SOURCE: Cyril Bailey, "Atoms and Space," in The Greek Atomists and Epicurus, Oxford at the Clarendon Press, 1928, pp. 274-99.

[Bailey's work on Epicurus has often been cited by fellow scholars as fundamental to the field—particularly his 1926 translation of the philosopher's works. The following chapter from his well-respected The Greek Atomists and Epicurus concentrates on Epicurus's concept of the atom. Bailey elucidates the originality of Epicurus's system, countering claims by earlier critics that he simply lifted Democritus 's thought.]

In passing from Leucippus to Democritus the atomic theory … [grows] in consistency and harmony: with Epicurus the change is even more marked. It is now felt to be a system of interrelated parts: the connexion of one proposition with another has been thought out and the various conceptions involved in Atomism ordered and organized on fundamental principles. This impression is due in some degree, no doubt, to the form in which our information has reached us: the theories of the earlier Atomists have to be pieced together from scattered fragments, the accounts of the doxographers and the detached criticisms of later philosophers; for Epicurus we have the compressed and rather confused, though far better ordered, account in his own letter to Herodotus, and the continuous commentary of the poem of Lucretius. But there is much more than this: Epicurus had the master mind, which would not rest content with a mere 'adoption' of Democritus' Atomism, as hasty critics have been too ready to suppose, but insisted on development, modification, and improvement, and above all on the correlation of the whole system under the central principle of the infallibility of sense-perception. No account can do justice to Epicurus' physics which does not attempt to grasp it as a whole, to emphasize the interdependence of its parts and the constant control of the principles of the Canonice. It is from this point of view that I shall attempt in the following pages to describe it.

Epicurus makes his start, like Democritus, from the principle of causality and permanence: 'nothing is created out of the non-existent', but unlike his predecessor he does not leave the principle as an ex cathedra assumption, but supports it by argument. Here we are dealing with perceptible and imperceptible alike; the problem is universal and cannot be solved directly by the senses: we must ask whether the senses give us any 'indication' to support the principle or whether they in any way contradict it. Such an 'indication' Epicurus finds in the ordered generation of things in the perceptible world: 'nothing is created out of the nonexistent; for, if it were, everything would be created out of everything with no need of seeds'. Lucretius follows the same argument and brings it out with a wealth of illustration. The proof is tersely put, but is clearly on the lines demanded by the Canon. Critics have proclaimed it unsatisfactory on the ground that Epicurus, to put it in modern phraseology, is arguing against 'spontaneous generation' by denying 'sporadic creation'. The truth is surely that he proves more than he need: all it was necessary for him to show was that every created thing was sprung from an antecedent something, was created of substance which already existed. Epicurus has gone beyond this and pointed out that not merely is there always pre-existing substance, but in each case substance in a particular form, a 'seed', which can only produce one particular thing and nothing else. Suppose for a moment that the opposite were true, that things could suddenly come into existence without being formed from pre-existing substance? What is the evidence of phenomena? That things require definite 'seeds' for their creation. The evidence of sensation interposes its veto…, and the supposition is untenable: it must be true that 'nothing is created out of the non-existent'. There is no confusion in the argument: it is, if anything, gratuitously specific. It may be noticed that it has a double application: (1) the sum total of things is never increased by new additions, (2) every material thing has a material cause.

The second principle—the complement of the first—is next stated and proved. 'If that which disappears were destroyed into the non-existent, all things would have perished, since that into which they were dissolved would not exist.' The statement here is less lucid, principle and proof being run into one: Lucretius puts the principle more clearly: 'nature breaks up each thing again into its own first-bodies, nor does she destroy ought into nothing', nothing, in other words, ceases entirely to exist: as nothing is added to the sum of things, so nothing is entirely taken from it. The proof again is from phenomena: if things were utterly destroyed, and by the first principle nothing new could be added, the sum total of the universe must gradually be diminished, and ultimately would pass out of existence altogether. But this is not the evidence of the senses: we do indeed see things perish, cease, that is, to be what they were before, but this perishing means only the assumption of another form. Change we see all around us, but not the absolute cessation of existence. Lucretius is fond of using this principle as an axiom in the converse form, 'whatever changes and departs from its own limits is straightway the death of that which was before'. Once again there is a double implication in the principle: (1) the sum of matter is never decreased by absolute loss—this is the modern idea of the 'permanence of matter', (2) no individual thing is utterly destroyed, but only resolved into its component atoms.

