Leucippus & Democritus
Life and Works
We know very little about Leucippus, but he did live in the fifth century BC and he may have lived in Elea, Abdera, or Miletus. He may also have been a student of Zeno of Elea. Some scholars suggest that Leucippus may not even have existed. Democritus was born about 460 BC and lived in Abdera or Miletus, though he visited Athens, apparently enjoying his lack of fame there. He wrote a work on euthemia, or “good-spiritedness,” which gave him the moniker of the Laughing Philosopher in the ancient world. The Roman author Lucian also satirized him. Thus Heraclitus was the crying philosopher while Democritus was the laughing one . [i] Democritus allegedly saw life as a mere drift of atoms while Heraclitus saw it as subjective, filled with stupidity, and doomed to perish in change. It is not certain when Democritus died, but he may have lived to advanced old age. His large body of work has regrettably survived only in fragments––accounts given by other thinkers critical of his work that are not altogether reliable—and a group of ethical aphorisms. It is said that Plato wanted all of Democritus’s works burned, though this account [ii] is not reliable. A polymath student of Leucippus, Democritus built a system of thought around the teachings of his mentor. His interests included mathematics, astronomy, meteorology, and even economics as well as other subjects. Two primary works on ancient atomism from Leucippus and Democritus have been found: Great World System and Little World System. Sometimes Great World System is attributed to Leucippus, but no one is certain who wrote it.
Scholars have tended to bundle Democritus and Leucippus together as one, but some differences between them are known.[iii] The ancient Greeks were generally animists with respect to physical matter, and Democritus and Leucippus were no different. Only in modern times has the notion of pure materialism (an exclusive focus on matter rather than metaphysics or religion) emerged. [iv] In fact, modern atomists like John Dalton (best known for proposing the modern theory of atomism) owe a great debt to Leucippus, Democritus, Epicurus, and Lucretius, who thought of atoms as tiny pieces of matter. The ancient theory of the atom as we have it, first proposed by Leucippus, was most probably developed and refined by Democritus with later development and some alterations by Epicurus [v] and the Roman Lucretius. The ancient atomic theory covered here is primarily Democritus's effort, though we cannot say definitively where Leucippus leaves off and Democritus begins. Thus several quotes below refer to Leucippus, but they may just as well be those of Democritus.
Ancient atomists had differing attitudes about the senses, but Democritus seems to have held the most scientific position on them. He believed that the senses captured something quite different from atoms. In other words, things like color, taste, and smell were conventional, arising from within the perceiver rather than from the thing perceived. All things were made only of motions, collisions, and atoms. Some scholars interpret this stance as a sense of objectivity. [vi] While there is some truth to this assertion, the full and proper notion of objectivity was far from the grasp of ancient thinkers. Leucippus and Democritus followed the Eleatic path and believed that being and non-being are not mixed. [vii] They claimed that there were two aspects of material reality ascertainable to a certain degree with the senses: fullness and void. Fullness and void make the objects that we encounter in the world, as Aristotle confirms:
Having agreed that these things pertain to appearances, [Leucippus] also said to those who construct an argument for the one that movement would not exist without void, that void is nonbeing and that no non-being is being. For the thing existing properly is altogether full (of being). But to be this sort of thing is not to be one; rather, the great multitude of them are boundless and not visible on account of the smallness of their size. These things are born along in the void (for void exists); on the one hand, bringing themselves together, they produce a genesis; on the other, being loosened, they fall to destruction. (Aristotle, De Gen. et Corr. A8, 325a2)
Aristotle states further,
Democritus . . . calls space by these names: “the void,” “nothing,” and “the boundless”; and he calls each of the existing things “hing” [“nothing” without “not”], the “close-pressed,” and “being.” He believes these beings to be so small as to flee our senses, and he believes there are all sorts of forms and shapes and differences in magnitude of them that exist. From these things already, just as from elements, come forth compoundings, sizes perceived by the eyes and the senses. (Aristotle, On Democritus ap. Simplicium, De Caelo 295, I)
Being does not change into non-being, and so what exists cannot change because it would then alter into what is not. As a result, there is a lack of being in objects that is not actually the object itself, but rather is part of something only in that an object has non-being, or what we may call empty space, as a part of it. Atoms are literally “uncut” tiny bits of material reality––being––that compose the objects and things in the universe. Change and becoming in the universe are the breaking up of these bits and their rearrangement. [viii] There is much scholarly discussion on the precise nature of fullness, void, and the general composition of atoms in ancient atomism. [ix] Likely, Democritus meant “nothing” when he wrote “nothing.”
