Ἀχλὺν δ' αὖ τοι ἀπ' ὀφθαλμῶν ἕλον, ἣ πρὶν ἐπῆεν.[108]
§ 24. Of the Misapplication of the Law of Causality.
From the foregoing exposition it follows, that the application of the causal law to anything but changes in the material, empirically given world, is an abuse of it. For instance, it is a misapplication to make use of it with reference to physical forces, without which no changes could take place; or to Matter, on which they take place; or to the world, to which we must in that case attribute an absolutely objective existence independently of our intellect; indeed in many other cases besides. I refer the reader to what I have said on this subject in my chief work.[109] Such misapplications always arise, partly, through our taking the conception of cause, like many other metaphysical and ethical conceptions, in far too wide a sense; partly, through our forgetting that the causal law is certainly a presupposition which we bring with us into the world, by which the perception of things outside us becomes possible; but that, just on that account, we are not authorized in extending beyond the range and independently of our cognitive faculty a principle, which has its origin in the equipment of that faculty, nor in assuming it to hold good as the everlasting order of the universe and of all that exists.
§ 25. The Time in which a Change takes place.
As the Principle of Sufficient Reason of Becoming is exclusively applicable to changes, we must not omit to mention here, that the ancient philosophers had already raised the question as to the time in which a change takes place, there being no possibility of it taking place during the existence of the preceding state nor after the new one has supervened. Yet, if we assign a special time to it between both states, a body would, during this time, be neither in the first nor in the second state: a dying man, for instance, would be neither alive nor dead; a body neither at rest nor in movement: which would be absurd. The scruples and sophistic subtleties which this question has evoked, may be found collected together in Sextus Empiricus "Adv. Mathem." lib. ix. 267-271, and "Hypat." iii. c. 14; the subject is likewise dealt with by Gellius, l. vi. c. 13—Plato[110] had disposed somewhat cavalierly of this knotty point, by maintaining that changes take place suddenly and occupy no time at all; they occur, he says, in the ἐξαίφνης (in repentino), which he calls an ἄτοπος φύσις, ἐν χρόνῳ οὐδὲν οὖσα; a strange, timeless existence (which nevertheless comes within Time).
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.
This law of the continuity and gradual taking place of all changes which Aristotle was thus the first to lay down and prove, we find stated three times by Kant: in his "Dissertatio de mundi sensibilis et intelligibilis forma," § 14, in the "Critique of Pure Reason,"[111] and finally in his "Metaphysical First Principles of Natural Science."[112] In all three places his exposition is brief, but also less thorough than that of Aristotle; still, in the main, both entirely agree. We can therefore hardly doubt that, directly or indirectly, Kant must have derived these ideas from Aristotle, though he does not mention him. Aristotle's proposition—οὐκ ἔστι ἀλλήλων ἐχόμενα τὰ νῦν ("the moments of the present are not continuous")—we here find expressed as follows: "between two moments there is always a time," to which may be objected that "even between two centuries there is none; because in Time as in Space, there must always be a pure limit."—Thus Kant, instead of mentioning Aristotle, endeavours in the first and earliest of his three statements to identify the theory he is advancing with Leibnitz' lex continuitatis. If they really were the same, Leibnitz must have derived his from Aristotle. Now Leibnitz[113] first stated this Loi de la continuité in a letter to Bayle.[114] There, however, he calls it Principe de l'ordre général, and gives under this name a very general, vague, chiefly geometrical argumentation, having no direct bearing on the time of change, which he does not even mention.