There follows a third principle: 'the sum of things always was such as it is now and always will be the same'. This is in part a direct deduction from the other two: if nothing is added, the universe cannot increase; if nothing perishes, it cannot decrease. But Epicurus adds other arguments: 'there is nothing into which it changes: for outside the universe there is nothing which could come into it and bring about the change'. This is the reference to sense-experience. Among phenomena two conditions are always required for change, (1) something for the original 'thing' to change into, something which it may become, (2) some external agent to effect the change—by means, as Epicurus held, of a blow. But by 'mental apprehension', by 'looking at' the concept we have already formed of the universe, we can see that neither of these conditions can in its case be fulfilled: the universe cannot change into something else, for there is nothing else which it could become, nor is there anything external to it, which could effect the change. The argument is put in a more elaborate form by Lucretius in a passage probably based on the Greater Epitome. He seems to imply three possibilities by which the universe might change, (1) if there were anything outside it into which any part of it might escape, (2) if there were anywhere from which a new force might come into the universe and alter it, (3) if change could be caused by internal-rearrangement. Epicurus in the letter to Herodotus seems to have the first two of these causes most prominently in his mind. The third might at first sight seem to be at work in the universe in the constant dissolution and recomposition of the atomic compounds, but Epicurus' answer would lie in his conception of equilibrium…; the atoms have long ago entered into all possible combinations and cannot create anything new which could alter the sum total. The universe then cannot change for there is nothing for it to change into and no external or internal force to change it. It is birthless, deathless, and immutable.

In these three primary principles themselves there is nothing new: they were practically implied in the Parmenidean conception, they were enunciated by Empedocles and Anaxagoras and explicitly stated by Democritus. But Epicurus has done more than 'adopt' them: he has adduced proof for them, and in doing so has linked them directly to the base principles of his whole system. The proofs from phenomena and the trust in sensation which they involve are the new and characteristic addition.

In what form then does this eternal universe exist? 'In the form of body (or matter) and space (or, as Epicurus here says, "place").' That body exists is testified by universal sensation: all men through all their senses are made conscious of matter. That space exists is shown by the existence and motion of matter: 'if there were not that which we term void and place and intangible existence … bodies would have nowhere to exist and nothing through which to move, as they are seen to move.'

At this point certain difficulties arise, though rather from a modern than an ancient point of view. In the first place it is true that the sensation of matter is universal, but that has not hindered philosophers from calling in question the objective reality of the external world, or asking what meaning, if any, can be attached to the statement of its existence as apart from a percipient intelligence. But, if we are inclined to raise this objection, we must bear in mind that it is essentially a modern difficulty, unknown to the ancient world, and secondly that Epicurus spoke here, as always, as the average man of common sense. To him, as to the modern man of science, the existence of matter is sufficiently testified and its properties sufficiently made known by the sense. Once again he is content to take as his starting-point what 'common sense' would say, without any attempt to get behind it.

The difficulty connected with the syllogistic argument by which Epicurus inferred space from the fact of motion is more serious, for it was a problem which antiquity had very fully discussed. Parmenides and the Eleatics had, as has been seen, in order to preserve the unity of the world, denied both space and motion: the world was a single corporeal plenum, compact 'body' without space, and the appearance of motion was merely a delusion of the senses. As against this theory Epicurus was justified, indeed impelled, by his own first principles to reassert the evidence of the senses: we perceive motion, therefore motion is a reality. But is it necessary to infer from this the existence of void? Some modern scientists, holding the hypothesis of ether, would answer in the negative, and a very similar solution was put forward by Epicurus' contemporaries, the Stoics. They, under the stress of their desire to assert the divine unity of the world, maintained that the whole world was but one primary substance, which however was elastic and capable of existing in various degrees of tension; under the greatest strain it appeared as fire, with less tension as air, with less again as water, and with least of all as earth. Motion, on this view, then is but an interchange of parts, much as one might move about the various portions of a piece of putty without causing a break, or as one sees changes of position in a kaleidoscope. With this possibility Epicurus does not concern himself, though it must have been current at the time of the writing of his letter, but that it did become a real question to the later Epicureans, we may infer from the fact that Lucretius consents to deal with it. His main answer is, in effect, simply the restatement of the common-sense view: there must be empty space in order that there may be a beginning of motion; a thing cannot begin to move unless there is 'room' for it to move into. His second argument is an illustration from experience—if you clash two broad bodies, e.g. boards, together and then quickly draw them apart, the air rushes round to fill up the space between them: but there must be an interval of time in which that space is empty or 'void'. That Epicurus' own answer would have been on these lines may safely be inferred from the fact that in the controversial passages about the Epicurean view of space the examples are drawn from such illustrations as the interior of a cask or a vessel—not of course that Epicurus would have denied that they were filled with air; but would have argued rather that they afforded an 'indication' of that real empty space which lay between atom and atom. More cogent is Lucretius' third argument that the 'elasticity' of the primary substance, its power to condense and rarify, must itself imply the existence of void. The Stoic view, Epicurus would have maintained, is not that immediately suggested by sensation: it is an 'addition of the mind' which the 'clear facts' of sensation refute. Once again 'common sense' is good enough. Matter then and space are the sole independent existences: 'and besides these two nothing can be thought of … such as could be grasped as whole existences and not spoken of as the accidents or properties of such existences'.

