[In the following excerpt, Hussey summarizes the atomistic theory and explains in what ways it was revolutionary.]

THE ATOMISTS: LEUCIPPUS AND DEMOCRITUS

Of the life of Leucippus we know next to nothing, and there is little trustworthy information about that of Democritus. Both were citizens of Abdera, a small city on the northern shores of the Aegean, which like Elea had been founded by refugees from old Ionia. Democritus was perhaps the younger and, born like Socrates around 470, he lived on well into the fourth century.

Leucippus and Democritus were responsible for the Atomistic theory. Even though they were contemporaries of Socrates, their speculations are traditionally and reasonably grouped under the heading ‘Presocratic’, for the Atomistic theory is the last and greatest original effort in that kind of physical speculation which originated with the Milesians. The respective shares of Leucippus and Democritus in its creation cannot be certainly defined, but it seems likely that the leading ideas of the theory were due to Leucippus, and that Democritus, a more prolific and many-sided but less original thinker, worked out the applications in greater detail. There are a few inessential points on which the opinions of the two are said to have differed, but it is not possible to prove disagreement on any fundamental question.

The starting-point for the Atomists, as for Anaxagoras, was the effort to find a way of reconciling the Eleatic arguments, so far as they were taken to be valid, with the construction of a cosmology that accounted for the perceptible world. But while Anaxagoras tried to create a multiplicity without definite units, the Atomists took very seriously the need for indisputable and absolute units of whatever existed, and therefore collided with Parmenides and Zeno at a different set of points.

Zeno had argued that two things that are can be distinguished into two units only by means of some third thing ‘between’ them, that must itself be; and thence arises an infinite progression. For this reason, Leucippus, according to Aristotle (de Gen. et Corr. 325^a 23-9; Metaphysics 985^b 4-10), took a drastic step: he proposed to introduce ‘that which is not’ (to mē on) as a factor in the explanation of the world, and so to assert (it would seem) that it somehow was. As Aristotle puts it, the proposal of Leucippus is unintelligible because it is so blatantly self-contradictory; but there are good reasons for thinking that Aristotle is mistaken. For another remark, by Democritus, says, not that ‘the non-existent exists just as much as the existent’, but that ‘the “nothing” exists just as much as the “thing”’. Here the words translated by ‘the “nothing”’ are ‘to mēden’, ‘that which is nothing’, and the words translated by ‘the “thing”’ are ‘to den’, where ‘den’ is a nonce-word, formed from ‘mēden’ by the removal of the negative prefix ‘mē-’. The point of this linguistic joke must be that ‘to mēden’ is not to be taken, as Aristotle wrongly takes it, as equivalent to ‘the non-existent’, since what is not to mēden is not to on but to den. The point that Democritus seems to be indicating is that ‘nothingness’ is just as real as any ‘thing’, but differs in not being a ‘thing’, or, as one might say, not being an individual or a primary object of reference, though to say this is to import a higher level of sophistication than was available at the time. How does this distinction help to answer Zeno? If ‘things’ are separated by ‘the nothing’, what separates or distinguishes ‘the nothing’ from any ‘thing’? There are no reports on what the Atomists replied or would have replied to this question, but it seems that consistently with their position they had just one convincing answer. Qualitatively, ‘the nothing’ is distinguished from any ‘thing’ simply by lack of ‘thingness’, by not being an individual with all that that implies. Spatially, there is no further entity required to divide ‘nothing’ from any ‘thing’. For though there must be a boundary, this can perfectly well be part of the ‘thing’. This kind of question about the topology of space was later treated elaborately by Aristotle, but it must be admitted that he gives no hint that the Atomists had contributed anything to the debate. Some indication that Democritus was interested in these questions is given by a puzzle of his preserved by a later writer (dk 68 b 155). The substance of it is this: suppose on a line there can be two points ‘next to’ one another with no intervening point. Then let a right cone be intersected by a plane parallel to its base and passing through the point on its axis which is ‘next above’ the point where the axis meets the base. Will the circle of intersection be smaller than or equal to the base? Clearly either answer leads to absurd results, which shows that two points on a line cannot be ‘next to’ one another in this way. It is interesting that Democritus should be arguing like this since the density of points on a line is crucial for the suggested answer to Zeno. If points on a line were not dense, then one could ask what separated the last point in a ‘thing’ from the first point in ‘the nothing’, and there would be no plausible answer.

