by Tim O'Keefe
An obvious objection to Epicurus’ doctrine is that the notion of spatial minima is inconceivable. Take any spatial magnitude you wish. No matter how small it is, you can conceive (at least theoretically) of dividing it in half, and hence it is not a minimum. Epicurus anticipates this objection and tries to reply to it by drawing an analogy between spatial and perceptible minima (Ep. Hdt. 58–9). In vision, objects can get smaller and smaller, to the point where they can get no smaller without becoming imperceptible. Think of minute dust motes, or a car shrinking as it moves further away, until the last moment in which it can be seen before it vanishes. Such objects will have extension: they must in order to be visible. But they will have no perceptible subparts, because any spatial sub-parts would be below our threshold to see them. Such perceptible minima are not literally spatial minima; dust motes are both physically and theoretically divisible. But perceptible minima allow us to conceive of what theoretical spatial minima are like, as extended yet partless, and to answer the objection.
Epicureans draw a number of startling conclusions from this theory (Simpl. in Phys. 934, 23–30).2 Besides space, both motion and time will have minima. The smallest amount one can move is by one spatial unit. Think of a video character moving across a pixellated screen, one pixel at a time. It cannot move half a pixel. And because time is a measure of motion, there will also be temporal “atoms”: the interval of a body moving one spatial minimum. Time and motion both will be “jerky”, then: a series of snapshots, like the stills making up a film reel, of bodies moving on a pixellated background.
This theory also allows the Epicureans to declare a universal speed limit. Assuming that bodies cannot “skip” spatial minima when moving, then the fastest speed would be going from A to B in a number of temporal “atoms” equal to the number of spatial minima from A to B, that is, making the trip entirely unimpeded.
The doctrine of spatial minima also raises interesting problems for geometry. For instance, the Pythagoreans had already demonstrated that certain magnitudes, such as the length of a side of a square and of its diagonal, are incommensurable. But if magnitudes are composed of a whole number of spatial minima, it follows that all magnitudes are commensurable with one another. Too bad for geometry, conclude the Epicureans. Cicero relates the story of a follower of Epicurus, Polyaenus (Academica II 106), who started as a mathematician but, after converting to Epicureanism, became convinced that all of geometry was false.3
Conclusion
To account for a world of bodies in motion, there must be void, and to account for the order and stability we see around us, there must be a changeless stock of uncuttable basic particles out of which all of the bodies we perceive are composed. These basic particles possess only a Spartan set of qualities. The Epicureans believe, over-optimistically, that only this view of the world is consistent with the phenomena. In any case, having now (purportedly) established the basic principle of their physics on the basis of observation, the task of going back up to the phenomena and adequately explaining them via their physics still lies open. Before we follow them there, however, let us briefly linger at the level of atoms and the causes of their motion.
THREE
Atomic motion
Weight and the swerve
Up to this point, Epicurus’ atomism has largely followed the path already taken by Democritus. Since we have fairly little information about Democritus, it is possible that some of the particular arguments that Epicurus and Lucretius give for the existence of atoms are original, but the basic argument that void is necessary for there to be motion, and the characterization of atoms and void, are more or less the same.
But when accounting for atomic motion, Epicurus makes major modifications to the system he inherited from Democritus. For Democritus, atoms eternally fly through the void in all directions. They collide with and rebound from one another, occasionally becoming entangled and forming larger bodies. Atomic motion, then, is the result of inertia – although one must always be careful of anachronism when applying such terms – plus collisions.
Epicurus adds two additional causes of atomic motion. The first is weight (DRN II 184–215). For Epicurus, “weight” is simply the natural tendency of atoms to move downwards.1 What way is “down”? If you stand upright (no leaning!) and draw a line from the top of your head down to your feet, it is that way, below you, whereas “up” is the opposite direction. Epicurus (like Democritus) believes that the universe is spatially unlimited (we shall explore the reasons for this in Chapter 5). So one can go downwards forever; imagine following the y-axis in a Cartesian coordinate grid from 0, through -1 and -2 and so on, indefinitely. So, contra Aristotle (Ph. IV 8, 215a6–10), we can make perfectly good sense of the notion of “down” without the notion of a lowest point or bottom.
If unimpeded, atoms naturally fall downwards at equal speed, that is, at maximum speed, one spatial minimum per temporal minimum. Larger, heavier atoms do not travel faster than smaller ones. Instead, the reason why we experience that heavier bodies normally fall faster than lighter ones is that they are better able to push aside the impediments offered by air or water (Ep. Hdt. 61, DRN II 225–42).
But this raises a problem. As Lucretius puts it, if the only natural motion of atoms was to fall straight downwards at equal speeds, then the atoms would all “fall downwards, like drops of rain, through the deep void, and neither would a collision occur, nor a blow be produced among the primary bodies: in this way nature would have never produced anything” (DRN II 221–4, trans. Smith).