We must ask then next how are we to conceive these two existences, 'body' and space? 'Among bodies', Epicurus proceeds, 'some are compounds … and others those of which compounds are formed'. This is little more than a verbal explanation: the term 'body' is in itself ambiguous, for it may be applied alike to the 'bodies' or 'things' which we perceive by sensation or to the ultimate bodies of which they are composed. But the confusion is only momentary and does not produce any serious difficulty either in Epicurus or in Lucretius, who follows him in making the distinction: for as soon as the character of these ultimate bodies has been determined, there will be other descriptive names to apply to them in order to distinguish them from the bodies of sensation. What then are they? 'These latter', says Epicurus, 'are indivisible … and unalterable … (if, that is, all things are not to be destroyed into the non-existent, but something permanent … is to remain behind at the dissolution of compounds): they are completely solid … in nature and can by no means be dissolved in any part. So it must needs be that the first-beginnings are indivisible corporeal existences….' Here then is the first statement of the atomic position. The argument by which it is supported is put very briefly in the parenthesis and requires examination. It rests on the Atomic contention that there must be a limit to the divisibility of matter, but this is put both negatively and positively. In the first place Epicurus appears to maintain that, unless there were such a limit, things would pass out of existence altogether, which would be a contradiction of the principle that 'nothing is destroyed into the nonexistent'. The idea is that if it were possible to go on dividing and dividing you would ultimately find that matter had disappeared and you had reached 'nothing'. Strictly this is of course a fallacy: it is theoretically possible, apart from such a physical barrier as Epicurus supposes, to go on dividing and subdividing to infinity and yet to reach only smaller and smaller particles of matter. And it is improbable that Epicurus would seriously have maintained the point: it is rather a popular way of putting what he meant. For the stress of the argument lies on the other, the positive, side: 'something permanent (or "strong") must remain'. Here the argument is independent of the fallacy of ultimate resolution into nothing. For if infinite division were possible, all particles of matter however small would be compound bodies, for they could always be separated into smaller particles. But the compound body on Epicurus' view is always a mixture of matter and void, and the presence of void is a source of weakness: for it means the possibility of destruction by external blows. If, then, however low one may go in the scale of minuteness, nothing indestructible is ever reached, matter as we know it in external things could not exist; for there could be no solid and permanent substratum—'nothing strong'—to hold it together and to resist the shocks of collision.

The argument recurs in two other contexts in the letter, which will throw some light upon it. In the first Epicurus is arguing that the atoms have none of the 'secondary qualities', which we associate with things: 'for every quality changes; but the atoms do not change at all, since there must needs be something which remains solid and indissoluble at the dissolution of compounds, which can cause changes'. Just then as there must be indestrucible particles to explain the creation and the destruction of phenomena, so to explain their changes, there must be something unchanging: and this can be nothing else than the atom, the hard body without the admixture of void, which alone can resist the attacks of external blows. The second passage is more directly connected with our argument, for Epicurus is there proving that the atoms must have a definite size, they cannot be 'infinitely small'. 'We must', he says, 'do away with division into smaller and smaller parts to infinity in order that we may not make all things weak and so in the composition of aggregate bodies be compelled to crush and squander the things that exist into the non-existent.' Again the idea is the same: if there is no limit to the smallness of particles, there is no permanent strength in the substratum; things become weak and can be whittled away past the limits of material existence. A more striking and interesting form of the same proof occurs in a difficult passage of Lucretius, which has been clearly explained by Giussani. If there were no minimum, the poet maintains, but the infinite division of matter were possible, then, because the process of dissolution is quicker than that of creation, all things, i.e. perceptible things, must long ago have ceased to exist. Let us suppose, for instance, that the process of dissolution is twice as quick as that of creation, and that it takes ten years to create a living creature and bring it to its maturity: then in five years it can be dissolved into particles of the size from which it started, and in ten, if there is no limit to division, the particles will be as much smaller again. If out of these particles a similar creature is now to be formed, it will require twenty years, and on the next occasion forty and so on. In all the ages which have passed since the creation of the world, the powers of destruction would have so got the upper hand that by now no perceptible things would be left. Again, division cannot go on to infinity: there must be some permanent minimum 'with strength' to resist the influences of destruction. The passage is unusually interesting and throws considerable light on the general Epicurean argument.

