Lecture 5 — Resolution of Democritus' argument

But we must try to disentangle these perplexities, and must therefore formulate the whole problem over again.

On the one hand, then, it is in no way paradoxical that every perceptible body should be indivisible as well as divisible at any and every point. For the second predicate will attach to it potentially, but the first actually.

On the other hand, it would seem to be impossible for a body to be, even potentially, divisible at all points simultaneously. For if it were possible, then it might actually occur, with the result, not that the body would simultaneously be actually both (indivisible and divided), but that it would be simultaneously divided at any and every point. Consequently, nothing will remain and the body will have passed-away into what is incorporeal: and so it might come-to-be again either out of points or absolutely out of nothing. And how is that possible? But now it is obvious that a body is in fact divided into separable magnitudes which are smaller at each division—into magnitudes which fall apart from one another and are actually separated. Hence (it is urged) the process of dividing a body part by part is not a 'breaking up' which could continue ad infinitum; nor can a body be simultaneously divided at every point, for that is not possible; but there is a limit, beyond which the 'breaking up' cannot proceed.

The necessary consequence—especially if coming-to-be and passing-away are to take place by 'association' and 'dissociation' respectively—is that a body must contain atomic magnitudes which are invisible.

Such is the argument which is believed to establish the necessity of atomic magnitudes: we must now show that it conceals a paralogism, and exactly where it conceals it. For, since point is not 'immediately-next' to point, magnitudes are 'divisible through and through' in one sense, and yet not in another. When, however, it is admitted that a magnitude is 'divisible through and through', it is thought there is a point not only anywhere, but also everywhere, in it: hence it is supposed to follow, from the admission, that the magnitude must be divided away into nothing. For it is supposed—there is a point everywhere within it, so that it consists either of contacts or of points. But it is only in one sense that the magnitude is 'divisible through and through', viz. in so far as there is one point anywhere within it and all its points are everywhere within it if you take them singly one by one. But there are not more points than one anywhere within it, for the points are not 'consecutive': hence it is not simultaneously 'divisible through and through'. For if it were, then, if it be divisible at its centre, it will be divisible also at a point 'immediately-next' to its centre. But it is not so divisible: for position is not 'immediately-next' to position, nor point to point—in other words, division is not 'immediately-next' to division, nor composition to composition. Hence there are both 'association' and 'dissociation', though neither (a) into, and out of, atomic magnitudes (for that involves many impossibilities), nor (b) so that division takes place through and through—for this would have resulted only if point had been 'immediately-next' to point: but 'dissociation' takes place into small (i.e. relatively small) parts, and 'association' takes place out of relatively small parts.

It is wrong, however, to suppose, as some assert, that coming-to-be and passing-away in the unqualified and complete sense are distinctively defined by 'association' and 'dissociation', while the change that takes place in what is continuous is 'alteration'. On the contrary, this is where the whole error lies. For unqualified coming-to-be and passing-away are not effected by 'association' and 'dissociation'. They take place when a thing changes, from this to that, as a whole. But the philosophers we are criticizing suppose that all such change is 'alteration': whereas in fact there is a difference. For in that which underlies the change there is a factor corresponding to the definition and there is a material factor. When, then, the change is in these constitutive factors, there will be coming-to-be or passing-away: but when it is in the thing's qualities, i.e. a change of the thing per accidents, there will be 'alteration'.

Dissociation and association affect the thing's susceptibility to passing-away. For if water has first been 'dissociated' into smallish drops, air comes-to-be out of it more quickly: while, if drops of water have first been 'associated', air comes-to-be more slowly. Our doctrine will become clearer in the sequel.'

Meantime, so much may be taken as established—viz. that coming-to-be cannot be 'association', at least not the kind of 'association' some philosophers assert it to be.

34. Having presented Democritus' argument, he now proceeds to answer it.

First he states his intention (316b18), saying that one must attempt to solve the aforesaid problem. Consequently, the better to solve it, the question must be review from the very beginning, for when one gets a brief look at what the force of the question consists in, the easier it will be seen where to apply the solution.

Second, at on the one hand, then (316b19), he carries out his proposal.

First, he presents the truth;

second, he presents Democritus' objections against the truth, at the necessary consequence (316b33; [37]);

third, he answers them, at such is the argument (317a1; [38]).

