LECTURE 5 (233 b 33-234 b 20)

THE 'NOW' OF TIME IS INDIVISIBLE. IN THE 'NOW' OF TIME NOTHING IS EITHER MOVED OR AT REST. WHATEVER IS MOVED IS DIVISIBLE. CERTAIN DIFFICULTIES ARE ANSWERED

             787. The Philosopher has shown that no continuum is indivisible or composed of indivisible parts. From this it is clear that motion is divisible. Hence he here treats the division of motion.

             First he sets forth certain things which are necessary for the division of motion. Secondly, where he says, 'Now motion is divisible . . .' (234 b 21), he determines the division of motion.

             Concerning the first part he makes two points. First he shows that there is neither motion nor rest in an indivisible point of time. Secondly, where he says, 'Further, everything that changes . . .' (234 b 10), he shows that that which is indivisible cannot be moved.

             Concerning the first part he makes two points. First he shows that the indivisible point of time is the 'now'. Secondly, where he says, 'We will now show . . .' (234 a 24), he shows that in the 'now' nothing is moved or is at rest.

             Concerning the first part he makes three points. First he states his intention. Secondly, where he says, 'For the present . . .' (234 a 1), he gives certain things from which his position can be proven. Thirdly, where he says, 'Now the present . . .' (234 a 5), he brings out the consequence of these points.

             788. It must first be realized that 'now' is sometimes used, not in its proper meaning, but in an extended meaning. For example, we say that something which is done in the whole of the present day is done now. Now the whole present day is not called present in the proper sense, but in an extended sense. For it is clear that part of the present day has passed, and another part is yet to come. That which is past or future is not now. Thus it is clear that the whole present day is not a 'now' primarily and per se, but only in regard to part of itself. And the same is true of an hour and of any other time.

             Hence he says that that which is called a 'now' primarily and per se, and not in the extended sense, is necessarily indivisible. And further this 'now' is necessarily in every time.

             789. Next where he says, 'For the present . . .' (234 a 1), he proves his position.

             It is clear that for every finite continuum there is some extremity outside of which there is nothing of that of which it is the extremity. For example, there is no line outside of the point which terminates the line. And past time is a continuum which is terminated at the present.

             Therefore, there is an extremity of the past outside of which there is no past and within which there is no future. And likewise, there is an extremity of the future, within which there is no past. This extremity is the terminus of both the past and the future. For since the whole of time is a continuum, the past and the future must be joined at one terminus. Hence, if it be demonstrated that there is something which is a 'now' in itself and not just in regard to a part of itself, it will simultaneously be clear that this 'now' is indivisible.

             790. Next where he says, 'Now the present . . .' (234 a 5), he brings out a certain consequence of the foregoing.

             Concerning this he makes two points. First he shows that on the supposition that the 'now' is indivisible the same 'now' must be both the terminus of the past and the terminus of the future. Secondly, where he says, 'But if this is so . . .' (234 a 20), he shows conversely that the 'now' is indivisible if the same 'now' is the terminus of both past and future.

             Concerning the first part he makes two points. First he concludes from what has been said that the same 'now' must be the terminus of both the past and the future.

             791. Secondly, where he says, 'For if each extremity . . .' (234 a 6), he proves this with the following argument. If the 'now' which is the beginning of the future is different than the 'now' which is the end of the past, then these two 'nows' must be either in succession to each other such that they immediately succeed each other, or else one of them must be separated from and at some distance from the other. But it cannot be said that one succeeds the other. For thus it would follow that time is composed of an aggregate of 'nows', which is impossible because no continuum is composed of indivisible parts, as was shown above. Nor can it be said that the one is separated from and at some distance from the other. For then it would be necessary for there to be an intermediate time between these two 'nows'. It is the nature of every continuum that there is an intermediate continuum between any two of its indivisible points. For example, there is a line between any two points.

             He shows in two ways that this is impossible. First, if there is some intermediate time between the two above-mentioned 'nows', it would follow that there is something of the same genus between the two termini. This is impossible. For there cannot be an intermediate line between the extremes of two lines which are touching or are in succession. This would be contrary to the nature [ratio] of succession. For, as was said above, things are in succession when there is no intermediary of the proximate genus. And thus, since future time succeeds past time, there cannot be any intermediate time between the terminus of the past and the terminus of the future.

             He proves the same thing in another way as follows. Whatever is intermediate between past and future is called the 'now'. Hence, if there be an intermediate time between the extremities of the past and the future, it would follow that this whole time is called a 'now'. But every time is divisible, as was shown. Thus it would follow that the 'now' is divisible.

