<2a1> B

<2a2> Proof

(The previous axiom has shown that absolutely every appearance of temporal succession is only an alteration — that is, a successive being and not-being of determinations of a substance which persists throughout the succession. Consequently, the being of the substance itself cannot follow its not-being, nor can its not-being follow its being. In other words, [B233] a substance cannot begin or cease to exist. The principle could also have been formulated as follows: Every change (succession) of appearances is only an alteration. For if a substance began or ceased to exist, this would not be an alteration to it, because the concept of alteration presupposes one and the same subject as existing with two mutually exclusive determinations, and hence as persisting. After this preliminary note, the proof follows.)

<2a3> I perceive that appearances follow one another — i.e. that the state of things at a given time is contrary to their previous state. So what I am essentially doing is to combine two perceptions in time. Now combining is not the work of sensation by itself, or of intuition, but here it is the product of a synthetic capacity of the imagination, which determines inner sense in respect of relationship in time. However, it can combine these two states in two ways, so that either the one or the other comes first in time. This is because time cannot be perceived in itself, and it is impossible to determine what comes first and what follows in the object by reference to time in a quasi-empirical way.

<2a4> So all I am conscious of is the fact that my imagination puts one first and the other second, and not that the one state precedes the other in the object. In other words, the objective relationship between the appearances which follow one another remains [B234] undetermined through perception by itself. Now in order for it to be known as determined, the relationship between the two states must be thought, in such a way that it is thereby determined as necessary which of them must be put first and which second, rather than the other way round. But the only sort of concept which carries with it a necessary synthetic unity is a pure concept of the understanding, which is not to be found in perception.

<2a5> In the present case, it is the concept of the relation of cause and effect. Of these, the cause determines the effect in time, as that which follows, and not as something which could come first (or even not be perceived at all), as would be the case if only the imagination were involved. So experience (i.e. empirical knowledge of appearances) is possible only through our subjecting the succession of appearances, and hence all alterations, to the law of causality. Hence appearances themselves, as objects of experience, are possible only in accordance with just this law.

<2a6> The apprehension of the multiplicity of appearance is always successive. The representations of its parts follow one after another. It is quite a separate question, not yet raised, whether the representations are also successive in the object.

<2a6> Now we can, of course, call anything an ‘object’, in so far as we are conscious of it — and this even includes any representation whatever. But there is a deeper question as to what this word means when it is applied to [B235] appearances — not in so far as they are objects by virtue of being representations, but only in so far as they represent an object. In so far as they are at the same time objects of consciousness (simply as representations), they are no different from apprehension, i.e. being included in the synthesis of imagination. And so it must be said that the multiplicity of appearances is created successively at every instant in the mind.

<2a7> If appearances were things in themselves, no-one would be able to use the successiveness of the multiplicity of representations to work out how the multiplicity was connected in the object. For we are limited to our representations; and the way in which things in themselves might exist is entirely out of our sphere of knowledge, without reference to the representations through which they affect us. Appearances are not things in themselves; but nothing else can be given to us for knowledge.

<2a8> Nevertheless, I must show what belongs to the multiplicity of appearances itself in order for it to be connected in time, given that the representation of the multiplicity in apprehension is always successive at any given time. For example, the apprehension of the multiplicity in the appearance of a house which stands before me is successive. The question is whether the multiplicity of this house is also in itself successive — which obviously no-one will accept. But as soon as I elevate my concepts [B236] of an object to a transcendental sense, the house is not a thing in itself, but only an appearance, i.e. a representation of which the transcendental object is unknown.

<2a9> So what do I mean when I ask how the multiplicity might be unified in the appearance itself (even though it is nothing in itself)? Here, whatever belongs to the successive apprehension is considered as a representation; whereas the appearance which is given to me (although it is nothing other than a collection of such representations), is considered as their object; and it is to this object that my concept (which I derive from the representations of apprehension) must correspond.

<2a10> Since truth consists in correspondence between knowledge and its object, we can immediately see that here we are concerned only with the formal conditions of empirical truth. An appearance (as contrasted with the representations of apprehension) can be represented through them, as their object distinct from them, only if it stands under a rule which distinguishes it from every other apprehension, and makes necessary a single way of unifying the multiplicity. That in the appearance which contains the condition of this necessary rule of apprehension is the object.

