Aristotle, Metaphysics

[1068b] [1] E.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 perishing¹; 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 .²

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), [20] but the passive quality in virtue of which a thing is said to be acted upon or to be immune from being acted upon.³ 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 sense⁴ 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.⁵ 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.⁶ "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.