             792. He has stated above the principles by which it can be proven that the 'now' is indivisible. However, since he has not yet deduced this conclusion from the principles, he next shows that the 'now' is indivisible. He does this where he says, 'But if the present . . .' (234 a 12).

             He proves this with three arguments.

             The first is that, if the 'now' is divisible, then it would follow that part of the past is in the future and part of the future is in the past. For the 'now' is the extremity of both the past and the future. And every extremity is in that of which it is the extremity, as the point is in the line. Thus it is necessary that the whole 'now' is both in the past as its end and also in the future as its beginning. But if the 'now' is divided, this division must determine a past and a future. For every division in time distinguishes a past from a future, because of all the parts of time one is related to another as past to future. Hence it would follow that part of the 'now' is past and part is future. And thus, since the 'now' is in both the past and the future, it would follow that part of the future is in the past and part of the past is in the future.

             He gives the second argument where he says, 'Also the present . . .' (234 a 14). If the 'now' is divisible, it will not be a 'now' in the proper sense, but in an extended sense. For nothing which is divisible is the very division by which it is divided. And the division of time is the 'now'. For the division of a continuum is nothing other than the terminus which is common to the two parts. And this is what we mean by the 'now': the common terminus of past and future. Thus it is clear that that which is divisible cannot be a 'now' in the proper sense.

             He gives the third argument where he says, 'Furthermore, there will be . . .' (234 a 16). The argument is as follows.

             When time is divided, there is always one part which is past and another which is future. Hence, if the 'now' is divided, part of it must be past and part future. But the past and the future are not the same. Therefore it would follow that the 'now' is not the same as itself, as a whole existing all at once. (This is contrary to the nature [ratio] of what is called a 'now'. For when we say 'now', we mean 'all at once in present existence'.) Rather there would have to be much diversity and succession in the 'now', just as there is in time, which is divided in many ways.

             793. He has shown that the 'now' would be divisible if the extremity of the past and the extremity of the future were not the same 'now'. Now, after having denied the consequent, he concludes by denying the antecedent.

             He says that since it is impossible for the 'now' to be divisible, it must be said that the same 'now' is the extremity of both times.

             Next where he says, 'But if this is so . . .' (234 a 20), he shows conversely that, if the 'now' of the past and the future is the same, then the 'now' must be indivisible. For if it were divisible, all of the above-mentioned impossibilities would follow. It cannot be said that the 'now' is divisible as though there exists one 'now' for the past and another 'now' for the future. Nor can it be said that the 'now' is divisible if there is the same 'now' for past and future. From this he concludes that there clearly must be in time something which is indivisible. This is called the 'now'.

             794. Next where he says, 'We will now show . . .' (234 a 24), he shows that there can be neither motion nor rest in the 'now'. He does this first in regard to motion, and secondly in regard to rest, where he says, 'Nor can anything . . .' (234a 32).

             He says, therefore, first that it is clear from what follows that nothing can be moved in the 'now'. If there could be motion in the 'now', then in that 'now' two mobile beings, one of which is faster than the other, could be moved. Thus, let the 'now' be M, and let the faster body be moved through the magnitude A B in M. But in an equal time a slower body is moved through a smaller magnitude. Hence, in this time the slower body is moved through the smaller magnitude A C. But the faster body crosses this same space in a shorter time. Therefore, since the slower body was moved through the magnitude A C in the whole 'now', it follows that the faster body is moved through this same magnitude in a time smaller than the now'. Hence the 'now' is divided. But it was shown that the 'now' is indivisible. Therefore nothing can be moved in the 'now'.

             795. Next where he says, 'Nor can anything . . .' (234 a 32), he shows with three arguments that the same is true of rest.

             The first argument is as follows. It was said in Book V that a thing is at rest when it can by nature be moved, but is not being moved when, and how, and in what respect it is natural for it to be moved. For example, it cannot be said that there is a privation of sight in the following cases: when a being which does not naturally have sight, like a stone, lacks it; or when a thing lacks the time in which it would naturally have sight, like a dog before the ninth day; or when a thing lacks a part, like a foot or hand, in which it does not naturally have sight; or when a thing lacks a manner of sight which it does not have naturally, like a man who does not see as acutely as an eagle. Now rest is a privation of motion. Hence only that which by nature can be moved when and how it is natural for it to be moved is at rest. But it was shown that nothing is naturally moved in the 'now'. Thus it is clear that nothing is at rest in the 'now'.

