LECTURE 7 (228 a 20-229 a 6)

MORE CONCERNING THE NUMERICAL UNITY OF MOTION. TWO SECONDARY TYPES OF UNITY IN MOTION

             703. The Philosopher has stated that three things are required for motion to be one simply; namely, unity of time, unity of that in which there is motion, and unity of subject. Here he intends to prove this.

             'To be one simply' has many meanings. One meaning is to be one as indivisible. Another is to be one as continuous. Motion cannot be called simply one as something indivisible, because no motion is indivisible. Hence it follows that motion is called one as something continuous. For motion to be simply one, it must be continuous. And this continuity of motion is sufficient for its unity. Hence motion is one if it is continuous. Therefore, whatever is required for the continuity of motion is also required for the unity of motion.

             704. Three things are required for motion to be continuous. The first requirement is unity of the species. Every motion cannot be continuous with every other motion. The same applies to other cases of continuity. For not just anything can be continuous with anything else, whatever this other happens to be. Rather those things can be continuous whose extremities are one. This is the definition [ratio] of continuity, as was said above.

             But certain things have no extremities; for example, forms and all indivisible things. Hence there cannot be continuity in such things. There are other things which have extremities and which are divisible and quantified, but they are not the same in name or in nature [ratio]. These things also cannot be continuous. For there can be no contact between any of them. One cannot say that a line and walking touch each other, or that they have one extremity, which is required for them to be continuous.

             From this it is clear that things which belong to different genera and species cannot be continuous with each other.

             Hence, motions which differ in genus or species can be consecutive to each other; thus, someone after running can immediately develop a fever. But the running and the development of the fever are in different genera. And even in the same genus, for example, local motion, one local motion can be consecutive to another but not continuous with it. This occurs in the 'diffusion of the torch'--when the torch is transferred from one hand to another. These diverse motions are not continuous. Or one might understand this as follows. The local motion of the liquid which sustains the flame (which is called 'diffusion') is followed by the local motion of the flame (which is called 'light').

             The above mentioned mutations, which differ in genus or species, are not continuous. For they do not have one extremity, which belongs to the nature [ratio] of continuity. Hence, motions which differ in genus or species can be consecutive to each other, that is, can in some way touch each other, without any interruption of time, insofar as time is continuous. Time is continuous for the same reason [ratio] that motion is continuous, that is, insofar as there is one extremity. For in one instant of time whose parts are continuous, there is nothing to prevent one motion from ending and another motion of a different genus or species from beginning. Such motions will be consecutive, but not continuous. Hence it follows from the foregoing that, for motion to be continuous, it must be one in species. This unity of species is in the motion from the thing in which the motion occurs, insofar as it is indivisible in species.

             705. The second requirement for the continuity of motion is that there be one object. For the motions of different objects can be consecutive, but not continuous, as was said of the torch which is moved by different hands.

             706. The third requirement for the unity and continuity of motion is the unity of time. There can be no intervening state of immobility or rest. If there is an interruption of the time of a motion such that the object is not moved, then it follows that at that time there is rest. For if rest intervenes, there are many motions and not one. Rather than one motion there are many motions between which is rest. Hence, if there is a motion which is interrupted by rest, it is neither one nor continuous. Motion is interrupted by rest if there is time in between, as was shown. Hence, for motion to be continuous, there must be one continuous time.

             Nevertheless this is not enough. Motion which is not one in species is not continuous, even if the time is not interrupted. Although it is one in respect to time, it will be different in respect to species. For motion to be one continuum, it must be one in species. But it does not follow that motion which is one in respect to species is one simply.

             Hence it is clear that all three of the above are required for motion to be one simply. He concludes that he has now explained which motion is one simply.

             707. Next where he says, 'Further, a motion is also . . .' (228 b 12), after having given the three principal modes of unity in motion, he gives two other secondary modes, which pertain to a certain form of unity rather than to unity itself.

             He gives the second secondary mode where he says, 'And besides the cases . . .' (228 b 15).

             He says, therefore, first that motion is said to be one in genus or in species or in substance in the same way that motion is said to be numerically one, that is, because it is completed. Likewise in other cases completeness and wholeness pertain to the nature [ratio] of unity. For we do not speak of one man or one shoe unless it be a whole.

             Sometimes the incomplete, as long as it is continuous, is called one. The reason for this is that oneness can pertain to quantity (and thus only continuity is sufficient for unity) or to substantial form, which is the perfection of the whole (and thus that which is complete and whole is called one).

             708. Next where he says, 'And besides the cases . . .' (228 b 15), he gives the other secondary mode of unity. Motion which is regular or uniform is said to be one, just as in other cases that which is the same in all of its parts is said to be one.

