<ap1> 2.
ANTICIPATIONS OF PERCEPTION
[B207] The principle of the Anticipations of Perception is: In all appearances, the real which is an object of sensation has intensive quantity, that is, a degree.
<ap2> Proof
Perception is empirical consciousness, that is, a consciousness in which there is also sensation. Appearances, as objects of perception, are not pure or merely formal intuitions like space and time, since space and time cannot be perceived in themselves. So in addition to pure intuition, appearances also contain the material for any object in general, through which something existent will be represented in space or time. This material is that which is real in sensation, and it is therefore a merely subjective representation. The only consciousness we can have of it is that the subject is affected by it, and that we relate it [B208] to an object in general.
<ap3> Now it is possible for there to be a gradual transition from empirical consciousness to pure consciousness, such that the real in empirical consciousness completely disappears, and all that remains is a formal apriori consciousness of the multiplicity in space and time. So it is also possible for there to be a synthesis which generates the quantity of a sensation, starting from a pure intuition = 0, up to any quantity of it whatever. Now this certainly cannot be an extensive quantity, since sensation in itself is not a representation of an object, and it does not include the intuition either of space or of time. Yet the sensation does have a quantity. This quantity is generated through the apprehension of the sensation, and the empirical consciousness of it can grow from nothing = 0, to its given size over a certain time. So it is an intensive quantity. And corresponding to the intensive quantity of sensations, all objects of perception must have an intensive quantity, since they include sensation. This intensive quantity is the degree of influence on the senses.
<ap4> Any knowledge through which one can know and determine apriori anything that belongs to empirical knowledge can be called an ‘anticipation’. Without a doubt, this is the sense in which Epicurus used his expression prolepsis. However, appearances include sensation (as the matter of perception), which can never be known apriori, and which therefore constitutes the essential difference between empirical and apriori knowledge. [B209] It follows that sensation is essentially that which cannot be anticipated at all.
<ap5> By contrast, we could give the name ‘anticipations of appearances’ to pure determinations in space and time (whether in respect of shape or of quantity), because they represent apriori everything that can ever be given in experience aposteriori. But suppose there is also something else which lets itself be known apriori in every sensation, as sensation in general, without any particular sensation being given. This ought to be called an ‘anticipation’ in a more eminent sense, since it seems contradictory to anticipate experience in that which belongs specifically to its matter, which one can extract only through experience. And this is what is actually the case here.
<ap6> In so far as apprehension is through sensation alone, it takes place in an instant (here I am not talking about a succession of many sensations). So it is an element of appearance which has no extensive quantity, since its apprehension is not a successive synthesis proceeding from parts to a whole representation. The absence of sensation in the same instant would represent the instant as empty, and hence = 0. Now the element of empirical intuition which corresponds to sensation is (phenomenal) reality; and that which corresponds to the lack of it is negation = 0. But every sensation [B210] is capable of diminution, and can decrease and gradually disappear. So in appearance, there is a continuous chain of many possible intermediate sensations between reality and negation; and the difference between these intermediate sensations is always less than the difference between any given sensation and zero, or utter negation. In other words, that which is real in appearance always has some quantity, even if it is not apprehended. This is because its apprehension takes place by means of sensation alone in an instant, and not through the successive synthesis of many sensations; and hence it does not proceed from parts to a whole. So it does indeed have a quantity; but not an extensive one.
<ap7> Now I call an intensive quantity any quantity which is apprehended only as a unity, and the quantifiability of which can be represented only as its distance from negation = 0. So everything that is real in appearance has an intensive quantity, or a degree. This reality can be considered as a cause — whether of sensation, or of some other reality in appearance, such as an alteration. In such cases, the degree of reality as cause is called a ‘moment’, for example, the ‘moment of gravity’. And the reason for this is precisely because the degree denotes only a quantity which is apprehended instantaneously, and not successively. But I touch on this here only in passing, since I am not yet dealing with causality.
