It was accordingly reserved for the perspicacity of Aristotle to clear up this difficult point, which he has done profoundly and exhaustively in the sixth Book of Physics, chap. i.-viii. His proof that no change takes place suddenly (in Plato's ἐξαίφνης), but that each occurs only gradually and therefore occupies a certain time, is based entirely upon the pure, _à priori_ intuition of Time and of Space; but it is also very subtle. The pith of this very lengthy demonstration may, however, be reduced to the following propositions. When we say of objects that they limit each other, we mean, that both have their extreme ends in common; therefore only two extended things can be conterminous, never two indivisible ones, for then they would be _one_--_i.e._ only lines, but not mere points, can be conterminous. He then transfers this from Space to Time. As there always remains a line between two points, so there always remains a time between two _nows_; this is the time in which a change takes place--_i.e._ when _one_ state is in the first, and _another_ in the second, _now_. This time, like every other, is divisible to infinity; consequently, whatever is changing passes through an infinite number of degrees within that time, through which the second state gradually grows out of that _first_ one.--The process may perhaps be made more intelligible by the following explanation. Between two consecutive states the difference of which is perceptible to our senses, there are always several intermediate states, the difference between which is not perceptible to us; because, in order to be sensuously perceptible, the newly arising state must have reached a certain degree of intensity or of magnitude: it is therefore preceded by degrees of lesser intensity or extension, in passing through which it gradually arises. Taken collectively, these are comprised under the name of _change_, and the time occupied by them is called _the time of change_. Now, if we apply this to a body being propelled, the first effect is a certain vibration of its inner parts, which, after communicating the impulse to other parts, breaks out into external motion.--Aristotle infers quite rightly from the infinite divisibility of Time, that everything which fills it, therefore every change, _i.e._ every passage from one state to another, must likewise be susceptible of endless subdivision, so that all that arises, does so in fact by the concourse of an infinite multitude of parts; accordingly its genesis is always gradual, never sudden. From these principles and the consequent gradual arising of each movement, he draws the weighty inference in the last chapter of this Book, that nothing indivisible, no mere _point_ can move. And with this conclusion Kant's definition of Matter, as "that which moves in Space," completely harmonizes.