This, as I understand it, is the contention of Epicurus for the existence of indivisible particles as the permanent substratum of matter: not that, without them, matter would cease altogether to exist—for however minutely divided, it must still continue to be matter—but that without a limit to division, it is impossible to arrive at anything completely solid, and so sufficiently strong to resist the attacks of destruction, in other words, the blows of other particles. The result would be continuous destruction and no formation: in this sense 'all things would be dissolved into the non-existent', for there would be no power to keep existing things as they were, or to create similar new ones.

The atom then is a necessary postulate for the existence of the world as we know it. How is it to be conceived? Certain characteristics follow immediately from its definition as an 'indivisible existence'. It must be completely solid, completely compact, and entirely without void: it is, that is to say, pure body without any intervals. From this it immediately follows that it is 'unchangeable': for change is due to the alteration of the position of parts and that can only be brought about in compound bodies, in which there is an admixture of void. What then are the properties of this indissoluble, unalterable body? They are according to Epicurus, three in number, size, shape, and weight.

The question of the size of the atom was already, as we have seen, a problem with a history in the Atomic theory. Leucippus wishing to insist on their extreme minuteness had stated that they were 'without parts' … : Democritus, seeing that it might then also be said that they were without magnitude, i.e. without material existence, had denied this and gone so far as to maintain that some of them were even 'very large'. Epicurus dealt with the question in a more systematic and philosophic manner.

'We must not suppose', he says, 'that every size exists among the atoms, in order that the evidence of phenomena may not contradict us, but we must suppose that there are some variations of size…. The existence of atoms of every size is not required to explain the differences of qualities in things, and at the same time some atoms would be bound to come within our ken and be visible: but this is never seen to be the case, nor is it possible to imagine how an atom could become visible.'

Here then is the answer to Democritus: sense-perception is against his theory: there must be an upward limit of magnitude, otherwise atoms could be seen. What of the downward limit? It follows of course from the very definition of an atom, as a limit of division, that it cannot be of infinite smallness, but Epicurus proceeds to treat the question in a subtle and very characteristic argument. This argument must be studied in the original and compared with the rather more lucid, but less far-reaching version of Lucretius. I shall here attempt to give the gist of it in as simple a form as possible. Epicurus appeals as usual to the facts of sensation: and the appeal involves the expression of strong controversial views with regard to area and extension. 'Not merely can we not admit infinite division, but we cannot suppose an 'infinite progression from less to less….' His contention here is directed primarily against the geometrical view of surface or area, which held that surface was perfectly continuous, and that it was possible, in considering for instance a line to pass continually to smaller and smaller sections to infinity: the idea is clearly expressed in the wellknown story of Achilles and the tortoise. As against this theory Epicurus upholds the view of common sense based upon the experience of sensation. If we take any object and try by looking at it to analyse its surface, we find that we may indeed proceed from smaller to smaller parts for a long distance: but ultimately we come to a point—not a geometrical but a material point—which is the smallest visible thing. If we attempted to see any smaller part, we should pass out of the range of the perceptible altogether. Indeed, this point itself is only visible as a part of a larger whole: it is 'distinguishable, but not perceptible by itself …, and if we try to look at its 'right-hand or left-hand part', we shall find that our eye has in reality wandered to the next similar point. We have then in this point reached something from which further progression to anything smaller is impossible …: in other words, surface is not continuous and does not permit of infinite progression, but is a series of discrete minima. Further, these 'least parts' (minimae partes) afford a standard of measure: as we pass from one of them to another, we can—or could, if we had patience—go on till we reached the last point, then count them up and so from their number reckon the size of the object. This, Epicurus holds, is the only view of surface which is warranted by the 'clear vision of perception', and the opposite view is due to the contamination of the senseperception by the false addition of opinion. Yet, if we pass from the world of sensation to the world of thought, we know that even these 'points', the 'least parts' for perception, are themselves aggregates… of infinitely smaller particles: in thought division may still be carried on. But in the world of thought the analogy still holds: ultimately we come to the 'least possible'…, the minima of extension. They similarly are not separable: they can only exist as parts of the atom. They never come together to form it, they are not parted in it by void, they could themselves have no 'powers', but they may in thought be distinguished. They too are 'boundary marks'… and by their number the size of the atom which they compose may in thought be calculated. The world of thought corresponds exactly… to the world of sense: in the world of sense we have the visible body composed of 'distinguishable' points, in the world of thought the atom composed of 'inseparable' parts. This imaginative analogy has then given us the answer to Leucippus and his critics and to Democritus: the atoms are not 'without parts'… in the sense that they have magnitude and parts 'distinguishable' by thought; they are on the other hand without parts in the sense that they are not formed of parts which could be separated. In other words the atom has size, i.e. measurable extension, but it remains an 'indivisible existence'. The size of the atom then is neither 'very great' nor infinitely small: it is extremely minute but with a lower as well as an upper limit.