<2a11> Now let us continue with our task. Something happens when there comes into being a thing, or a state of a thing, which did not previously exist. But it cannot be empirically perceived that something happens, [B237] unless there is a preceding appearance which does not include this state. For an actuality which follows an empty time, and hence a coming into existence which is not preceded by any state of things, can no more be apprehended than empty time itself. Thus every apprehension of an event is one perception following another. But since this is what happens in every synthesis of apprehension (as I showed above with the appearance of a house), it does not yet serve to distinguish an event from other cases.

<2a12> But I also note the following. In an appearance which involves an event, let us call the earlier state of the perception A, and the later state B. Then B can only follow A in apprehension, and the perception A cannot follow B, but can only precede it. For example, I see a ship drifting along with the current. My perception of its position downstream in the course of the river follows my perception of its position upstream, and in the apprehension of this appearance, it is impossible for the ship to be perceived first downstream and then upstream. The order in the sequence of perceptions in the apprehension is determined as such, and the apprehension is tied to this order.

<2a13> In the earlier example of a house, my perceptions could begin with the apprehension of the top and end with the bottom, or equally [B238] begin from the bottom and end with the top. Similarly, my perceptions could apprehend the multiplicity of empirical intuition starting from the right, or starting from the left. So in this sequence of perceptions there was no determinate order making it necessary where I had to begin my apprehension in order to combine the multiplicity empirically. Whereas there is always such a rule in perceptions of events; and this rule makes the order of successive perceptions (in the apprehension of such an appearance) a necessary order.

<2a14> So, in the case we are considering, I must derive the subjective succession of apprehension from the objective succession of appearance, because otherwise the subjective succession is completely indeterminate, and does not distinguish any one appearance from any other. By itself, subjective succession proves nothing about the connection of the multiplicity in the object, because it is completely arbitrary. Thus the objective connection will consist in an order of the multiplicity of appearance, such that the apprehension of an event follows the apprehension of what precedes it in accordance with a rule. This is the only way I can be justified in saying that appearance itself contains a succession, and not merely my apprehension — which amounts to saying that I can order the apprehension only with precisely this succession.

<2a15> So in accordance with such a rule, that which precedes an event (taken as a universal) must contain the precondition [B239] for a rule in accordance with which this event always and necessarily follows. On the other hand, I cannot argue backwards from the event, and determine, through apprehension, precisely what precedes it. For no appearance goes back from a later point in time to the preceding one, though it does relate to some or other previous point in time. By contrast, the advance from a given time to the determinate following time is necessary. Hence, because there is still something which follows, I must necessarily relate it to something else in general which precedes it, and from which it follows in accordance with a rule — i.e. necessarily. Consequently, the event, as that which is preconditioned, clearly indicates that there is some precondition or other; but it is this precondition that determines the event.

<2a16> If it is supposed that an event is not preceded by anything which it must follow in accordance with a rule, then every succession of perceptions would be determined only arbitrarily in apprehension — i.e. merely subjectively. And this would certainly not determine objectively which of the perceptions must really be the preceding one, and which the following one. On this supposition, we would have only a play of representations, which would not relate to any object at all. That is, our perception would provide no distinction whatever between one appearance and any other on the basis of their time-relations. This is because the successiveness in apprehending would always be the same, and thus there would be nothing in the appearance which determined the successiveness so as to make a [B240] particular succession necessary by virtue of being objective. So I would not be able to say that, in the realm of appearance, two states of affairs follow each other; but only that one apprehension follows another. This is merely something subjective, and it does not determine any object. Consequently, it cannot count as knowledge of any sort of object — not even in the realm of appearance.

<2a17> So if we experience that something happens, we always presuppose that it follows from something preceding it, in accordance with a rule. For otherwise I would not be attributing the succession to an object, because mere succession in my apprehension is no evidence for any succession in the object, unless it is determined through a rule relating it to something which went before. So it is always the case that I make my subjective synthesis of apprehension objective by reference to a rule, in accordance with which appearances are determined by their previous state as far as their successiveness is concerned — that is, as they actually happen. Only under this assumption alone is it possible for there to be any experience of something happening.