             Concerning this he makes three points. First he states this mode of unity, namely, regular motion is said to be one. Secondly, where he says, 'In every kind of motion . . .' (228 b 19), he shows where regularity and irregularity are found. Thirdly, where he says, 'The difference that makes . . .' (228 b 22), he explains the types of irregularity.

             He says, therefore, first that besides the above mentioned modes of unity, regular or uniform motion is said to be one. For it seems that regular or uniform motion is one rather than irregular or uneven motion. For example, motion which is wholly straight is uniform.

             Irregular motion does not seem to be one because it is divisible into dissimilar parts. But indivisibility belongs to the nature [ratio] of unity, because the one is undivided being. But, nevertheless, irregular motion is in some way one.

             The unity of regular and irregular motion seems to differ in respect to more or less. For regular motion is more one than irregular motion, just as a body of similar parts is more one than a body of dissimilar parts.

             709. Next where he says, 'In every kind of motion . . .' (228 b 19), he shows in what motions regularity and irregularity are found.

             He says that regular and irregular motions are found in every genus and species of motion. Thus, it is possible for a thing to be altered regularly, as when a whole alteration is regular. Also, it is possible for a thing to be moved locally through a regular or uniform magnitude, as when a thing is moved through a circle or a straight line. Likewise there is regular motion in increase and decrease.

             710. Next where he says, 'The difference that makes . . .' (228 b 22), he begins his treatment of irregular motion.

             First he establishes the modes of irregularity. Secondly, where he says, 'Irregular motion, therefore . . .' (229 a 1), he shows how irregular motion is one, as he had said above.

             Concerning the first part he makes two points. First he establishes two modes of irregularity in motion. Secondly, where he says, 'So quickness and slowness . . .' (228 b 28), he draws certain conclusions from this.

             He says, therefore, first that the differentia which causes the irregularity of motion sometimes is due to the thing in which the motion occurs. This is especially clear in local motion. For it is impossible for motion which does not cross through a regular or uniform magnitude to be regular or uniform.

             By a regular or uniform magnitude he means one in which each part uniformly follows another part, and thus any part could be replaced by any other part. This is clearly the case in a circular line and also in a straight line. And an irregular magnitude is one in which some part does not uniformly follow upon another part. A clear case of this is two lines which form an angle. The one line is not joined to the other in a straight line, although the parts of the line are added to each other in a straight line.

             Therefore, both circular and straight motions are regular. But reflex or oblique motions, which make an angle, are not regular and do not occur in a regular magnitude. And there might be some other motion through some other magnitude, some part of which is not uniformly added to some other part. Or one part of the magnitude may not properly touch another part. For if that part which contains the angle is replaced by a part which does not contain an angle, there will be no proper contact.

             711. The second differentia which causes irregularity is not due to the place, nor to the time, nor to that in which the motion occurs (for there is motion not only in place, but also in quality and quantity). This latter can be referred to the object in which there is motion.

             Rather this second mode of irregularity is due to diversity in the manner of the motion. This second mode of irregularity is called speed or slowness. A motion whose speed is the same throughout the whole is called regular. And it is called irregular when one part is faster than the others.

             712. Next where he says, 'So quickness and slowness . . .' (228 b 28), he draws two corollaries from the above.

             The first is that speed and slowness are neither species nor specific differences of motion, because they are found in all species of motion. For speed and slowness are determinations of regularity and irregularity, which are found in every species of motion, as was said above. And no species or differentia is found in every species of its own genus.

             The second corollary is that speed and slowness are not the same as heaviness and lightness. For each of these latter always moves to the same place. Thus, the motion of earth, which is heavy, is always toward its place, which is downward. And the motion of fire is toward its proper place, which is upward. But speed and slowness are found in diverse motions, as was said.

             713. Next where he says, 'Irregular motion, therefore . . .' (229 a 1), he explains how irregular motion is one. Secondly, where he says, 'And since every motion . . .' (229 a 3), he infers a corollary from this.

             He says, therefore, first that irregular motion can be called one insofar as it is continuous. But it is less one than regular motion is, just as a line which has an angle is said to be less one than a straight line. This is especially clear in reflex motion, for it seems that there are, as it were, two motions.

             That which is less one seems to have some kind of multitude. For a thing is less when it has a mixture of its contrary. Thus, that which is less white is mixed in some way with black, at least as approaching it in some way.

             Thus it is clear that irregular motion is both one, insofar as it is continuous, and is also in some way many, insofar as it is less one.

             714. Next where he says, 'And since every motion . . .' (229 a 3), he concludes from the immediate foregoing a point which he had stated above; namely, motions which are diverse in species cannot be continuous. Every motion that is one can be regular or irregular. But a motion which is composed of motions diverse in species cannot be regular. For how could a regular motion be composed of alteration and local motion? For a motion to be regular it is necessary that its parts agree with each other. Therefore, it follows that diverse motions which do not follow each other in the same species are not one continuous motion. This was stated above and was explained with an example.