Furthermore there are some variations in the sizes of atoms: 'for if this be the case, we can give a better account of what occurs in our feelings and sensations'. As will be seen later, difference in the size of the component atoms is a large factor in producing difference of qualities in things. That the atoms will have shape is manifest from the fact that they have size, but now that we have the theory of the least parts, we can go farther: for it is obvious that the shape of the atom varies according to the number and disposition of the 'least parts'. An ingenious critic [Brieger, Fahrbuch Fleck., 1875] has worked out some of these differences. If, for instance, we suppose the minimae partes to be cubes of exactly the same size, then, if an atom contains two only, it can have but one shape…; if it contains three, two shapes…; if four, five shapes on one plane,… and two more in two planes, according as one of the parts in the last figure be placed on top either of one of its neighbours, or of that at the opposite corner: with five or six parts the possibilities are very largely increased. Are we to suppose then that this process of variation may be infinitely continued, or is there a limit to the possible varieties? Epicurus' answer is again carefully thought out: the number of different atomic shapes is indefinitely great…, but not infinite. It must be 'inconceivably great': 'for it is not possible that such great varieties of things should arise from the same (atomic) shapes, if they are limited in number'. Phenomena, as usual, give the 'indication': the varieties of compound bodies are very largely due to the difference of shape in the component atoms, and it would not be possible to account for these varieties, if we conceived of any comparatively small number of atomic shapes. Why then is there a limit to the number? Epicurus does not himself give us any reason, but Lucretius suggests two proofs, so characteristically Epicurean that they must represent the regular tradition of the school. The first is an argument suggested by 'mental apprehension': variety of shape, as we have seen, can only be obtained by supposing an increase in the number of least parts: or, in other words, an increase of size. If this process were infinitely continued, we should again arrive at atoms so large as to be perceptible to the senses: we should be guilty of the fallacy of Democritus. The second is based on the 'indications' of phenomena: varieties of quality in things are caused by varieties of atomic shape: yet even the varieties of things are limited; there is an extreme of beauty and ugliness, just as there is of hot and cold. But if there were infinite varieties of atomic shape, there could be no such limitation of qualities: all that we find most beautiful and most hideous would long ago have been surpassed. We must conclude then that these varieties of shape in the atoms are indefinitely great, yet not infinite. On the other hand the number of atoms of each particular shape is infinite, for if it were not so (the reason is again given by Lucretius), the sum total of atoms would itself be limited—which is not the case. The ideas connected with the shape of the atoms are not so penetrating as those relating to their size, but are particularly well thought out and form an interesting example of the application of the principles of the Canon.

Thirdly, the atoms have weight. The question whether weight is a property of the atoms has, as has already been seen, a very perplexing history in the Atomic theory. Leucippus makes no mention of weight and it may be taken for certain that he did not assign weight to the atoms. Over the attitude of Democritus controversy still rages, but we have seen reason to think that he did not regard it as an absolute property of the atoms, but only as a derivative from their size which comes into action in the cosmic 'whirl'. We might therefore naturally suppose that the idea was introduced into the system by Epicurus himself in order to account for the 'downward' motion of the atoms in space. This conclusion is however made improbable by a passage in Lucretius in which, evidently following Epicurus, he argues against the idea that variation in weight was the cause which enabled the atoms to meet in the downward fall, on the ground that in the void, which offers no resistance, all bodies, whatever their weight, must fall at an equal 'atomic' pace. It is true that Lucretius puts this idea as a supposition, but it is hard to believe that he is not arguing against some definite suggestion on these lines, and if so, the idea of weight as the absolute property of the atoms and the cause of downward motion must have been introduced by some one into the atomic theory before Epicurus—possibly by Nausiphanes. In view of the history of the discussion it is certainly strange that we find no argument on the question in Epicurus. He is content with the mere mention of weight together with size and shape as one of the properties of the atoms. Lucretius assumes it all through, and it is only in a passage of the Placita that we find any kind of proof recorded, a proof, as might be expected, from the fact of motion: 'it must needs be, says Epicurus, that the bodies (i.e. the atoms) are moved by the blow of their weight: for otherwise they will not move'. That this was Epicurus' own argument is clear, apart from the testimony of Plutarch, from the passages in which he speaks of the 'natural downward motion of the atoms owing to their weight'. There are reasons too which may be suggested for the absence of explicit argument on the subject. On the one hand the weight of the atoms is an immediate deduction from their size: solid matter, having size, must also have weight: demonstration is hardly needed as soon as the idea of 'weight' had become explicit. On the other hand—a more subtle consideration—though differences of size and shape in the atoms were productive of important results, difference of weight is not effective. For to the atoms, always moving in the void at an equal rate, difference of weight does not produce difference of motion, and in compound bodies where difference of weight first begins to tell, it is not the weight of individual atoms that matters, but the weight of the aggregate of matter compared with the aggregate of void. The atoms then have weight, and since they are solid matter with no admixture of void, their weight varies directly with their size: their weight is moreover the cause of their natural 'downward' motion, but difference of weight has no effect so far as rate of motion is concerned.