Once ‘the nothing’ was admitted, it could perform two functions: it separated ‘things’ from one another, and so made a plurality possible, and it allowed change of place by things, so making possible all change which could be reduced to rearrangements of unit ‘things’. ‘The nothing’ therefore functioned as ‘empty space’, or ‘void’, and the sources usually call it ‘the void’ (to kenon). It was the first time that a well-thought out concept of a purely passive and empty space had been propounded, though it may well be that the mysterious ‘Pythagoreans’, of whose opinions Aristotle tells (see Chapter Four) had hit upon the idea of a unit-separating void before the Atomists did. Though condemned in ancient times by the high authority of Aristotle, and in modern times by many influential thinkers, the notion of a purely passive space has a way of persisting and of making itself indispensable to physics; so its introduction by the Atomists is a noteworthy landmark.

The ‘things’, the units that moved about in, and were separated by, ‘the nothing’, were to be indisputably units; so each of them was uncreated and imperishable, and could not be divided, whence the name atomon, ‘indivisible thing’. Each atom was in fact the heir to many properties of Parmenides’ ‘that which is’. But not to all; most obviously, the atoms were in space, and might be of any shape.

Some confusion has existed ever since the time of Aristotle over the question whether the atoms were ‘mathematically’ or ‘theoretically’ as well as physically indivisible. The problem arises in this way: it is clear from many pieces of evidence that the atoms were thought of as spatially extended and as having various shapes, which could (for instance) cause them to interlock, and as possessing weight in proportion to their volume. They could vary in size, and according to one (late) witness Democritus imposed no upper limit of size on his atoms. Not all of the evidence available is totally reliable; there are some contradictions, and a suspicion that the doxographic tradition has been infected by the misrepresentations of an Epicurean writer. Nevertheless, it is clear that the atoms were spatially extended, three-dimensional objects. Any such object can be said to be ‘theoretically’ divisible, in the sense that one can always distinguish, at least in thought, as Zeno had pointed out, two or more distinct and spatially separate three-dimensional regions within it—that is to say, this is possible if one accepts ordinary ideas about the local topological structure of space, and in particular those assumptions about that structure which are enshrined in Euclidean geometry.

The Atomists, then, were in a dilemma. Either they had to deny that atoms were ‘theoretically’ divisible, which in turn meant either overturning ordinary notions of space or refusing size and shape to atoms; or they had to allow ‘theoretical’ divisibility and thereby to fall foul of the arguments of Zeno, that what was even ‘theoretically’ divisible had ceased to be a true unit and contained infinitely many sub-units. Since it is clear that atoms did have size, and almost certain that no innovations were made in ordinary notions of space by the Atomists, it would seem to follow that atoms must have been ‘theoretically’ divisible. The difficulty is that Aristotle, who would be expected to be the most competent witness, speaks in a way that seems to mean that the atoms were not ‘theoretically’ divisible. Aristotle, however, had his own theory about the relationship between ‘theoretical’ and ‘physical’ divisibility, and it is likely that he did not prevent his private assumptions from colouring the account he gave of the Atomists. The doxographical evidence is self-contradictory and of doubtful value.

It is necessary, therefore, to suppose that the Atomists acknowledged the ‘theoretical’ divisibility of the atoms while denying their physical divisibility. The problems discovered by Zeno about space and change would still, of course, remain, and how the Atomists proposed to deal with them is not known.

The atoms, then, were spatially extended and physically indivisible. They were also unlimited in number, unchanging in shape, size and internal structure, and they moved for ever in a limitless void. The Atomists now had the task of accounting for the observed structure of the world and the contents of personal experience on these economical foundations.

It is natural to begin by asking about the ways in which the atoms moved. The evidence is conflicting and there may have been deliberate distortion by Epicurean sources. Aristotle, so far as he goes, is the most reliable witness. His testimony (dk 68 a 37) seems to show that the atoms had no inherent tendency to move, and that there was not (as there was in Epicurus' universe) an absolute ‘upwards’ or ‘downwards’—the void was symmetrical in every respect. Accordingly, atoms moved only because impelled by the impact of other atoms. They were said to have weight in proportion to their size, and weight could be explained in terms of resistance to impact. Whether an atom, if undisturbed, was thought to continue in its state of motion indefinitely or gradually to come to rest, is not clear.