<ap8> [B211] It follows that every sensation, and hence every reality in appearance, has a degree, however small it might be. Its degree is an intensive quantity, which can always become even smaller; and between reality and negation there is a continuous chain of possible realities, and of possible smaller perceptions. Every colour (for example red) has a degree, which, however small, is never the smallest possible; and the same holds universally, with heat, the moment of gravity, etc.
<ap9> The property of quantities which means that they have no smallest possible part (or no simple part) is called their continuity. Space and time are continuous quanta, because no part of them (points or instants) can be given, except as being contained between boundaries, and hence only in such a way that this part itself is again a space or a time. So space consists only of spaces, and time consists only of times. Points and instants are only boundaries, or positions defined by the limitation of space and time. But positions always presuppose the intuitions which must limit or define them. Neither space nor time can be put together out of mere positions, as component parts which could be given even before space or time. Continuous quantities can also be called flowing, because the synthesis (by the productive imagination) involved in their production is a process in time, and its continuity [B212] is usually given special emphasis through the term ‘flowing’ (or ‘elapsing’).
<ap10> Consequently, all appearances without exception are continuous quantities. They are extensive with respect to their intuition, and intensive with respect to their mere perception (or sensation, and hence their reality). If the synthesis of the multiplicity of appearances is interrupted, then the multiplicity is an aggregate of many appearances, and not essentially an appearance as a quantum. This aggregate is produced not through the simple continuation of productive synthesis of a certain sort, but through the repetition of a constantly ceasing synthesis. If I call 13 dollars a quantum of money, I do so correctly as long as I mean the value of a particular weight of fine silver. This is certainly a continuous quantity, since there is no smallest part, and every part could make up a coin containing enough matter for an even smaller one. But if by what I call 13 dollars I mean 13 round 1-dollar coins (whatever their silver content), then I am wrong to call it a quantum of dollars. Instead, I must call it an aggregate — that is, a number of coins. Now since unity must lie at the basis of all number, appearance as unity is a quantum, and as such it is always a continuum.
<ap11> Now if all appearances are continuous quantities, whether considered as extensive or as intensive ones, it might be thought easy to prove here, with mathematical self-evidence, [B213] the proposition that all alteration (the transition of a thing from one state to another) is also continuous. However, the causality of an alteration in general lies quite outside the limits of a transcendental philosophy, and presupposes empirical principles. For the understanding gives us no apriori information at all as to whether it is possible for there to be a cause which changes the state of the thing — that is, which determines it to the opposite of a certain given state. This is not simply because the understanding has no insight into its possibility, since we lack such insight in many cases of apriori knowledge. Rather, it is because alterability concerns only certain determinations of appearances; and only experience can tell us about these determinations; whereas their cause lies in that which is unalterable. Here we have before us nothing we can use except the pure basic concepts of all possible experience, which must exclude everything empirical. Consequently, we cannot prejudge general natural science without damaging the unity of our system, since this science is founded on certain basic experiences.
<ap12> However, we do not lack evidence of the great contribution this axiom of ours makes to anticipating perceptions. It even makes up for lack of perceptions, by ruling out false conclusions which might be drawn from their absence.
<ap13> [B214] Everything which is real in perception has a degree, and between that degree and nothing there is an infinite series of smaller and smaller degrees. Similarly, every one of our senses must have a particular degree of sensitivity to sensations. On these assumptions, there can be no perception, and hence also no experience, which could prove a total lack of any reality in the realm of appearance, whether directly or indirectly (however complicated the reasoning). In other words, experience can never provide any proof of empty space or an empty time. For firstly, a complete lack of reality in sensory intuition can never itself be perceived. And secondly, it cannot be deduced from any single appearance and the differentiation in its degree of reality. Nor is it ever legitimate even to assume it in order to explain the differentiation.
