Now since the categories are distinguished as substance, quality, place, activity or passivity, relation and quantity,¹ there must be three kinds of motion, in respect of quality, quantity and place. There is no motion² in respect of substance, because substance has no contrary; nor of the relative, because it is possible that when one of two related things changes the relation to it of the other thing, even though the thing itself does not change, may become untrue; therefore the motion of these related things is accidental. Nor is there motion of the agent or patient, or of the mover and the thing moved, because there is no motion of motion nor no generation of generation, nor in general is there change of change. There are two ways in which there might be motion of motion: (1) Motion might be the subject of motion, as, e.g., a man is moved because he changes from white to black; in this way motion might be heated or cooled or might change its place or increase. But this is impossible, because the change is not a subject. Or (2) some other subject might change from change to some other form of existence, as, e.g., a man changes from sickness to health. But this is also impossible except accidentally. Every motion is a change from one thing into something else; and the same is true of generation and destruction, except that these are changes into opposites in one sense,³ while the other, i.e. motion, is a change into opposites in another sense.⁴ Hence a thing changes at the same time from health to sickness, and from this change itself into another. Now clearly if it has fallen ill it will be already changed (for it cannot remain at rest) into that other change, whatever it may be; and further this cannot be, in any given case, any chance change; and it also must be from something into something else. Therefore it will be the opposite change, viz. becoming healthy. But this is so accidentally; just as there is change from recollecting to forgetting because the subject changes, now in the direction of knowledge and now in that of ignorance. Further, we shall have an infinite series if there is to be change of change and becoming of becoming, because if the latter of two becomings comes to be from the former, the former must come to be too. 1068bE.g., if simple becoming was once coming to be, that which comes to be something was also once coming to be. Therefore that which simply comes to be was not yet, but there was already something coming to be coming to be something. But this too was at one time coming to be, and therefore it was not at that time coming to be something. But in infinite series there is no first term, and therefore in this series the first term cannot exist, nor can any subsequent term. Therefore nothing can be either generated or moved or changed. Further, the same thing which admits of motion admits also of the contrary motion and of rest, and that which admits of generation admits also of destruction. Therefore that which comes to be, when it has come to be coming to be, is then in course of perishing⁵; for it does not perish as soon as it is coming to be coming to be, nor afterwards, because that which is perishing must exist .⁶ Further, there must be some matter underlying that which is coming to be or changing. What then will it be? What is it that becomes motion or generation in the same way as it is body or soul that undergoes change? And moreover what is that which is the terminus of the motion? For that which we are considering must be a motion or generation of A from B into C. How then can these conditions be fulfilled? There can be no learning of learning, and therefore there can be no generation of generation. Since there is no motion of substance or of the relative or of activity and passivity, it remains that there is motion in respect of quality, quantity and place; for each of these admits of contrariety. By “quality” I mean not that which is in the substance (for indeed even the differentia is a quality), but the passive quality in virtue of which a thing is said to be acted upon or to be immune from being acted upon.⁷ The immovable is either that which is wholly incapable of being moved, or that which is scarcely moved in the course of a long time or is slow in starting, or that which would naturally be moved but cannot be moved at the time when and from the place whence and in the way in which it would naturally be moved. This last is the only kind of immovable thing which I recognize as being at rest; for rest is contrary to motion, and so must be a privation of that which admits of motion. Things are “together in place” which are in the primary sense⁸ in one place, and “separate” which are in different places. “Contrary in place” is that which is at a maximum distance in a straight line.⁹ Things are said to be “in contact” whose extremes are together in place. An “intermediate” is that at which a changing thing which changes continuously in accordance with its nature naturally arrives before it arrives at the extreme into which it is changing. Since all change takes place between opposites, and these are either contraries or contradictories, and contradictories have no middle term, clearly it is to the sphere of contraries that the intermediate belongs.¹⁰ “Successive” is that which comes after the beginning (the order being determined by position or form or in some other way) and has nothing of the same class between itself and that which it succeeds; e.g. lines in the case of a line, and units in that of a unit, and a house in the case of a house (but there is nothing to prevent something else from coming between). For that which is successive is a thing which is successive and posterior to some other thing. 1069a1 is not successive to 2, nor is the new moon¹¹ to the second day of the month. “Contiguous” is that which is successive and in contact. The “continuous” is a species of the contiguous. I call two things continuous when their respective boundaries, by which they are kept together in contact, become one and the same; hence clearly the continuous belongs to the sphere of things whose nature it is to become one by contiguity. Clearly “successive” is the most ultimate term; for the successive need not be in contact, but contact implies succession; and if there is continuity there is contact, but if there is contact there is not necessarily continuity; and where there is no contact there is no coalescence. Therefore a point is not the same as a unit; for points admit of contact, whereas units do not, but only of succession; and between points there is something intermediate, but between units there is not.