Causation and Cosmology
Void, according to Democritus, was that lack-into-which shape formed and bodies moved. For him it had to be nothing. Nothing else had the ability to make shape and movement possible. The shape, arrangement, and position of atoms are thus essential to the characteristics and therefore actions of objects in the universe. Once again Aristotle:
These men [Leucippus and Democritus] . . . say that the differences [between atoms] are the causes of other things. They say that these [differences] are three: shape, placement, and position. They say being differs by means of rhythm, by touch, and by turn. Of these, rhythm is shape, touch is placement, and turn is position; for A differs from N in shape, AN differs from NA in placement, and Z differs from N in position. (Aristotle, Met. A4, 985 b4)
Atoms are composed of a single substance with one nature to them. Each of the individual atoms are “one.” Leucippus seems to claim that the atom's indivisibility is due to its smallness. But for Democritus atoms fit into one another by means of shape and no matter how closely packed they are there is always some space between them. Things are composed by mere place and conjunction of atoms as well as conflict among them. [x] It is important to note that for Leucippus compounds in the modern sense––where the characteristics of the atoms themselves change–– do not truly form. The qualities of each atom retain their individuality for Leucippus and no characteristics are altered in the compounding. Democritus claims that there is a tendency of similar things to gather together. As animals gather in herds and as people gather in communities, so also do inanimate objects come together. A fragment of atomist thought survives in Sextus's commentary:
For creatures (he says) flock together with creatures similar in kind, doves with doves, cranes with cranes, and just the same with the others. And the same thing occurs with inanimate things, as can be seen with seeds put through a sieve and pebbles on the wave-breaking beach. (Fr. 164, Sextus, Adv. Math. VII, 117)
Such a gathering of similar objects is not the same as the ancient notion of like attracting like necessarily, but rather it is a tendency. It seems that Leucippus believed that all atoms are uniformly small, and so he might not have believed that shape and size were central to the properties that atoms exhibit. Democritus seems to have believed that atoms have different sizes and shapes, and those characteristics produce properties that we see in the conglomerations of atoms when we perceive objects. Apparently there was even more disagreement between the two men. [xi] Democritus claimed that atoms have mathematical rather than physical parts. Leucippus believed that all atoms were small, while Democritus believed they varied in size. For Leucippus the motion of atoms was always in all directions and they moved of their own nature. [xii] Still, the primary qualities of atoms for both men remain size and shape, and these qualities are their most significant differences. They agreed that atoms move in some manner, moving within themselves while seemingly at rest or moving as the things that they comprise.