<ap14> Let us suppose that the whole intuition of a particular space or time is real through and through — i.e. no part of it is empty. Now every reality has its degree, which can reduce to nothing (emptiness) through infinitely many steps, while the extensive quantity of the appearance remains constant. Consequently, there must be infinitely many degrees with which space or time is filled. So the intensive quantity can be more or less in different appearances, even though the extensive quantity of the intuition is the same.
<ap15> [B215] I should like to give an example of this. There is a great difference in the quantity of various kinds of matter occupying the same volume. We perceive this difference partly through their moment of gravity, or weight; and partly through their moment of resistance to other matter colliding into them. Nearly all physicists agree in concluding that this volume (the extensive quantity of the appearance) must, in all kinds of matter, be empty to a greater or lesser extent.
<ap16> These scientists are mostly mathematicians and mechanists, who strongly assert that metaphysics should be avoided. But which of them ever realised that they were basing their conclusion merely on a metaphysical assumption? For they assume that the real in space (here I should not call it impenetrability or weight, since these are empirical concepts) is the same everywhere, and that it can be differentiated only by virtue of its extensive quantity, or amount.
<ap17> This assumption is merely metaphysical, because it cannot have any foundation in experience; and I shall counter it with a transcendental proof. Admittedly, my proof cannot explain the different ways in which space is filled. On the other hand, it completely destroys the supposed necessity of the assumption that the differentiation can be explained only by supposing that there are empty spaces. It also has the merit of at least giving the understanding the freedom to think about this differentiation in an alternative way, [B216] in case scientific explanation requires some new hypothesis to explain it.
<ap18> Two spaces having the same volume can be completely filled with matter of different kinds, so that there is no point in either of them where its matter is not present. Nevertheless, we see that what is real in each has its own degree in respect of the above-mentioned qualities of resistance or weight. Without any diminution in extensive magnitude or amount, this degree can become infinitely smaller, before it crosses over into emptiness, and disappears. Consider anything which can spread around and fill a space, for example, warmth — and similarly every other reality in the realm of appearance. Without leaving even the tiniest part of this space empty, it can diminish infinitely in its degree, and yet fill the space with this lesser degree just as much as a different appearance fills it with a larger one.
<ap19> It is certainly not my intention here to claim that this is the actual explanation of why different kinds of matter have different specific gravities. It is merely to establish, on the basis of an axiom of pure understanding, that:
<ap20> [B217] Nevertheless, there must always be something shocking about this anticipation of perception for researchers who are used to the transcendental approach, and have therefore become cautious. They will doubt whether the understanding can anticipate a synthetic proposition like the one about the degree of everything which is real in appearances. They will therefore also doubt the possibility of the inner differentiation of sensation itself, when its empirical quality is left out of account. Thus there remains a question which deserves an answer, namely: how can the understanding make synthetic apriori pronouncements about appearances, and how can it anticipate them even in what is essentially only empirical, namely that which belongs to sensation?
<ap21> The quality of sensation (e.g. colours, taste, etc.) is always merely empirical, and can certainly not be represented apriori. However, the real which corresponds to sensations in general (in contrast to negation = 0) does represent something; but its concept is essentially only that of a being, and it signifies nothing other than synthesis in an empirical consciousness in general. That is to say, in inner sense, empirical consciousness can range from zero to any higher degree, so that a single extensive quantity of intuition (e.g. an illuminated surface) can excite the same quantity of sensation as an aggregate of many other less illuminated ones together. Thus we can leave the extensive quantity of the appearance [B218] completely out of account, and still represent, in pure sensation at an instant, a synthesis of the uniform increase from zero up to the degree of empirical consciousness as given. Hence all sensations as such are indeed given only aposteriori; but their property of having a degree can be known apriori.
<ap22> It is remarkable that, in the case of quantities in general, we can know just one quality, namely their continuity. Whereas in the case of all quality (that which is real in appearances), we can know apriori only their intensive quantity, namely that they have a degree. Every thing else is left to experience.