passing out' successively, produced a rhythm.


Here somebody is quite likely to suggest or even to insist that to make the causative force or forces external to the elements is not at all necessary, since all the demands of thought would be fully satisfied if the elements themselves possessed the powers of compensating for their finiteness. This, however, would be fatal treachery to the finite elements as elements, making them more than merely elements, and so directly and openly betraying the pluralistic position, or, if not that, it would be sheer occultism, and occultism is certainly of a piece with externalism. Empedocles’s interpreters have found him vacillating between thinking of his forces as independent realities acting ab extra, and thinking of them as only special properties of two, or of two groups, of his four elements, and his vacillation, whether real or imagined, would evidently be fully justified in that the two views really amount to one and the same thing. Occultism is externalism.


Still, thirdly, the state of mind to which vacillation between occultism and externalism points, showed itself in another way that has real importance. The two forces were often also other elements in Empedocles's consciousness, his original four becoming six. The forces were sources of limitation to the elements, and the finite can never be finite, or limited, except through its own kind. There were gaps between the elements, and these, again, could be filled only in kind. Or, once more, in the whole history of human thought, wherever appeal has been made to something outside, to something external or 'other,' the appeal has been satisfied only by some disguise, some new case or some new manifestation of that from which it was made, and sooner or later the disguise itself has been cast aside. Indeed, is it not even as much a law of thought that another world, even a negative of this, must be brought into this, made real in terms of this, as it is a law of physics that action always meets with an equivalent reaction? For my own part, I am far from prepared to say that the two laws are not one and the same. But, be that as it may, the two external forces of a finite pluralism have no choice after all but to enter the world as other elements.


Does not this flatly contradict the statement made above that thought in its effort to make pluralism an adequate account of a universe cannot possibly be satisfied with other elements? I think not, for the two added elements are now seen to be more than mere elements, being forces also, never losing their characters forces, and actually standing forth as witnesses to the inadequacy of the pluralistic conception of what an element really is. Indeed, we are here confronting what is only a special case of a very general principle. In brief, addition of others in kind to any given number of things really involves qualitative as well as quantitative change. Other elements cannot be merely other elements; the addition of elements, or cases, or points, or persons, or parts, really changes even that to which it is made. So in a finite pluralism (1) force as apart from mere substantial existence in the form of passive elements is a necessary supplementary or compensating conception; (2) this external arbitrary force is double, there being in reality two forces which counteract each other and give to the process of the universe a rhythmical character; and (3) the two forces have to figure as other elements, but other both quantitatively and qualitatively. A finite pluralism, therefore, both with regard to the fixed number, four or seventy or any other larger or smaller, upon which it establishes itself, and with regard to its idea of what an element is, evidently contains an irresistible motive or impulse of escape from itself. Quite from within itself it moves towards infinity. An infinite pluralism is its natural, logical goal. After Empedocles, Democritus.


But an infinite pluralism, obviously enough, can be pluralism only in form. I say obviously enough, because of course infinity is something more than one among the other numbers, being the very negative of all that makes mere numbers. At best, infinity is only a quantitative abstraction; it -is a projection of something that is not mere number or quantity on the plane of number or quantity ; it is, again, a witness within the very sphere of number or quantity to something else that must be true of number or quantity, say to quality, to intention; so that as number or extension it is only formal. In general, however, whatever is what it is only in form is bound to be full of paradoxes, self-contradictions, antinomies, so that in the infinite pluralism, the atomism of Democritus, the elements cannot be real elements, nor the vacuum or gaps real recue, nor the external forces really external forces, nor even the rhythm a real alternation, and in each case the formal character, the unreality, must show itself in a paradox. Multiplication, and one even so slight as from four to six involved Empedocles's finite pluralism in a movement of escape from itself, but at infinity the escape is fully accomplished except that there seems to be a need of somebody to call out the station.