Whatever the constitution and behavior of atoms, these uncut bits are infinite in number and are “being” in the Eleatic manner, which is to say that they do not change. Thus, they were uncut and eternal. According to the ancient atomists change and rearrangement are due to the void in the conglomerations of atoms packed together in objects. Again, Simplicius describes their position:
[Leucippus, Democritus, Epicurus] said that the beginning principles were limitless in number, which they thought to be indivisible and unaffected atoms on account of their close-pressed-ness, and they thought [them] to have no share of void; for they said that division comes about according to the void, the one in the bodies. (Simplicius, De Caelo 242)
Void and being exist equally, giving both fullness and emptiness to the universe. They interact in an equally powerful manner. [xiii] Fullness and void interact so as to form the earth and the apparent dome over it. The order of the universe is the infinite interactions of these two forces. They are responsible for creating the shape of the universe by attraction and repulsion from a whirl, which gathers together the heavy pieces of the universe and spreads out the thinner elements, “atoms,” into the void. We have some description from Diogenes Laertius:
Leucippus says that the all is infinite. . . . One section of this is full and another, different, section is void. . . . From this [combination] exist countless world orders, and into these things they dis-integrate. He says the world orders come to be in this manner: from a cutting away out of the infinite many bodies with all sorts of shapes are carried into a great void; the very things that are joined together complete one eddy, along which—striking against one another and in all sorts of ways circling—they separate apart, like to like. But on account of the multiplicity of them being no longer able to be carried around in an equal position, the fine ones separate into the outside void just like things sifted; the rest remain in conjunction and, weaving about themselves, run down together, and make a first sphere-formed conglomerate. (Diogenes Laertius, IX, 31)
The atoms that cling to one another owing to their shape and perhaps their size [xiv] conglomerate into the earth and its objects, he continues:
This is a kind of membrane that stands apart, holding around in itself all kinds of bodies; and the membrane of those bodies rotating around down along the resistance of the middle becomes thin, the bodies running together on account of the contact with the eddy. In this manner the earth came to be, the bodies remaining together after having been held in upon the middle. (Diogenes Laertius, IX, 32)
The fundamental forces that create and sustain objects are the same forces that shaped the entire universe. Still, different worlds arise through constant motion. These worlds are not only infinite, but also sometimes partial and sometimes complete, always in transition, as the ancient commentator Hippolytus writes:
Democritus speaks similarly to Leucippus about elements, full and void. . . . He said that beings themselves always become moved in the void; and the world orders are infinite and they differ in magnitude. He says in some there is neither sun nor moon, and in others they are bigger than the ones nearby us, and in yet others they are more numerous. (Hippolytus, Ref. I, 13, 2)
The motion and activity of the universe is different in Democritus's and Leucippus's conception, but the basic forces of attraction demonstrate similarities. The explanation for all of these happenstances is necessity, which is the same as the whirl. [xv] The whirl is necessary by means of determined and mechanical conglomerations and collisions of atoms by means of its necessary collisions and binding-together of atoms; these are mechanical and determinable. [xvi] The motion of atoms therefore plays a fundamental role in the formation of objects in this materialistic universe, although the composition of the world is not entirely mechanistic. [xvii] The ancient atomists emphasized that the chain of collisions along with the shape and size of atoms are responsible for everything that emerges in the universe. Nothing for Democritus and Leucippus occurs in vain because necessity or the eddy makes something out of the combinations; gravity is a primary force in the composition and dissolution of things because gravity is also in part necessity. Theirs is, however, not a teleological universe. At the same time that nothing transpires in vain, there are no fundamental essences of a deeper reality that comprise the universe. In other words, the combinations that make things are accidental; they are inadvertent actions of minuscule being, necessitated by their natures and gravity.
Weight for the ancient atomists is the tendency of objects to press down and it is the result of being that an object has weight, which means naturally that lighter objects have less being in them. Void is thus responsible for lightness, writes Theophrastus:
Democritus distinguishes heavy and light by magnitude. . . . Yet in things mixed together the lighter is the thing containing more void; the heavier is the thing containing less. (Theophrastus, De Sensu 61 [DK 68 A47])
Weight is here the tendency of an object to press down in the world by means of the eddy. Otherwise, objects may have no inherent heaviness to them and thus do not press down. [xviii] Movement among and around the atoms results from dissimilarities among them, which speaks to the gathering of similarities mentioned earlier.
[Atoms] clash and are carried in the void because of the dissimilarity and the other differences that have been said, and being carried they fall upon and are entwined round one another. . . . (Aristotle On Democritus ap Simplicium De Caelo 295). Democritus says, “Always the first bodies are moved.” (Aristotle, De Caelo, G. 2. 300b: cf. Hipp., Ref. I. 1; D.A.40: al).