Size, shape, and weight are thus proved to be properties of the atoms, but beyond these they have no other qualities. Here it might seem that the evidence of sensation was against such a conclusion: all things that we can perceive have other qualities, colour, smell, sound, cold, heat, and so on: we might reasonably conclude that the atoms too were similarly endowed, that white things were made of white atoms, black of black, and so forth. But this would be a false assumption. For all qualities are susceptible of change: the wave which was green one moment becomes white the next; the colours on the peacock's tail are always shifting, as the light strikes it: but the atoms cannot change. They are, as has been proved, unalterable and we must not attribute to them qualities which imply alteration. How then can we account on an atomic basis for the changing qualities of things? The unchangeable atoms are themselves the cause of change: 'there must be something which remains solid and indissoluble… which can cause changes: not changes into the nonexistent or from the non-existent, but changes effected by the shifting of position of some particles, and by the addition or departure of others'. All the qualities of things are thus due to their atomic conformation: their original qualities are given them by the size and shape and arrangement of the atoms which compose them, the change in their qualities is caused by the mutual change of position and order among the atoms, and in some cases because some of the original atoms break off or new ones are added. Nor is this difficult to conceive, when we remember that the atoms inside compound bodies are continually in motion, ever clashing against one another and starting off in new directions, so that in every perceptible moment of time their position and arrangement is altered: the marvel is rather on Epicurus' view that the qualities of things should remain as constant as they do. Here we are once more on the lines of atomic tradition: the differences of quality are due to the three 'differences' of the atoms originally postulated by Leucippus, the differences of shape, position, and arrangement. Epicurus of course is not contented with mere tradition, but as usual appeals to phenomena: even in things perceptible which change their shape by a mutual rearrangement of their parts, we see that other qualities are altered, but the shape of the parts remains the same. So then in all changes; the atoms with their unchangeable shapes cause the differences and alterations in the qualities of things. The idea is greatly elaborated by Lucretius, who adduces a series of proofs to show that the atoms are without colour and then conscientiously applies the same notion to the qualities perceptible by the other senses. We need not consider his arguments in detail, but we must here notice a very important addition, which is not suggested in Epicurus' more summary treatment. Not merely are the atoms without qualities, but they are also without sensation: here again analogy might lead us astray and we might suppose that those atoms which compose our 'soul' are themselves endowed with sensation. But this is not the case: all atoms are completely without sensation and sensation and consciousness in us are due merely to particular movements on the part of a particular combination of atoms: as arrangement results in qualities, so movement may produce sensation. It is manifest that this position will prove of great importance, when we come to consider the Epicurean psychology.

This denial of qualities to the atoms by Epicurus was the subject of considerable criticism in antiquity. In the first place the critics asked how could atoms without qualities merely by 'coming together' create things with qualities. In the second they argued that Epicurus' theory was in effect a denial of the reality of quality: if quality did not belong to the atoms—the only real material existences—it was in things a delusion: Democritus was right when he said that qualities existed only in appearance… : the senses were mistaken in attributing them to things, and were not therefore infallible. Both criticisms are discerning and important, but both rest on a failure to appreciate Epicurus' true view of the nature of a compound body. If a compound body were a mere aggregate of atoms—a collection of atoms, as it were, arbitrarily separated off from the hosts of surrounding atoms (much as the old astronomers separated off a 'constellation' from the surrounding stars), then these criticisms would hold true: the atoms could acquire no new powers in the compound body and must remain as they ever were. But this was by no means Epicurus' view: the compound body to him was not a mere aggregate, but a new entity, an 'organism' almost…, or, as Lucretius calls it again and again, a concilium. In the organism of the whole the atoms did collectively acquire new properties and characteristics which as detached individuals they could never possess: no number of independent atoms could have colour, but unite them in the new entity of the whole, and it acquired colour. The idea is important and fruitful and we shall meet it again in the Epicurean kinetics and psychology. Moreover this whole is a reality, not a delusion: its reality for sense is as great as the reality of the atoms for thought: it is directly grasped by sense-perception, as the atoms are by 'mental apprehension'. And this carries with it the reality of its qualities: indeed, it is by the perception of its qualities that a thing's existence is known. To argue then that no quality which is not possessed by the individual atoms is 'real' in the compound, is to misunderstand fundamentally the Epicurean position. There are two worlds, or rather two departments of the same world, the one known by sense, the other by 'mental apprehension'; both are equally real, and in passing from the one to the other, matter acquires new qualities. The notion is in reality, as we have seen, underlying the Canonice, and to lose sight of it in the physical theory is to misconstrue Epicurus all through.