<2a18> It certainly seems that this contradicts everything that has always been said about the way we apply our understanding. The usual account is that we are first led to discover a rule only by perceiving and comparing many sequences of events following in the same way from preceding appearances; [B241] and according to this rule, certain events always follow certain appearances. This is what first stimulates us to construct for ourselves the concept of cause. But on this footing, the concept would be merely empirical, and the rule it supplies (namely that everything that happens has a cause) would be just as contingent as experience itself. The universality and necessity of the rule would then be only spurious, and have no genuine universal validity, since they would not have an apriori foundation, but would depend only on induction.

<2a19> Here the case is the same as with other pure apriori representations, such as those of space and time. We can extract them from experience as clear concepts only because we have put them into experience, and hence used them to bring experience about in the first place. I admit that this representation of a rule determining the sequence of events can attain the logical clarity of a concept of cause only after we have applied it to experience. However, acceptance of the rule, as a precondition of the synthetic unity of appearances in time, was the foundation of experience itself, and therefore preceded it apriori.

<2a20> So in the present case, it is important to show that, even in experience, we never attribute a succession (of an event, in which something happens which previously did not exist) to an object, and distinguish it from the subjective succession of our [B242] apprehension, except on the basis of a rule which necessitates us to observe just this order of perceptions rather than some other order. Indeed, this necessitating is essentially what first makes possible the representation of a succession in the object.

<2a21> We have representations within us, and we can also become conscious of them. But however widely this consciousness might extend, and however exact and precise it might be, there still always remain only representations — that is, inner determinations of our mind in this or that time-relation. So how do we come to provide an object for these representations? Or how do we come to attribute to them some unknown kind of objective reality, over and above their subjective reality as modifications?

<2a22> Objective reference cannot consist in a relationship with another representation, i.e. a representation of what we would want to call an ‘object’. For the same question recurs: how does this second representation in turn get outside itself, and acquire objective reference, over and above the subjective reference which is proper to it as a determination of the state of the mind? So let us consider what sort of new nature is given to our representations by relation to an object, and what status they acquire as a result. We find that all it does is to necessitate us to combine the representations in a particular way, and to subject them to a rule. Conversely, they acquire objective reference only because [B243] a particular order in the time-relations of our representations is necessary.

<2a23> In the synthesis of appearances, the multiplicity of representations is always successive. So far, no object at all is represented, because nothing is distinguished from anything else through this successiveness, since it is common to all apprehensions. But as soon as I perceive or assume that, in this succession, there is a relation to the preceding state, such that the representation follows from that state in accordance with a rule, then something is represented as an event, or as something that happens. In other words, I know an object, which I must locate at a certain determinate position in time; and because of the preceding state, I cannot locate it at any other position.

<2a24> So when I perceive that something happens, the first thing contained in this representation is that something preceded it. For it is precisely in relation to what preceded it that the appearance obtains its time-relation — namely its existing after a preceding time in which it did not exist. But it can obtain its determinate position in this time relation only in so far as the previous state presupposes something by virtue of which it always follows — i.e. in accordance with a rule. From this it turns out, firstly, that I cannot reverse the sequence, and place what happens before what it follows from. Secondly, it turns out that, if the state which precedes [B244] is assumed, then this particular event follows inevitably and necessarily.

<2a25> This is how it comes about that there is an order among our representations. In this order, the present, in so far as it has come into being, indicates some preceding state or other, as a still undetermined correlate of the given event. But the correlate has a determining relationship to the given event as its successor, and it necessarily connects it to itself in the time-series.

<2a26> Let as assume, then, that it is a necessary law of our sensibility, and hence a formal precondition of all perceptions, that the earlier time necessarily determines the later time, since I can arrive at the succeeding time only through the preceding one. Then it will also be an inexorable law of the empirical representation of the time-series, that appearances at an earlier time determine every existence at the following time. Furthermore, these last, as events, can occur only in so far as the earlier appearances determine their existence in time — that is, establish it in accordance with a rule. For it is only through appearances that we can have empirical knowledge of this continuity in the interconnection of times.