Atoms collide with one another constantly and in that mass of tiny corpuscles is a “vibration,” which is the movement of the thing itself, as Bailey noted. So the very existence of atoms and void carried with them atomic motion and the first motion comes about from “necessity” as an element of the constitution of things, yet forced motion and motion from “blows” are both derived from it. [xix] In other words, the gathering of atoms in similarities and the cohesion of atoms seem to arise from the weight, size, and shape of atoms along with a tendency of these bits of material reality to flock together. [xx] There seem to be two attracting forces: one attracts like atoms to like atoms and the other binds them together. How precisely these attractions occur is not clear; modern science would call them forces, electromagnetic or otherwise. Thus arise objects in the natural world, as Simplicius states:
Carrying themselves and being carried [the atoms] fall upon and are entwined round one another in an entanglement that makes them touch one another and puts them near to one another, and that truly engenders not any sort of single nature out of them whatsoever; for it is altogether simple minded that two or more would come to be at some time one. [Democritus] claims that up to a certain point the interchanges and the exchanges of bodies cause these beings to remain together, for some of them are uneven and others are hooked, still others are hollow, while others are curved, possessing innumerable other differences. He believes them to cling to one another in turn and remain together up to such time when some more powerful necessity, coming to be from that which surrounds, thoroughly shakes and breaks them apart. (Aristotle, On Democritus ap. Simplicius, De Caelo 295, II)
Atoms seem to conglomerate into objects more by congruence and less by similarity of kind. Perhaps their combination and dissolution result from randomness, [xxi] while atoms themselves in their continued sameness preserve a kind of necessity. Still, the compounding of Democritus's and Leucippus's atoms into new objects and living things is debated.
The chemical molecule that results from the combining of atoms may have been possible in the atomists' universe, but the issue is far from clear. On the one hand, atoms may have cohered because of their shapes or perhaps their sizes, creating temporary new substances, as we have seen. On the other hand, even considering all the ancient atomist theories, it is hard to imagine how a molecule could arise if atoms must lose certain characteristics for the new substance to come to be. [xxii] It is certain that the atomists believed the atoms themselves to be unchangeable, which would prevent such chemical processes from taking place. [xxiii] The theory of Democritus and Leucippus may be interpreted as a play of forces that interact with one another. Modern science supposes something similar: that there are forces operating in the universe that comprise all objects (the strong, weak, electromagnetic, and gravitational). Understanding these forces is understanding the universe. [xxiv] Something similar is true of ancient atomists who thought of the void as a driving force in conjunction with the shape and size of atoms. No matter the particulars, ancient atomists thought in terms of powerful active pieces of the universe that drive into and compose things from their conglomerations. All of these notions arise from imagination, which Democritus and Leucippus seem to have possessed in abundance.
Democritus and Leucippus do not speculate on or categorize the precise shapes of different atoms except to say that mind and fire are sphere shaped[xxv] and that other elements are comprised of conglomerations of differing size and magnitude. As Aristotle writes,
What sort and what shape of each of the elements Leucippus and Democritus did not demarcate, but only to fire did they assign the sphere; air and water and the others they differentiated by largeness and smallness, as if their nature was a mixture of all kinds of seeds of all elements. (Aristotle, De Caelo G 4, 303a 12)
Atoms, it seems, must be differently shaped in order to conglomerate, yet in some instances—like fire and mind—they must conglomerate through the concept of like to like, which seems antithetical to the original conception of atoms as forming objects by differences of shapes. In other words, atoms need to be compatible, which implies that they have different shapes, yet they must have a similar shape in certain substances, like fire and mind, in order for them to function. Fire and mind are the most penetrative of substances because of their consistency of shape, a conception inconsistent with the idea of compatibility through different shapes. If Leucippus claimed that all atoms are the same size (small), then the idea of size producing the activity and function of atoms may have been a development of Democritus. It is difficult to determine.
One may ask whence came the first motion of atoms, but surviving material gives no definitive explanation about an initial motion, only the continued motion of the atoms themselves or the motions of conglomerations of atoms. Perhaps it was believed that motion simply always existed, but given the difficulty of determining the origin of motion, it is plain to see why an answer would not be forthcoming. Indeed, science has no sufficient answer for that question today, except perhaps to suggest that at some time there was an initial explosion, or bang, and even that is now doubted. Nevertheless, we have seen that motion in the void is suggested by the dissimilarities among atoms and by gravity. If atoms always existed and dissimilarities cause movement, then motion would be inevitable; and if gravity is somehow an aspect of a physical thing, then another sort of motion exists because of the conglomerations that comprise things.[xxvi] It seems safe to say that the ordinary movements that comprise objects arise from the above-mentioned collisions and “rebounds,” whether motion is of one kind and origin or another.