Democritus's elements were elements only in form, because quantity or number, historically Pythagorean number, was the only ground of their differentiation. They had only 'primary qualities,' only properties of mathematical determination; they differed in size and shape and weight, but not in substance. Their substance was one, not many. Never in the history of thought was a doctrine more timely than that number-doctrine of the Pythagoreans; it filled such a real want, such a positive need of the contemporary pluralism ; for as quanta the elements, the infinite atoms, could retain at least a specious independence; they could be at least the shells of a lost reality. An important result, too, of Pythagoreanism, or of the speculation of the Greek thinkers generally, conspicuously of the subtle Zeno, was the separation of the idea of number from that of mass witness among other things the book of proportions in Euclid and the fact that this separation was made through reflection on infinite or infinitesimal quantities, and incommensurable quantities only adds to the inner significance of Democritus’s infinite number-atoms. The atoms could be numbers or quanta independently of any mere massiveness.


But, furthermore, between those number-atoms there were, and could be no real gaps, since infinite elements must be at least physically contiguous as well as of a substance physically homogeneous and must make accordingly a physical plenum. A vacuum, too, that is vacuum relatively to elements, whose characteristic quality is number, must itself be quite independent of the determinations of number, and, recognizing and truly appreciating this, one can conclude only that the elements were in a vacuum of which the following paradoxes are strictly true: (1) it existed between things without separating them by any distance; (2) it permeated the things themselves, without losing its own reality; and (3) as if in justification of Melissos, not only it did not separate things by existing between them, but also it really made all things in it coextensive or mutually inclusive, Or say even mutually penetrating. In short, Democritus's vacuum was as purely formal or empty? as his plena. “vacuum," he insisted, “are as real as plena"; a paradox if there ever was one, and a paradox which could not but lurk in both of its members, the separate plena being empty shells, the separating vacuum full of all that was. The space of vacuum, in other words, was virtually, logically, that of the infinite or infinitesimal as quality, as an intensive unity, while the space of the elements was quantitative or extensive. Democritus, however, did not clearly see this, if he saw it at all. This is only the inner logic of his teaching. He simply did not know or does not seem to have known where he was, being in this respect not unlike some atomists of more recent times; he did not seem to see how formal and paradoxical his world was in all its aspects; but, I repeat, because infinite, his pluralism was formal and paradoxical throughout.


The Greek atomist's concept of vacuum simply teems with interest for anyone who makes history more than antiquarianism. Thus, again, he saw the infinity of his elements and the ' number ‘by which he characterized them only quantitatively, so that, since infinity is really a witness to something besides mere quantity, he was obliged to recognize something else, outside of the elements and other than them, and his concept of vacuum was the result. In that, then, he made compensation for his pluralism even as Empedocles had done before him in the idea of force. Vacuum was force, not, it is true, as some external embodied force, but as a basis, even the passive and so ultimate basis of the possibility of change or motion; it was force, so to speak, as absolutely latent, which to my mind is force as only formally external to that upon which it is supposed to act, as really but not openly or visibly immanent. A finite pluralism had no choice but to see the needed force as both external and embodied, but an infinite pluralism escapes from all but the form of the external and embodied force. More directly, too, or more positively, Democritus made force virtually immanent by referring the motion, which vacuum only made possible, to differences of weight. These differences, moreover, made counter-motions, the lighter elements by falling more slowly, moving upward at least relatively to the heavier, and rotation and integration were the result; and, in view of this ingenious account of things, we may even regard the force of Democritus as not only virtually immanent, but as also single or only formally double witness the counter-motions due to the single cause of weight; but I do not care to complicate my present case by too much subtle analysis. Suffice it, therefore, to say that an immanent force or an only formally external force, a latent or purely passive force, like that of Democritus's vacuum, could not possibly be arbitrary and so would not need outside control or counteraction; it would control itself; its virtual immanency would protect it from excess, from doing violence to reality. It would also make progress or change continuous; not broken and rhythmical, not vibratory.