35. He says therefore first (316b19) that it is not inadmissible to maintain both of these statements, namely, that every sensible body is divisible with respect to any and every sign [point] (denominated above as being wholly divisible), or that it is not divisible. For one of these is true in potency, namely, that a sensible body is divisible with respect to any and every sign; the other is true in entelechy, i.e., in act, namely, that a sensible body is not divisible according to every sign in act.

36. Then, at on the other hand (316b21), he presents Democritus' two arguments against this truth. Concerning the first of these, he [Aristotle] says that according to Democritus' objection it seems impossible for a sensible body to be all at once "wholly" divisible in potency, as was said above. For Democritus believed that whatever could be all at one time in potency, could be all at one time in act, and he argued that, just as it is possible for a body to be all at one time wholly divided in potency, this could also take place in act — not in the sense that it would be at one and the same time potentially divisible and actually divided, but in the sense that it would be divided in act according to every point. But this he showed to be impossible, because as is evident from what was said above, it would follow that nothing bodily would be left as a residue of division, and that the body would be dissolved into something incorporeal, and as a consequence a body would be generated from something incorporeal, i.e., from points or from absolute nothing. But this is impossible. Therefore it is not possible for a sensible body to be all at one time wholly divided. Neither, then, could it have been potentially so divisible.

But because our senses reveal that a sensible body is divided into parts that can be separated one from the other or even into divisible parts, and that a larger magnitude is always divided into smaller magnitudes, and that a connected whole is divided into separate and isolated parts, it is evident that that is the way things are. It is therefore not possible for there to be division to infinity according to part, in such a way, namely, that part after part be separated from the whole sensible body; neither is it possible for a sensible body to be divided all at one time according to every sign. (Neither of these is possible since in both cases the same impossible situation occurs.) But one sees that the division of a sensible body can proceed up to a certain limit. Hence it follows that there must be certain indivisible magnitudes and certain indivisible bodies, according to Democritus.

37. The second objection of Democritus] is presented at the necessary consequence (316b33), in which he says that, for another reason also, it seems to be necessary that there be indivisible bodies, namely, if generation comes about through assembling, and corruption through separation. And Democritus was forced to posit this, because he laid down that the forms and natures of things are determined on the basis of position and order; for we see that a whole whose form consists in position and order, as for example a house, is generated only by assembling, and destroyed only by separating. Consequently, since it is not possible to proceed to infinity with regard to principles of generation and corruption, he laid down that there were certain first principles from which bodies are assembled and into which they are separated, And he said the indivisible bodies were such things.

Aristotle, summing up, concludes that the aforesaid exposition is that which seems to compel us to hold for indivisible magnitudes.

38. Then, at such is the argument (317a1), he answers the aforesaid arguments:

first, the first one;

second, the second one, at dissociation and association (317a27; [41]).

With respect to the first (317a1) it should be noted that the whole force of Democritus' first argument lies in this, that if a sensible body is all at one time wholly divisible in potency, it is all at one time wholly divided in act. But this consequent does not hold in all things. For there are some things in which to be in potency enters into their very notion. Hence in such things it is not possible to posit that to be all at one time in act which is all at one time in potency, since it would remove the very notion and nature of that thing.

This is manifest first of all in successive things. For, in the beginning of a day, it is possible all at one time for the hours to be, but it is impossible to posit all the hours of that day to exist all at one time in act, because that would destroy the very nature of time, in whose notion there is that it be the number of motion according to prior and subsequent. If all its parts existed at once, it would not be according to prior and subsequent.

Second, it appears in permanent things. For in the substance of air is matter, which is in potency to all forms, yet it cannot be posited that whatever can be generated from air has been generated therefrom. That would destroy the very nature of matter, which is always in potency to all forms. Consequently, it is against the notion of magnitude, for example, of a line, that it be at any time wholly divided in act. Therefore, from the fact that it is all at one time wholly divisible in potency, it does not follow that it can be posited as all at one time divided in act.

That such a thing is against the notion of a line is plain. For the division of a line in act is nothing more than a point in act. If, therefore, a line were all at one time wholly divided in act, it would be necessary for a point to be everywhere in act in the line and, consequently, the points would have to be contiguous or consecutive in the line. But this cannot be: because, since points are indivisible, given many contiguous points, one would not extend beyond another, for one would touch another in its entirety. Thus all the points taken together would amount only to one point. Therefore, it cannot be said that the points are everywhere in act in the line. Consequently, it is against the notion of a line that it be all at one time wholly divided in act. And therefore it does not follow that, if something be all at one time wholly divisible in potency, one can posit it to be wholly divided in act.