It remains for us to examine a few arguments central to the atomist theory in order to make clear some essential parts of their doctrine. Recall that these are not necessarily the precise arguments that Democritus or Leucippus formed, but they follow the same way of reasoning we saw first in Greek literature; they seek patterns and then seek the relationships between patterns discovered. The patterns are the empirical observations that a thinker perceives as regular occurrences. These observations are compared and an inference results. It may have been that Leucippus and Democritus reasoned with constants and in a much more systematic way, and so their thought would have been much more similar to that of a modern scientist,[xxvii] but we do not know. The arguments assessed here are based on some of the evidence we possess, in an attempt to understand some of the more important aspects of ancient atomic theory. The most fundamental aspects of the atomists’ argument come from their conception of being and non-being. In some places we must assume elements of the argument, and by necessity some elements must be left out.
- No things possessing absolute fullness are things that have no being.
- All things that have being are things possessing an absolute fullness.
- No things that have being are things that have no being.
“Things that have being” are here the atoms themselves, not the more complex conglomerations making up objects. The objects we perceive and use have void in them. Otherwise, they would not be able to change and no motion would be possible. So these things that have being must not be in the field of change. This argument assumes that void exists and that void is nonbeing.
- All true beings in the universe are beings made invisible by their size.
- All full beings are true beings in the universe.
- All full beings are beings made invisible by their size.
Naturally, there is no middle ground here. Atomists seem to believe that either a complete being—fullness—exists and there is no lack to being at all, or an absolute lack exists. The absolute fullness is their acceptance of Parmenides's stance. Still, we are able to interpret this atomist argument as valid. It is not sound, but it makes some proper connections. Coming-to-be results from the movement of being into that part of material reality where absolute lack exists. There is no conception of void as an actual existing thing or a partial lack—some existing thing or space into which another existing thing can be placed—yet void “exists” no less than being. Movement comes from being, fullness, sliding into the void that is a fundamental force in the universe equal in realness to fullness.
- All places where motion takes place are void-spaces.
- No absolute fullnesses are void-spaces.
- No absolute fullnesses are places where motion takes place.
- All beings without void-spaces are beings that move into void-spaces.
- All absolute fullnesses are beings without void-spaces.
- All absolute fullnesses are beings that move into void-spaces.
The above two syllogisms are a part of the atomist assertion that void and absolute fullness exist. They appear to be based on common sense observation and experience in the world—Democritus cannot have analyzed the changes and consistencies of the universe on the microscopic level, obviously. Here is where he naturally engages in speculation and an observational form of induction, but Democritus also has found patterns through observation and linked them to other patterns: things with absolute fullness (being) and void-spaces (empty spaces where things may stand). His argument for the interchange of void and fullness explains being and becoming in a materialistic manner:
- All interchanges and exchanges of atoms are changes in material objects.
- All changes in material objects are comings-into-substance and dissolutions.
- All interchanges and exchanges of atoms are comings-into-substance and dissolutions.
Changes come from the void space and the lack that void makes possible by its nature:
- All complete lacks of space and being are voids.
- All places where motion is possible are complete lacks of space and being.
- All places where motion is possible are voids.
- All motions are changes made possible from void-space.
- All comings-into-substance and dissolutions are motions.
- All comings-into-substance and dissolutions are changes made possible from void-space.