             He gives the second argument where he says, 'Moreover, inasmuch as . . .' (234 a 34). The argument is as follows.

             That which is moved in some whole time is moved in each part of that time in which it is natural for it to be moved. And likewise that which is at rest in some whole time is at rest in each part of that time in which it is natural for it to be at rest. But when there are two times, in one of which there is rest and in the other of which there is motion, the same 'now' is in both of these times. An example of this is the case of something which is moved after a state of rest, or is at rest after being moved. Hence, if something is naturally in motion and is at rest in the 'now', it would follow that something could be simultaneously at rest and in motion. This is impossible.

             He gives the third argument where he says, 'Again, when we say . . .' (234 b 5). The argument is as follows.

             We say that a thing is at rest when, in respect to both its whole and its parts, it is the same now as it was previously. And thus a thing is said to be moved when it is not the same now as it was previously, either in respect to place, or quantity, or quality. But in the 'now' there is no 'previous'. For the 'now' would otherwise be divisible since the 'previous' pertains to the past. Hence nothing is at rest in the 'now'. From this he further concludes that whatever is moved and whatever is at rest is moved and is at rest in time.

             796. Next where he says, 'Further, everything that changes . . .' (234 b 10), he shows with the following argument that whatever is moved is divisible.

             Every mutation is from something to something. But when a thing is in the terminus to which it is being changed, it is not being changed any more, but has been changed. For nothing is simultaneously being changed and already changed, as was said above. When a thing in respect to its whole and all of its parts is still in the terminus from which it might change, it is not then being changed. For it was said above that that which is the same in itself and in all of its parts is not being moved, but rather is at rest. He adds 'all of its parts' because when a thing begins to be changed it leaves the place which it previously occupied, not totally, but part by part.

             Nor can it be said that, while a thing is being moved, it is in both of the termini in respect to both its whole and its parts. For then it would be in two places simultaneously.

             Nor can it be said that it is in neither of the termini. We are speaking here of the proximate terminus to which it is changed, and not of the ultimate terminus. For example, if a thing is being changed from white to black, black is the ultimate extreme, and grey is the proximate extreme. And likewise, if a line, A B C D, is divided into three equal parts, it is clear that the mobile body, which at the beginning of the motion is in the part A B as in a place equal to itself, at another part of its motion is in neither A B nor C D. This is when it is wholly in B C.

             Hence, when it is said that that which is moved, while it is being moved, must be in both termini, we are speaking of the proximate terminus, not the ultimate terminus.

             It follows, therefore, that whatever is changed, while it is changing, is in one of the termini in respect to part of itself and is in the other terminus in respect to part of itself. For example, when a thing is changed from A B to B C, then in this motion the part which is leaving the place A B is entering the place B C. And when a thing is moved from white to black, the part which ceases to be white becomes grey or pale.

             Thus it is clear that whatever is changed is divisible, because it is partly in one terminus and partly in the other.

             797. However it should be realized that the Commentator raises a difficulty concerning this. If Aristotle intends here to prove that only mobile bodies which are moved by motions in the genera of quantity, quality and 'where' are divisible, then his proof is not universal but particular. But that which is changed in respect to substance is also found to be divisible. Hence it seems that, when he speaks of that which is changed by any transmutation, he includes generation and corruption in substance. This is also apparent from the words he uses. He does not speak of 'that which is moved' but of 'that which is changed' (234 b 10).

             But then it seems that his proof is not valid. For some transmutations are indivisible; for example, substantial generations and corruptions, which do not occur in time. In such transmutations it is not true that that which is changed is partly in one terminus and partly in the other. For when fire is generated, it is not partly fire and partly not fire.

             798. He brings forth many solutions of this difficulty. One is the solution of Alexander, who says that no transmutation is indivisible or not in time.

             But he refutes this. For otherwise one denies a certain probable position for which Aristotle and all the Peripatetics are well known; namely, certain transmutations are not in time, for example, illumination and such things.

             He also mentions the solution of Themistius who says that, although some transmutations are not in time, this is overlooked here. And Aristotle uses that which is clear; namely, transmutation occurs in time.

             But he refutes this. The division of mutation is the same as the division of mutable objects. And at the present the divisibility of mobile objects is more obscure than the divisibility of mutation. Hence Aristotle's demonstration would not be effective. For one might say that, although things which are changed by clearly divisible mutations are divisible, nevertheless there are other, overlooked mutable objects which are indivisible.