This leads to the second additional cause of atomic motion: the swerve. At “uncertain times and places” (DRN II 218–19) atoms swerve to the side by one spatial minimum. This additional cause of atomic motion is needed for the atoms ever to have collided and produced the bodies we see: without the swerve, the atoms would be like cars being driven along a multi-lane highway at equal speed, staying in their lanes. An occasional swerve to the side, however, is enough not only to cause a collision, but to start a chain reaction of additional collisions as a result of the blow started by the sideways swerve. (This may be dubbed the “cosmogonic” argument for the swerve, as the swerve is supposed to be needed for the creation for all macroscopic bodies and a fortiori our cosmos. More famously, the indeterminate atomic swerve is supposed to be needed to preserve our freedom from the “decrees of fate”. We shall look at that role of the swerve in Chapter 8.)
The basic form of Lucretius’ cosmogonic argument is the same as that for the existence of void. We start from something evident in our experience (that there is motion, that there are macroscopic bodies), and on its basis we infer a conclusion about what is not in itself directly observable (the existence of absolutely empty space, or of tiny atomic swerves). It goes as follows:
1.
If the atoms did not swerve, there would be no
collisions and no macroscopic bodies.
2.
There are collisions and macroscopic bodies.
* * *
3.
Thus, the atoms swerve.
The crucial premise, of course, is the first. A natural way of reading this “cosmogonic” argument is parallel to kalam-type cosmological arguments for God’s existence advanced by Islamic thinkers who think the world must have some temporal starting-point: given that there are collisions, there must be some first collision in order to get the sequence of collisions started.2 And given the Epicurean theory of the natural downwards motion of atoms at a uniform velocity, the only way for the sequence of collisions to get started is for the atoms (or at least one atom) to depart from their usual motion and to bump into neighbouring atoms.
But on this interpretation, the argument is pitifully deficient. It suffers from two crippling problems, one philosophical, the other textual. The philosophical problem is that there is no reason for the Epicureans to suppose that there needs to be an initial collision to get collisions started. Instead, one can simply suppose that there is an infinite series of collisions ex
tending backwards in time. Any particular collision is caused by the velocities and directions of motion of the atoms that collide, which in turn are caused (in part) by the past collisions of those atoms, and so on, on down the line. And indeed, this is precisely the theory advanced by Democritus. Since there is already an economical explanation of collisions available, adding the swerve would be gratuitous.
The textual problem is that the Epicureans explicitly deny that there ever was an initial atomic collision to get things started. The universe (i.e. the totality of atoms and void) has existed forever, since there is nothing else that exists from which it could come into existence (Ep. Hdt. 39), and nothing comes into being from nothing. More crucially, atomic collisions have been going on forever. Epicurus describes the different sorts of atomic motions: he asserts that atoms are constantly moving, with some atoms separated far from others in solitary motion, while others are tangled together, but even these are vibrating back and forth as they collide with one another. He then adds that there is no beginning to these sorts of motions, since the atoms and void are eternal (Ep. Hdt. 43–4). Likewise, Lucretius says that generation and destruction have always existed (DRN II 569–80), and that every possible combination of atoms has already come into existence, since the atoms have always been driven by collisions and their weight (DRN V 187–91).
Since postulating the swerve to give a temporal start to collisions (a) is gratuitous and (b) contradicts what the Epicureans say elsewhere, we have strong grounds on the principle of charity to seek a different interpretation of the argument.3 (Basically, the principle of charity is a methodological principle on how to interpret texts or speech, in which you give the person the benefit of the doubt and presume that what is being said is reasonable. So if a person appears to be saying something incoherent, utterly unjustified or incredibly obtuse, instead of jumping all over the person for his failures, you should step back and consider whether you have misunderstood what is being said, and try to find a plausible way of understanding it so that it is not so bad.)
Aristotle’s criticisms of Democritus
Since Epicurus probably added weight and the swerve as causes of atomic motion in order to overcome difficulties of Democritus’ theory, a promising place to look for some problems would be previous criticisms of that theory. The most extensive such criticisms were by Aristotle.
Aristotle’s criticisms of Democritus are largely based on the distinction between natural and forced motion. For Aristotle, natural motion is caused by an individual’s own nature: an internal source of change. For instance, earth is by nature heavy, and it naturally falls down (where “down”, for Aristotle, is towards the centre of the cosmos, the goal of its downwards motion). But sometimes this natural motion can be impeded, and something will engage in forced motion; for example, if I cruelly hoist a clod of earth up in the air in order to prevent it from fulfilling its goal, the upwards motion of the earth caused by my intervention is forced. According to Aristotle, all atomic motion is forced, since all motions are simply the result of blows by other atoms, and no atomic motion is natural, since atoms have no natural direction of motion. Aristotle thinks that the absence of natural motion makes any motion whatsoever impossible (Ph. IV 8, 215a1–13; Cael. III 2, 300b9–16).