Within a kosmos other dynamical principles were thought to apply, of which the justification in terms of collisions of atoms is not obvious. Heavier atoms were more drawn towards the centre than light atoms, and there was also a tendency for atoms of like size and shape to congregate together. Democritus appealed (fr. 164), in support of this principle, to the analogy provided by the arrangements of pebbles of various configurations on a sea-shore. It is likely that this kind of analogy was the most that could be offered by the Atomists to make plausible some of the steps postulated in the creation of kosmoi from atoms and void. There is no sign that they made any real advance towards a systematic treatment of dynamics, much less a mathematical one.

For this reason, the cosmological devices used by the Atomists to explain the creation and working of kosmoi do not differ much from those well-established in the Presocratic tradition. They give the impression of being artificially pasted on to the new metaphysical foundations. The formation of a kosmos was roughly as follows. A chance and sudden congregation of atoms of the same order of size in a relatively crowded space caused a rotatory movement to occur. This may have been supported by analogies in observed facts: vortices are observed to form in water when it runs out of a large vessel through a narrow passage. What was further required, then, was a way of shutting atoms in from the rest of the universe. This was done by supposing the formation by random movements of a ‘fence’ of interlocked atoms. In favour of this step, it can at least be said that there would be a kind of ‘natural selection’ at work; atoms once interlocked would stay interlocked unless subject to exceptionally strong and well-directed blows from outside. The principle of ‘like to like’ would guarantee that ‘fences’, once in existence, would tend to extend themselves, and that the atoms shut into any kosmos were all of more or the less the same size, a point important for the theory of perception.

Once the rotation had begun, the cosmogony proceeded on familiar lines. By a process of segration by weight, the four elements—which were explained by four particularly natural and stable kinds of ‘molecule’—are created and sorted into the usual arrangement, and function thereafter in traditional fashion. Traditional also was the possibility of the existence of an unlimited number of kosmoi simultaneously in different parts of the void; possibly new was the idea that the collapse of a kosmos, which occurred eventually upon excessive pressure from outside, left ‘ruins’ which often furnished material for a new kosmos.

In one respect the system of the Atomists was revolutionary. All their predecessors had asserted, either explicitly or implicitly, that the intelligibility and rationality of the universe depended ultimately upon its subjection to a divine power which in some sense was conscious and intelligent. The earliest thinkers had no doubt said rather little about the nature and purposes of the deity. Heraclitus and Anaxagoras had said more. Even in Parmenides, ‘that which is’ is a timeless unified thought; and the same is true, with some qualification, for the ‘Sphere of Love’ in Empedocles. It is true that the Sphere comes to be only intermittently; yet because ‘everything has thought and a share of intelligence’, it is always potentially present in the scattered thoughts of the various particles of matter. The Atomists went counter to the whole tradition by removing everything ‘mental’ from the list of ultimate constituents, a noteworthy act which must be examined more closely.

The reduction of everything to atoms and ‘void’ did not by itself entail the denial of an ultimate ‘mental’ constituent, for it would have been possible to suppose that each atom was a mind—again, a suggestion of Leibniz's monads. But such minds would have had to be timeless, since the internal structure of atoms could not be allowed to change in time; and therefore would not have been able to play any part, as minds, in the determination of events in the universe. The inner logic of the Atomist theory, therefore, led straight to the conclusion that consciousness and perception, as they are known in ordinary experiences, are epiphenomena, determined and accounted for completely by the states and rearrangements of components not themselves capable of consciousness or perception. (It is for this reason that Democritus has to say that perceptible qualities exist ‘by courtesy’ only (see Chapter Six).) It followed that the whole history of the universe was determined, if at all, by a ‘meaningless’ necessity inherent in the laws governing the collision and rebound of atoms, a force which was devoid of any inherent tendency to the better, or of any regard for the wishes and requirements of such accidental by-products as conscious beings. Democritus conceded, indeed, that ‘gods’ might exist; but by ‘gods’ he meant only conscious beings which were created and perishable, though noticeably superior to human beings in size, beauty, strength, intelligence and moral qualities.

The last and greatest representative of the Milesian tradition, therefore, was the first explicit materialist. It would be wrong to conclude from this that materialism had been ‘in’ the tradition all along. Anaxagoras' system represents another equally possible line of development. Neither of these lines was to be taken any further, however, for a long time. The sophistic age had undermined the whole tradition of cosmology, and when in the fourth century cosmological ideas began again to be discussed, the dominant minds, shaped in the fire of philosophical debate, gave them a different turn and subordinated them to other considerations.

Works Cited

The Atomists: C. Bailey, The Greek Atomists and Epicurus (Oxford, 1928); V. E. Alfieri, Atomos Idea (Florence, 1953).