             He also gives the solution of Avempace who says that he is not here dealing with the division of mutable bodies in respect to quantity but in respect to the subject being divided by contrary accidents, from one of which it is changed to the other.

             799. He later adds his own solution that those mutations which are said to occur not in time are the termini of certain divisible motions. Thus it can happen that a thing is changed in no time insofar as any motion is terminated in an instant. And since that which is per accidens is omitted in demonstrations, Aristotle in this demonstration uses the proposition that every mutation is divisible and in time.

             800. But if one considers the matter rightly, this objection is not to the point. For in his demonstration Aristotle does not use as a principle the proposition that every mutation is divisible. Rather he proceeds on the contrary from the division of the mobile body to the division of mutation, as will be clear below. And he says later that divisibility is in the mobile body before it is in motion or mutation. He uses per se known principles which must be conceded in regard to any mutation; namely, that there is not yet any mutation when that which is to change is wholly and in all its parts still in the terminus from which it changes; that it is not being changed, but already has been changed, when it is in the terminus to which; and that the whole cannot be in both the termini nor in neither of them. This was explained above. Hence it necessarily follows that in any mutation that which is changed, while it is being changed, is partly in one terminus and partly in the other.

             But this is found in different ways in different mutations. In mutations in which there is a middle between the extremes, that which is changed, while it is being changed, is partly in one extreme and partly in the other, in respect to the extremes themselves. In mutations in which there is no middle between the termini, that which is being changed is not according to its diverse parts in the diverse extremes in respect to the extremes themselves, but in respect to something which is joined to them. Thus, when matter is changed from the privation to the form of fire, while it is being changed it is indeed under a privation in respect to itself. But it is partly under the form of fire, not in respect to itself, but in respect to something joined to it; namely, in respect to the proper disposition for fire which it partially receives before it has the form of fire. Hence Aristotle will prove below that even generation and corruption are divisible. For that which is generated was generated previously. And that which is corrupted was corrupted previously.

             And perhaps this is what Alexander means when he says that every transmutation is divisible; namely, either in respect to itself or in respect to a motion joined to it.

             Also Themistius thinks that Aristotle has assumed what was clear and omits what was not clear. For this is not yet the place for treating of the divisibility or indivisibility of mutations. This is reserved for later treatment.

             What Aristotle says here holds good for all mutations, divisible or indivisible. For indivisible mutations are also in a way divisible, not in respect to their own proper extremes, but in respect to things which are joined to them. And this is what Averroes wishes to convey when he says that it is per accidens that some mutations are not in time.

             801. There is also another difficulty here. In alterations it does not seem to be true that that which is altered, while it is being altered, is partly in one terminus and partly in the other. For the motion of alteration does not proceed in such a way that first one part is altered and then another. Rather the whole is first less warm and afterwards is more warm. Further, in De Sensu et Sensato Aristotle says, 'And in general, even in qualitative change the case is different from what it is in local movement [both being different species of kinesis]. Local movements, of course, arrive first at a point midway before reaching their goal (and Sound, it is currently believed, is a movement of something locally moved), but we cannot go on to assert this [arrival at a point midway] in like manner of things which undergo qualitative change. For this kind of change may conceivably take place in a thing all at once, without one half of it being changed before the other; e.g., it is conceivable that water should be frozen simultaneously in every part.'

             802. In answer to this it must be said that here in Book VI Aristotle is treating motion insofar as it is continuous. Now continuity primarily and per se and properly is found only in local motion. For only local motion can be continuous and regular, as will be shown in Book VIII. Hence the demonstrations given in this book pertain to local motion perfectly and to other motions not totally, but insofar as they participate in continuity and regularity.

             Thus it must be said that a locally moved body always partially enters the place to which it is tending before it enters this place wholly. But in regard to alteration this is true in a certain way and in another way it is not. For it is clear that every alteration occurs by means of the power of the agent who alters. Now the greater this power is, the more it can alter the body. Therefore, since the altering agent has a finite power, the alterable body is subjected to the determinate quantity of its power and receives the impression of the agent all at once. Thus the whole is altered simultaneously and not part by part. But that which is altered further alters something else which is joined to it, although it is less effective as an agent. Thus the power of altering becomes progressively less potent. For example, fire immediately warms one part of the air, and the air which is warmed warms another part. In this way one part is altered after another. Hence, after the text of De Sensu et Sensato quoted above, Aristotle adds, 'But still, for all that, if the body which is heated or frozen is extensive, each part of it successively is affected by the part contiguous, while the part first changed in quality is so changed by the cause itself which originates the change, and thus the change throughout the whole need not take place co-instantaneously and all at once.'

