Aristotle (Phys. IV. 9) now comes to the second point, to the proof of the vacuum because of the difference in specific gravity. “Many believe that the vacuum exists because of the rare and the dense;” the former is said to be a rare body, and the latter a perfect continuity; or they at least differ quantitatively from one another through greater or less density. “For if air should be generated from a quantity of water, a given quantity of water must produce a quantity of air the same in bulk, or there must necessarily be a vacuum; for it is only on the hypothesis of a vacuum that compression and rarefaction are explicable. Now if, as they say, the less dense were that which has many separate void spaces, it is evident that since a vacuum cannot be separated any more than a space can have intervals, neither can the rare subsist in this manner. But if it is not separable, and yet a vacuum is said to exist in the body, in the first place movement could thus only be upwards; for the rare is the light, and hence they say that fire is rare,” because it always moves upwards. “In the next place the vacuum cannot be the cause of motion as that in which something moves, but must resemble bladders that carry up that which adheres to them. But how is it possible that a vacuum can move, or that there can be a place where there is a vacuum? For that into which it is carried would be the vacuum of a vacuum. In short, as there can be no movement in vacuum, so also a vacuum cannot move.” Aristotle set against these ideas the true state of matters, and states generally the ideal conception of nature: “that the opposites, hot and cold, and the other physical contraries, have one and the same matter, and that from what is in capacity that which is in energy is produced; that matter is not separable though it is different in essence[94] (τῷ εἶναι), and that it remains one and the same in number (ἀριθμῷ) even if it possesses colour, or is hot and cold. And again, the matter of a small body and a large is the same, because at one time a greater proceeds from a smaller, and at another time a smaller from a greater. If air is generated from water it is expanded, but the matter remains the same and without taking to itself anything else; for that which it was in capacity it becomes in actuality. In a similar way if air is compressed from a greater into a less volume, the process will be reversed, and air will similarly pass into water, because the matter which is in capacity both air and water, also becomes both.” Aristotle likewise asserts that increase and decrease of warmth, and its transition into cold, is no addition or otherwise of warm matter, and also one and the same is both dense and rare. This is very different from the physical conceptions which assert more or less matter to correspond with more or less density, thus comprehending the difference in specific weight as the external addition of matter. Aristotle, on the contrary, takes