We must turn now to Epicurus' conception of space, for, although from the nature of the case it is not so complicated as that of the atoms, it involves certain difficulties which cannot be disguised. The syllogistic argument by which he inferred the existence of space from the fact of motion has been discussed already: we must now inquire more closely what it was that he meant by space. The mathematical conception of space as extension may be put out of court: it is impossible that Epicurus should have meant that for several reasons; (1) it would have been inconsistent with his whole attitude to the mathematical point of view, (2) it would have clashed with his theory of area as a succession of discrete minima, (3) it is sufficiently contradicted by the many synonyms which he employs to describe it, and particularly with its definition as 'intangible existence'. Space is an 'existence' just as much as body, it is not mere measurement or extension: it is a 'thing', but a thing whose sole property is that it cannot touch or be touched, it can offer no sort of resistance to body. Here then is his answer to the difficulties of the earlier Atomists: he does not trouble himself with their subtle discussions as to whether space is 'nothing'…, or 'nonexistent'…; he simply affirms, with the same meaning but much closer precision, that it is an 'in-tangible existence'. The conception is not abstract but concrete: it is derived from that of body by a negation of its properties.

Yet considerable difficulty remains. Are we to conceive space as absolutely continuous and universal, coextensive with the universe itself, or as discrete and consisting only of the intervals between bodies? In other words, is there space in a place which is occupied by body, or is there not? does he mean 'place' or 'empty space'? The question is a very difficult one to decide and there seem many indications on either side. If we consider the synonyms which Epicurus uses, we see that two of them, 'place'… and 'room',… are in favour of the former view, that by space he means occupied as well as empty space—a continuous whole: the same conclusion may be drawn from the definition of space as that 'in which things exist and through which they move', and possibly (though I think it need not be interpreted in this sense) the contention that space is infinite in extent: for if there is no space, where bodies are, then there is a limit to space. On the other side, we have the fourth synonym, 'the empty'…, which clearly suggests only unoccupied space, and the frequent reference to the void in compound bodies as 'intervals'… between the component atoms. Most of the ancient commentators too seem to interpret Epicurus in this sense, and among their comments is the express statement of Simplicius that the Epicureans regarded space as 'the interval between the boundaries of that which surrounds it'. A consideration of the main passages in Epicurus and Lucretius, where space is mentioned, seems to show that they both oscillate between the two conceptions. Are we then to leave this difficulty—so fundamental in the system—as a point which Epicurus never really thought out? I believe that it arises largely from the fact that we are not easily able to approach Epicurus with a sufficiently concrete conception. Giussani, in one of the most interesting of his Essays, has very largely cleared the matter up. He points out that we must think of Epicurus' notion primarily in relation to the ideas which he was combatting. The Parmenideans, for instance, would readily admit the conception of space in the sense of 'extension', but they would maintain that there is matter everywhere, there is no such thing as empty space. In strong opposition to this view Epicurus wished to maintain not merely that there was empty space between portions of matter, but that empty space was a necessary presupposition to that of matter: there must be empty space in order that things may exist at all; otherwise there would be 'nowhere for them to be and nothing through which they might move'. 'Void' then is the fundamental notion always in the mind of Epicurus and his disciple, and therefore he is most often apt to think of it as completely empty space, or the intervals between matter. Yet even where matter is present, he can still speak of 'place' or 'room', and think not of something which has ceased to be void, but rather of potential void: it is indeed empty space which happens temporarily to be occupied. Space then does mean to Epicurus primarily 'empty space', but he is not inconsistent when at times he includes in it the 'place' which matter is for the moment filling. The two ideas are significantly combined in another passage of Simplicius, where he says that the Atomists say that 'empty space is infinite, and exceeds bodies in infinity (i.e. of extension), and for this reason can admit different things in its different parts'. Here the conception works outwards, as it were, from the notion of 'interval' to that of omnipresence. But the unity of the two conceptions is made very much more intelligible, if we remember that in Epicurus' idea matter is in perpetual motion: the atoms even in compound bodies are never still. Consequently the occupation of empty space by matter is never more than instantaneous: for no two consecutive instants is the same space occupied by the same atom. The idea then of occupied space becomes almost an abstraction: it is an attempt to take a static view of what is always kinetic. Our difficulty thus arises in great part from the fact of our approaching the question with the presupposition of a world of (mostly) stationary objects: if we can put ourselves back in thought to Epicurus' world of evermoving atoms, the contradiction between the two views of space very largely disappears. Space thus means 'void', any portion of which may momentarily, but not more, be occupied by an atom.