The changes made possible from void-space are then motions. The observations taken as universals make the argument for motion as a fundamental part of change and seeming creation. The things not subject to change are the elements of the universe that have an Eleatic aspect to them. The atomists get around the problem of the illusion of change, found in Parmenides's thought, by claiming there is an aspect of material reality that does not change and that has as part of its nature continued existence. These bits of reality are rearranged and instead of comprehending all change as an illusion, as does Parmenides, atomists claim that change happens on the predication of changeless elements that are too small to see. The atomist arguments are valid, yet the arguments themselves are based on unproven and as-yet unaccepted premises, like that there is such a thing as an absolute fullness in the field of material reality. Thus, one flaw of the above arguments is that they, like other ancient arguments we have seen, take these premises as universal and already apparent; they are accepted patterns in need of argument or proof. Atomists like Leucippus and Democritus seem to craft arguments with an empirical dimension to them, all the while accepting as part of their premises empirically unproven elements. There is for them an absolute fullness to material reality, which explains why you cannot pass your hand through a leaden ball. The leaden ball does also have in it void, which makes the ball able to be cut or broken into parts. We think immediately of the modern notion of matter being made up of mostly empty space, but of course modern empty space is not the ancient atomists' void. The ancient void is absolute nothing, while science is finding today that “empty” space is not as lacking in activity as once thought.
The conglomerations of atoms and their separation are made possible by specific aspects of atoms' size and shape, as in the following argument:
- All determiners of atom function are aspects of atoms that allow conglomeration or separation.
- All shapes and sizes of atoms are determiners of atom function.
- All shapes and sizes of atoms are aspects of atoms that allow conglomeration or separation.
It seems that Leucippus and Democritus believed that atoms have a specific character, and that character accounts for the integrity of a given object. When a “necessity” or a movement that results in a collision, or some other material force, interacts with them, their present constitution changes. The interactions of these tiny bits of fixed material reality could be called coming-to-substance or dissolutions, though the only real beings are the atoms themselves. Complex structures made from the atoms are only beings in that they are composed of tiny beings:
- All spaces in which motion may occur are spaces in the universe responsible for alteration or cohesion.
- All void-spaces in material objects are spaces in which motion may occur.
- All void-spaces in material objects are spaces in the universe responsible for alteration or cohesion.
Again, movement into void is primary for things in the world, cohesion and change. As can be expected, Leucippus and Democritus seem to have made little attempt to differentiate the various atoms in the material universe, but rather they seem to have imagined how only some of them may cling to one another or possibly repel one another. If we accept their premises, which are based on a great deal of speculation, then their arguments are reasonable, but if we question one of these unsubstantiated and very difficult to prove assertions, then their system falls apart quickly. Atoms are not eternal and unchanging; change does not come about through mere rearrangement of void-spaces and completely filled beings. The ancient atomists simply had no way to prove, or even to assert with any degree of certainty, what they wished to assert and prove, yet they perceived repeated manifestations of things, patterns, that they explained with speculation. They saw that some objects are hard and cannot be penetrated, except by “blows”. They reasoned that there must be holes or “void” where things may separate, which is a not terrible explanation–given their ability to observe. Their theory does assert something true about material reality. Atoms do exist, of course, but not in the way they believed. Objects are filled with mostly empty space, but there is no absolute void in them that makes space possible. The atomists discovered truths still held to be true in the modern world, but these truths were not precisely as they imagined them. The observations and the repeatable interactions of substances in the universe were explainable by means of the atomists' doctrine, but only because the ancient Greeks did not have the tools and methods to disprove them. They possessed falsifiable theories that they were unable to falsify. Again, they speculated. Their first principles of everything were ultimately provable necessary pieces of reality: uncuttable pieces of matter that were innumerable and perhaps quite varied in size and shape. Perhaps there were empirical proofs of these arguments. We possess the thoughts of the atomists only indirectly, so their arguments may have been much more nuanced, or different. They made use of earlier insights into material reality and explained how things operate by advancing a radical idea, and their idea was proven correct, in a qualified sense, several centuries later.
- [i] See Cora E. Lutz, “Democritus and Heraclitus,” Classical Journal 49, no. 7 (1954): 309-314.
- [ii] Diogenes Laertius, IX 40.
- [iii] For more on the disagreements between the two men, see Cyril Bailey, The Greek Atomists and Epicurus: A Study (Oxford: Clarendon, 1928). For the dates of Democritus and a discussion of the debated existence of Leucippus, see Herman de Ley, “Democritus and Leucippus: Two Notes on Ancient Atomism,” L'Antiquité Classique 37, no. 2 (1968): 620–633.