But now the motion, that vacuum, which was itself without magnitude and motionless or with only an infinite or infinitesimal magnitude, made possible, needs to be considered carefully. Whatever may have been Democritus's direct consciousness of it, evidently it could not have been merely extensive, merely in terms of so much distance. Motion for infinite or infinitesimal distance or motion in a vacuum which virtually, although not openly, made all things that it contained co-extensive or mutually penetrating, was bound to involve intention as well as extension, or, perhaps I may be allowed to say, to express a process among things that was chemical, if not also vital or mental, as well as physical. This may seem like mere fanciful interpretation, extravagant and perhaps ‘pathological’ but the Greeks of the time were not without some sense of a difference between physical and chemical change and as possibly more to the point the same interpretation may if not must be put upon the motion which modern scientist's motionless but transmitting medium renders possible among things. This medium, at its ideal limit, is a perfect vacuum relatively to the things in it, and also it exists between things without separating them, permeates things without losing its own reality, and makes all that it contains virtually co-extensive, and motion in it or through it, being instantaneous for an infinite distance or eternal for an infinitesimal distance, is certainly intensive as well as extensive. Like Democritus's vacuum, then, it is only a physical disguise or indirection for what is chemical, if not vital or mental, as well as physical. Darkly, negatively, the scientist admits this when he confesses that his transmitting medium is no dogma about things as they really are but only a working hypothesis logically necessary to the integrity of the purely physical point of view; for a working hypothesis, especially when in such a paradoxical form as that of a motionless cause or basis of motion, can be only an abstraction, subject to the peculiar standpoint of the science that finds it workable, for some other science or sciences, for some other point of view. The paradox always takes thought beyond its adopted forms. In general, then, any science's working hypotheses, peculiarly prone as they are to the paradoxical, are as doors in the paneling which other sciences enter secretly. But, general principles and specific illustrations aside, I must return to Democritus. Whatever may be said for the knowledge of chemistry or even for that of biology in his time, a mental science and a purely physical science were existing side by side and it is safe to say that each had to have its secret entrance for the other. Theocratic philosophy with all that it implied, developed contemporaneously with the infinite pluralism, the materialism of Democritus, so that at least as I have to see it Democritus's vacuum, immaterial as it was and really without magnitude, 'equal' or homogeneous and indivisible, cannot but have been his substitute for the Socratic mind or concept, and motion in it was the motion of a world to which the intensive conserving unity of mind belongs.


And now just one thing more. The Greek atomist's well known doctrine of emanation has an important place in the logic of his system, for it is a tertium quid between the doctrine of material elements as having only primary qualities and that of vacuum as a witness, although an unappreciated witness, to something besides mere quantity and matter, namely to quality and mind. Elements that were only so many numbers or quanta could not have secondary qualities, but at the same time, because of their infinite plurality or of the infinity from which their individual quantities were judged, they could not but make secondary qualities, that is, intensive unities, to emanate from them. The process, as a matter of course, was conceived by Democritus in a strictly physical way, in the way of elements coming from objects, however distant, and impinging on the sense-organs, but this only shows to what pass the physical pluralist is obliged to come; it does not affect at all the significance of the need of the conception. The logic of thought is often bound to make the form of expression absurd. And furthermore, as regards the doctrine of emanation is it not a general truth that whatever is as paradoxical or self-contradictory in its nature as the infinite number-elements of Democritus must not only point to something outside and different, but also be itself a sphere of constant movement away from itself? Our modern theories are no doubt free from the letter of Democritus's account of secondary qualities, but it would be far from safe to say that they are free from the spirit, so that the logic here uncovered might possibly be applied to them with much effect, though for the present only Democritus’s infinite pluralism, a pluralism rather of number-elements than of number-vibrations or wave-lengths, is directly in question.


As already more than merely hinted, infinite pluralism leads to something. Its very paradoxes are necessarily prophetic. Democritus put a pure mechanicalize in the place of Empedocles’s dynamism, but Democritus's mechanicalize was only a subtle disguise for something else. His elements as quanta were only disguises for the relations of an organic life or for ' centers of force'; his external vacuum, as we saw specifically, was only an indirection for force as immanent and conservative, not external and arbitrary; his infinity, for quality or intension; and his motion, for chemical or vital or mental change; so that whoever runs may read in his pluralistic mechanical philosophy only a disguise, and a very thin disguise, for Relationism, or Organicism, the philosophy of evolution. This, however, is 'another story’ which accordingly does not belong here.


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