             Nevertheless we must realize that there is a certain succession even in that which is altered all at once. Since alteration occurs by means of the contact of the altering agent, then the parts of the altered body which are closer to the altering agent receive the impression of the altering agent more perfectly at the beginning. And the body arrives at perfect alteration successively according to the order of its parts. This is especially true when there is in the alterable body something which resists the altering agent.

             Hence his conclusion, namely, that that which is changed, while it is changing, is partly in the terminus from which and partly in the terminus to which, as though one part arrives at the terminus to which before the others, is true simply and absolutely for local motion. But in the motion of alteration this is true in a qualified way, as was said.

             803. But some have said conversely that that which is said here applies more to the motion of alteration than to local motion.

             They say that the proposition--'that which is being changed is partly in the terminus from which and partly in the terminus to which'--does not mean that one part of that which is being moved is in one terminus and another part in the other terminus. Rather this proposition refers to the parts of the termini. For that which is being moved has part of the terminus from which and part of the terminus to which. For example, that which is being moved from whiteness to blackness does not primarily have whiteness perfectly nor blackness perfectly. Rather it participates imperfectly in both. But in local motion this is true only insofar as that which is being moved, while it is in between the two extremes, participates in both extremes in a qualified way. For example, if earth is being moved to the place of fire, then while it is being moved through the proper place of air, it has part of each terminus insofar as the place of air is both up in respect to the place of earth and down in respect to the place of fire.

             804. But this explanation is forced and contrary to the opinion of Aristotle.

             This is clear first from Aristotle's own words. For he concludes '. . . it follows, therefore, that part of that which is changing must be at the starting-point and part at the goal' (234 b 15-16). Hence, he is speaking of the parts of the mobile body and not the parts of the termini.

             Secondly, this is clear from his intention. For he is trying to prove that that which is changed is divisible. This could not be concluded from the foregoing explanation. Hence Avempace says that he does not intend here to prove that the mobile body is divisible into quantitative parts, but rather is divisible in respect to its forms. In other words, that which is changed from contrary to contrary, while it is being changed, has part of each contrary. But Aristotle's expressed intention is to show that the mobile body is divisible into its quantitative parts, as is the case with other continua. Furthermore, he uses this point in the following demonstrations.

             Moreover, it does not seem to be true that he proves the divisibility of the mobile body in respect to continuity by means of the divisibility of motion, as some say. For from the fact that the mobile body, while it is being moved, participates in both termini and does not immediately have the terminus to which perfectly, it is clear that mutation is divisible in respect to continuity. And thus, since the divisible cannot be divided into indivisible parts, it also follows that the mobile body is a continuum. In what follows Aristotle clearly establishes the division of motion by means of the division of the mobile body. Hence, if he intends here to conclude to the division of the mobile body from the division of motion, his proof would be circular.

             Thirdly, this explanation seems to be inconsistent with Aristotle's own explanation where he says, 'Here by "goal of change" I mean that which comes first in the process of change . . .' (234 b 17). From this it is clear that he does not mean to say that the mobile body is partly in the terminus from which and partly in the terminus to which because it is in the middle and, as it were, participates in both extremes. Rather he means that in respect to one of its parts the mobile body is in one extreme and in respect to another part it is in the middle.

             805. But when Aristotle in this explanation speaks of 'that which comes first' (234 b 17), there seems to be a difficulty. Because of the infinite divisibility of magnitude, it seems that there cannot be a 'that which comes first'.

             Hence it must be said that 'that which comes first' in local motion is the place which is contiguous to the place from which the body is changed. This place is not part of the first place. If this second place were part of the first place, then it would not be the first place to which the body is moved. This can be made clear as follows. Let A B be the place from which some mobile body is moved. And let B C be an equal place in contact with A B. Since A B is divisible, let it be divided at the point D. Further, let there be marked off in B C, beginning at C, a distance equal to B D. Let this distance be G C. Now it is clear that the mobile body is moved to the place D G before it is moved to the place B C. And further, since A D is divisible, there will be another prior place and so on to infinity.

             And likewise in the motion of alteration there must be a 'that which comes first'. This is an intermediate of another species. For example, when something is changed from white to black, grey, and not less-white, should be taken as the intermediate.