- [iv] For a greater sense of the debt of modern atomists to Democritus and Leucippus, see Joshua C. Gregory, “Dalton's Debt to Democritus,” Science Progress in the Twentieth Century (1919–1933) 14, no. 55 (1920): 479–486.
- [v] This book lacks space for Epicurus, but one section of his work will give an idea of his perspective. In his Letter to Herodotus (DLX 39–40) Epicurus claims, “Everything is body and empty. For how bodies exist, perception itself bears witness to all (of them), according to which it is necessary to show what is unclear to reason by signs. If there was not a thing which we call empty and place and impalpable nature, there would be no place for bodies to exist, nor anywhere for them to move themselves just as bodies appear to be moving things.” For more on Epicurus, see Saul Fisher, Pierre Gassendi's Philosophy and Science: Atomism for Empiricists (Boston: Brill, 2005).
- [vi] For some discussion on objectivity and sense perception in the atomists' system, see Demetris Nicolaides, In the Light of Science: Our Ancient Quest for Knowledge and the Measure of Modern Physics (New York: Prometheus, 2014); Bailey, The Greek Atomists and Epicuris; and S. Sambursky, The Physical World of the Greeks (New York: Routledge, 1956).
- [vii] Kirk and Raven suggest that the full being of materialism in the atomist universe is a response to Parmenides and his fullness of being. G. S. Kirk and J. E. Raven, The Presocratic Philosophers (Cambridge: Cambridge University Press, 1979) 408. Alfred Lloyd claims that the atomists needed paradox: plenum (fullness of being) and void must be immanent in all objects. Plenum and void involve paradox because they must be immanent. “A Study in the Logic of the Early Greek Philosophy: Pluralism: Empedocles and Democritus,” Philosophical Review 10, no. 3 (1901): 261–270. David Konstan claims that Democritus believed that atoms are being with no nothing in them; the void is nonbeing with nothing in it. “Democritus the Physicist,” Apeiron: A Journal for Ancient Philosophy and Science 33, no. 2 (2000): 125–144. For a sense of how the notion of fullness and void limited the atomists, see J. R. Milton, “The Limitations of Ancient Atomism,” in Science and Mathematics in Ancient Greek Culture, ed. C. J. Tuplin and T. E. Hill. (New York: Oxford University Press, 2002).
- [viii] For an in-depth summation of and one perspective on the debate on mathematical divisibility or indivisibility of the Democritean atom, see Richard W. Baldes, “‘Divisibility’ and ‘Division’ in Democritus,” Apeiron: A Journal for Ancient Philosophy and Science 12, no. 1 (1978): 1–12.
- [ix] Werner Heisenberg writes that the void “was the carrier for geometry and kinematics, making possible the various arrangements and movements of atoms.” Physics and Philosophy: The Revolution in Modern Science (New York: Harper & Row, 1962). Demetris Nicolaides argues that Democritus's notion of void was not really nothing because it was responsible in part for movement and geometry; it made possible different arrangements and motion. In the Light of Science, 89. Bernard Pullman asserts that clustering of atoms “is promoted by the diverse shapes atoms can have—polished, rough, pointed, hooked, twisted, bent.” The Atom in the History of Human Thought (New York: Oxford, 1998), 33. Thomas Cole points out that the ordering of atoms for Democritus tended to become larger, thus making perceptible things. He claimed that atoms are a multiplicity that is one. They are infinite in number and “one” in two senses. Democritus and the Sources of Greek Anthropology (Chapel Hill, NC: Press of Western Reserve University, 1967),107. Cyril Bailey claims that “the atoms continue to perform tiny trajects, greater or less according to the texture of the compound, colliding with one another in infinitesimal periods of time, and recoiling again to another collision: every compound body, every 'thing' that we perceive by the senses is in a constant state of internal atomic vibration.” Atoms do form compounds because “into the tiny intervals of empty space in the compound new atoms will enter in their flight from outside. Occasionally their 'shape or position or order' will fit them to become entangled in their turn and increase the bulk of the compound: as long as this happens the thing grows.” The Greek Atomists and Epicuris, 88–89.