39. Therefore the Philosopher says that Democritus conceals a paralogism, i.e., that he commits a hidden fallacy, and that one must show where its defect lies hidden. Now, since one point cannot be contiguous to another, it is impossible for a line to be wholly divided in act. Consequently, the property of being everywhere divisible, although it belongs in some sense to magnitudes, i.e., in potency, yet in another sense it does not belong to them, i.e., in act. For when it [a line] is assumed to be everywhere divided, one implies also that it is everywhere a point, for a point in act is nothing else than a division of the line in act. But if a point is everywhere in act in a line, then the magnitude must be divided into points, since nothing else is found anywhere in the magnitude. Or else, according to another version, it must be divided into nothing, because nothing will remain but division, if everywhere there is a point, which is a division. Consequently, it follows that a magnitude will be constituted, either out of points, or out of contacts between parts of the line, or out of divisions of the line (which is the same thing) for the assumption, according to the above, is that what exists everywhere in the line, if it be all at one time wholly divided, is either a point, or a contact, or a division.

But this cannot be, because it would follow that one single point would be everywhere, i.e., in each part of the line, and that all the points of the line would occupy no more space than each one. Indeed, there would be no more than one point nor more divisions than one. For the points assumed to be present could not be consecutive in the sense of one being after another; neither could they be in contact as to their extremities only while being in other respects separated, because, being indivisible, they are in contact according to their wholes. Therefore all the points so conjoined are just one point. Hence, it is impossible for a point to be everywhere in a line. For if a line were divisible through its middle and point touched point, that line could also be divided according to a contiguous point, the line being wholly divisible. But this is impossible, because point is not contiguous to point nor had, i.e., consecutive, nor is any sign so to another point. This point in act is nothing other than an actual division of the line, or the composition or contact of the parts of the line.

Hence it must be conceded that in sensible bodies combination and separation are found, but not separation into indivisible bodies or combination out of indivisible bodies (for otherwise many impossibilities would follow, as was said in On the Heavens III). Neither can a line be actually divided everywhere (which would happen, if point were contiguous to point, which is impossible as is evident from what has been said). But the separation of bodies is into certain small and lesser things, and combination is out of certain small and lesser things, but not out of least things which have to be indivisibles.

40. Then, at** it is wrong, however** (317a17), he answers he second argument of Democritus by destroying its foundation.

First, he destroys the notion that simple generation and corruption are instances of assembling and separation, as Democritus believed;

second, he shows to what extent the dictum of Democritus can be verified, at meantime, so much may be taken (317a30).

He says therefore first (317a17) that one should not say, as some have said, that simple and perfect generation occurs through assembling, and corruption through separating, and that any change which takes place in a permanent continuum, i.e., which is not assembled or disintegrated, is alteration. For they thought that this occurred in natural things as it does in a house and in all such things, whose form consists in position and order, because these things come to be only by assembling the parts, and are disintegrated only by separating the parts. Whatever other change occurs in such things, provided it is not a dissolving of the continuous, is alteration.

It is from this belief that the entire fallacy proceeds. For there is generation and corruption in natural things, whose form does not consist in position and order, not indeed through assembling and separating, but because there is a change from this whole, i.e., from this whole not resolved into its parts, into that whole, which is not an assembly of parts. But the early philosophers thought that every such change, that occurs while the whole remains intact, is alteration. However, this is not true. For at one time there can be simple generation and at another alteration. They differ in this: In a subject there is present something according to notion, i.e., according to form, and something according to matter (for a natural body that exists in act is a composite of matter and form). When, therefore, there is a change according to matter and form, in such a way, namely, that the matter acquires a different substantial form, there will be simple generation and corruption; but when there is a change according to passions and accidents, it will be alteration.

41. Then, at dissociation and association (317a27), he shows in what sense Democritus' dictum is verified. For it is plain that some things, by the very fact that they are assembled or separated, are rendered more easy or more difficult to destroy or modify. For if water be divided into very small parts, it is less able to resist the action of a contrary agent, and in this way, from the corrupted water, air will be more quickly generated. But if much water is assembled, it will offer greater resistance to an agent and thus will be more slowly corrupted so as to allow air to be generated from it. But this will be clearer in what follows.

Finally, as a summary, he says that so much can be taken as established, namely that generation cannot be assembling, of the sort that some maintain, namely, that out of indivisible bodies.