We come back then to the original conception of the Universe as atoms moving in space and we must ask finally whether this universe and its two constituents are or are not infinite. Epicurus gives the traditional answer of the atomic school, but once again supports it with argument. 'The universe is boundless. For that which is bounded has an extreme point: and the extreme point is seen against something else. So that as it has no extreme point, it has no limit; and as it has no limit it must be boundless and not bounded.' Lucretius puts the proof rather more lucidly: 'it is seen that nothing can have an extreme point, unless there is something beyond to bound it, so that there is seen to be a spot farther than which the nature of our sense cannot follow it. As it is, since we must admit that there is nothing outside the whole sum, it has not an extreme point, it lacks therefore bound and limit.' The appeal is then once again to phenomena: the condition of limitation there, the existence of something else beyond, is one which cannot be applied to our mental conception of the universe. Lucretius brings out his point by the famous illustration of the hurling of the spear. 'Go, if you can, he challenges the doubter, to the extreme limit of the universe and hurl a spear: either it will be stopped or it will go on: if it is stopped, there will be matter beyond, if it goes on there will be empty space: in either case you did not start from the end of the universe. The same will happen wherever you take your stand.' The universe then cannot have a limit.

Moreover the two constituents are also infinite, though in different senses, the atoms in number and the void in extent. For, as Lucretius argues, in order that the sum total, the universe, may be unlimited, either both or one or other of its constituents must be infinite. Epicurus then deals with the two questions separately. 'If the void were boundless, and the bodies limited in number, the bodies could not stay anywhere, but would be carried about and scattered through the infinite void, not having other bodies to support them and keep them in place by means of collisions.' The statement is careful and precise: the condition of the creation of things is the constant collision of atoms and their crowding together in such numbers as to be able to enter into the combined existence of a compound, which in its turn is kept together and held in its place by the external blows of other countless atoms. That this may occur in an infinite universe, it is necessary that there should be an infinite supply of matter: otherwise the comparatively few collisions which would take place would just send individual atoms wandering far out into space, where they would have no chance of meeting their fellows. Lucretius elaborates the idea with a fine imaginative description of the chaos which must ensue.

Similarly, space is infinite in extent: for 'if the void were limited, the infinite bodies would have no room wherein to take their place'. Lucretius' argument here is rather different and perhaps less satisfactory: 'if space were limited, the atoms through the downward motion due to weight would all have sunk to the bottom and there remained in an inert mass: it is because there is no bottom that they are still kept in eternal restlessness'. The limitation of space would in fact preclude the ceaseless motion of the atoms which is an essential part of the atomic conception. The argument is more esoteric and less likely than Epicurus' own to convince a non-Epicurean. It is simpler and more cogent to maintain that unless space were infinite, there would not be room for infinite atoms.

The idea of the infinity of space raises again the question of the conception of space and presents the same difficulty. One is inclined to ask: does not the existence of the infinite number of atoms really preclude the infinity of space: for each atom, inasmuch as it is not itself empty space, is really a limitation to it? This question requires a careful answer. It is tempting to argue that the instantaneous occupation of any 'piece' of space by an atom does not interfere with the conception of space as continuous and infinite 'place', in which the atoms have their momentary station. But there is a good reason against this: if this were the Epicurean conception, then space would itself be coextensive with the universe, whereas Epicurus always speaks of the universe as 'body plus void': the sum total of matter, divided though it is into infinite particles in ceaseless motion has to be added to infinite void to make the sum total of the infinite universe. Similarly it is significant that in this section space is spoken of throughout as 'the void'… and not 'place'… as before. It would probably be a more correct solution of the difficulty to say that this 'internal' limitation of space, if it may be so described, was not here present to Epicurus' mind. He was thinking rather, as he clearly was when speaking of the infinity of the universe, of an 'external' limit.… In extension outward space is unlimited…, even though internally it might be thought of as limited by the presence of atomic matter. Once again the notion of 'empty space' seems to be uppermost and that from which Epicurus started: the kinetic view of matter helps to an understanding of his point of view, but the particular difficulty would not have troubled him.

We have then at last reached the traditional atomic conception of an infinite universe, consisting of atoms infinite in number moving in space infinite in extent. The conception has not varied since Democritus, but in its gradual unfolding in Epicurus it seems almost to have changed its nature. Each step in the argument has now been thought out under the definite rules of the Canonice: the detached notions about the character of the atoms have been correlated into a self-dependent whole: a universe seems not to have been assumed but created in thought. There has been occasion here and there to point out weak points in the argument or possibly hazy and ill-defined conceptions. But the result is one worthy of a great thinker: it is no mere wholesale adoption of the theory of Democritus—in certain places it has been seen to differ conspicuously from it: nor is it the work of a preacher, who hastily patched together some kind of physical theory to act as a basis for his moral teaching. With all its limitations, it is the construction of a mastermind, working on definite lines and with a deep and penetrating interest in his subject for its own sake.…