- [x] See Cole, Democritus and the Sources of Greek Anthropology.
- [xi] For more on the properties that atoms manifest when they are combined with other atoms, see Vijay Tankha, Ancient Greek Philosophy, 2nd ed. (Delhi, India: Pearson Education India, 2014).
- [xii] See Bailey, The Greek Atomists and Epicurus, 78.
- [xiii] Some scholars claim that Democritus did not necessarily take void and fullness to be equal in potency. For a discussion on a fragment relating to the problem, see W. I. Matson, “Democritus, Fragment 156,” Classical Quarterly 13, no. 1 (1963): 26–29.
- [xiv] For a discussion about why atoms cohere and their shape, see Sambursky, Physical World of the Greeks. Milton correctly points out that “the atoms postulated by Democritus and Epicurus were assigned their properties on the quite different ground of analogical extrapolation from macroscopic bodies, regulated by metaphysical debate.” “The Limitations of Ancient Atomism,” 186. The ancients were compelled to make analogies and to speculate. We ought not to fault them for their position in history, but rather we ought to admire their imagination and insight.
- [xv] Diog. Laertius, IX, 45.
- [xvi] Kirk and Raven, The Presocratic Philosophers, 412.
- [xvii] For the universe as a living thing, see Milton, “The Limitations of Ancient Atomism.” For mechanistic aspects of ancient atomism, see Raymond Godfrey, “Democritus and the Impossibility of Collision,” Philosophy 65, no. 252 (1990): 212–217; and David Kline and Carl A. Matheson, “The Logical Impossibility of Collision,” Philosophy 62, no. 242 (1987): 509–515.
- [xviii] See John Burnet, Early Greek Philosophy, 4th ed. (London: A. and C. Black, 1930).
- [xix] Bailey, The Greek Atomists and Epicurus, 133–136.
- [xx] David Konstan talks about ancient atoms adhering to one another without amalgamating. See “Democritus the Physicist.” Taylor talks about the attraction of like to like as in the animal analogy above. C. C. W. Taylor, The Atomists: Leucippus and Democritus (Toronto: University of Toronto Press, 1999).
- [xxi] See J. F. Duvernoy, L'Epicurisme et sa tradition antique (Paris: Bordas, 1990).
- [xxii] Pullman writes that “the elementary corpuscles of matter are indivisible. This property is due . . . to their 'impassivity' (hardness, incompressibility). They are compact and full, without parts, of homogeneous composition, and exhibit no qualitative difference.” The Atom in the History of Human Thought, 32.
- [xxiii] For more on the debate about compounds and molecules, see Pullman, The Atom in the History of Human Thought; and Benjamin Farrington, Greek Science: Its Meaning for Us (Nottingham: Spokesman, 1980).
- [xxiv] For more on the similarities between ancient and modern atomism, see Nicolaides, In the Light of Science, and Giorgio de Santillana, The Origins of Scientific Thought: From Anaximander to Proclus, 600 B.C. to 300 A.D. (Chicago: University of Chicago Press, 1961).
- [xxv] Democritus says that the most easily mobile of shapes is the sphere, and these kinds are both mind and fire. Aristotle De An. A2, 405a II.
- [xxvi] Kirk and Raven suggest that “irregular atoms are in a state of disequilibrium in the void, and so undergo movement.” Presocratic Philosophers, 417.
- [xxvii] Archimedes is said to have given Democritus a great deal of credit for first claiming that the cone is a third part of the cylinder, and the pyramid a third part of the prism, which have the same base and an equal height. Yet Archimedes claims that Democritus accomplished this feat without providing a proof. So Democritus may have learned some things from the Egyptians when he visited there, but he seems to have not reasoned deductively, that is to say, mathematically. Several of Democritus’s works may have demonstrated his mathematical ability, including On a Difference in an Angle; On Contact with the Circle or the Sphere; Geometrica; and Numbers, Irrational Lines and Solids. See Diogenes Laertius 9.47–48. We simply do not possess these works.
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