Democritus would seem to have a ready reply available (if he were around at the time): why should he accept Aristotle’s presupposition that there must be some natural motion in order for there to be motion at all, as opposed to simply conceding (using Aristotle’s vocabulary) that all motion is forced? After all, each “forced” motion has an explanation for why it occurs because of some previous “forced” motion, which in turn was the result of other past “forced” motions, and so on.
Aristotle, however, would not be satisfied by this reply. Aristotle is not looking for an explanation of any particular motion in terms of past motions, but for why there should be motion at all, and he sees no explanations forthcoming from Democritus. Simply saying that there has always been movement, as the early atomists do, is not sufficient to explain why movement occurs at all, and why it occurs in the way it does (Metaph. XII 6 1071b31–4; Ph. VIII 1 252a32-b2). Aristotle points out that there is nothing about the nature either of the atoms or of the void that explains why the atoms move rather than eternally sit still, since the atoms have no natural motion, and void does not move the atoms either, but simply gives space for things to move through.
Weight and the swerve as responses to Aristotle
Atomic weight gives Epicurus a reply to Aristotle. There are other decent grounds for positing the existence of a natural tendency for bodies to fall downwards: our daily experience makes it evident that bodies have weight, which gives them a natural motion “down”. (Ep. Hdt. 60 suggests this.) But weight also gives an explanation for why the atoms move at all rather than simply sitting still. Epicurus accepts Aristotle’s thesis that there must be some natural motion in order for there to be motion. A later report attributes to him the view that atoms would not move at all if they were not moved by their weight (Aëtius I.3.18ff., IG I-77). Weight does not start the atoms moving; instead, it explains why they have been moving eternally.
The swerve can fulfil a similar role, explaining why there are atomic collisions and the compound bodies that result from atomic collisions. If the only natural motion of the atoms were straight down, we would expect that the atoms would fall straight downwards, like drops of rain in the night, never touching. There would be no satisfactory explanation in terms of the properties of the atoms – their extension, solidity or weight – for why there are collisions at all. Once there is a swerve, however, we can appeal to a natural feature of atomic motion to account for the existence of collisions. The swerve does not get collisions started; instead, it explains why atoms have been eternally colliding.
This makes the introduction of the swerves more understandable, but the argument still suffers from at least two problems. The first stems from the swerves’ second function: to break the decrees of fate. The swerves happen at uncertain times and places. And because this uncertainty is supposed to prevent new atomic movements from being invariably linked to old ones, which is needed to preserve our freedom, Lucretius is not saying merely that we cannot know when swerves will occur. His point is metaphysical, not epistemic: there is nothing in the natures of the atoms or their past motions that determines where and when swerves will occur; they are genuinely indeterministic. Critics of Epicurus scorned this as introducing “motion without a cause” (e.g. Cic. Vat. 22–5). But if swerves have no cause, then introducing them does not help to explain why collisions occur. Epicurus would have been better off simply admitting that collisions have always been occurring. At least then there would be an explanation why the individual collisions occur, in terms of past collisions. Trying to explain the existence of collisions by introducing causeless atomic swerves, which are entirely inexplicable, just makes things worse.
This problem can be overcome. Atoms have a natural tendency to swerve occasionally to the side in an indeterministic manner, just as they have a natural tendency to fall straight downwards. So, an atom’s falling downwards has a cause: the latter natural tendency of the atom, which we call “weight”. Likewise, an atom’s swerving to the side has a cause: the former natural tendency of the atom. If we wish, we could call this atomic property “swerviness”. So swerves do have an atomic cause (swerviness), even though the particular time and place in which swerves occur is not causally necessitated. By its nature, swerviness operates erratically.4
The second problem is that the swerve is ad hoc. It gets around the difficulty at hand, but it is cheap and arbitrary. It is not very satisfactory simply to assert that atoms have an inherent tendency to swerve off to the side every once in a while and hit one another after one has realized that they would never collide if they all naturally fell downwards at equal speed.
Conclusion
Epicurus has three principles to explain atomic motion – weight, the swe
rve and collisions – whereas Democritus has only one, collisions. These additional principles, and the arguments for them, are problematic. Still, they show Epicurus’ willingness to modify even the fundamental principles of Democritean atomism in order to overcome its perceived shortcomings. For Epicurus, events in the world are supposed ultimately to be explained by appealing to atoms and atomic properties, but under the Democritean physics there is no good explanation for the motion of the atoms. Democritus can account for each individual motion, but not for why motion exists at all, or for the particular types of motion that one encounters. Epicurus’ modifications help to remedy this deficiency. The natural downwards motion accounts for the existence of motion, while the swerve accounts for the existence of collisions and compound bodies.
FOUR
Sensible qualities
While Epicurus does make significant changes to Democritean atomism by adding weight and the swerve as causes of atomic motion, his ontology at the level of atoms is basically the same: the ultimate constituents of the universe are void, which is simply empty space, and atoms, which are extended bits of matter, eternal and changeless except in their locations. We infer that these entities exist on the basis of our perception of a world of changeable, temporary objects, objects that, unlike the atoms, have properties such as being sweet, hot and red.1