<2a27> Understanding is required for all experience, and for the possibility of experience. The first thing it does to it is not to make the representation of objects clear, but to make possible the representation of an object in general. Now it does this [B245] by applying the time-order to appearances and their existence, assigning to each of them, as a succeeding appearance, a position in time determined apriori by reference to preceding appearances. If it did not do this, the appearances would not correspond to time itself, which determines the position of all its parts apriori.

<2a28> Now since time is not an object of perception, this determination of position in time cannot be derived from the relation of appearances to absolute time. Rather, the reverse is the case, and appearances must themselves determine each other’s position in time, and make it a necessary position in the time-order. In other words, that which follows or happens must follow, in accordance with a universal rule, from what was contained in the previous state. This gives rise to a sequence of appearances, which, thanks to the understanding, brings about, and makes necessary, exactly the same order and continuous interconnection in the sequence of possible perceptions, as is met with apriori in the form of intuition (time), in which all perceptions must have their position.

<2a29> That something happens is therefore a perception which belongs to a possible experience. This possible experience becomes actual when I regard the appearance as having a determinate position in time, and hence as an object which can always be found in the interconnection of perceptions in accordance with a rule. [B246] But this rule for determining something in accordance with the time-sequence is as follows: the precondition for an event to follow always (i.e. necessarily) is to be found in what precedes it. So the principle of sufficient reason is the foundation of possible experience, that is, of the objective knowledge of appearances, in respect of their relationship in the sequence of time.

<2a30> The proof of the principle of sufficient reason depends solely on the following stages. All empirical knowledge requires the synthesis of the multiple through the imagination, and it is always successive — i.e. the representations in it always follow one after another. But in the imagination, the order of the sequence (what must come first and what must follow) is quite undetermined, and the series of one representation following another can equally well be taken forwards or backwards.

<2a31> But if this synthesis is a synthesis of the apprehension of the multiplicity of a given appearance, then the order in the object is determined — or to be more precise, this apprehension contains an order of successive synthesis which determines an object. In accordance with this order, something necessarily precedes, and if it is given, the other must necessarily follow. So if my perception is to include knowledge of an event (i.e. knowledge that something actually happens), then it must be an empirical judgment including the thought that the sequence is determined. In other words, it includes the thought that it presupposes another appearance in [B427] time, upon which it follows necessarily, or in accordance with a rule. By contrast, if I supposed the preceding appearance without the event following from it necessarily, then I would have to take it as only a subjective play of my images; and if I still represented it to myself as something objective, I would have to call it a mere dream.

<2a32> The relation between appearances (as possible perceptions) such that the existence of the succeeding appearance (the event) is determined in time, necessarily and in accordance with a rule, by something preceding it, is the relation of cause and effect. This relation is the precondition of the objective validity of our empirical judgments as to the sequence of perceptions, and hence of their empirical truth, and thus of experience. Hence the axiom of the causal relation in the series of appearances is also valid for all objects of experience (since they are all subject to the preconditions of succession), because it is itself the basis of the possibility of such an experience.

<2a33> But here there arises yet another doubt which needs to be removed. As I have formulated it, the axiom of causal connection among appearances is restricted to successive appearances. But it so happens that the axiom also applies to appearances which coexist; and cause and effect can be simultaneous. For example, there is warmth in a room, which is absent from the open air outside. [B248] I look around for the cause, and I find a heated stove. Now the stove, as cause, is simultaneous with its effect, the warmth of the room. So here there is no sequence in time between the cause and the effect. They exist simultaneously, yet the law still holds.

<2a34> The large majority of efficient causes in nature are simultaneous with their effects, and the only reason why the effects are successive in time is because the cause cannot achieve its whole effect in a single instant. But at the instant when the effect first begins, it is always simultaneous with the causality of its cause. This is because, if the cause had ceased to exist an instant earlier, then the effect would not come into existence at all.

<2a35> Here it should be carefully noted that it is a question of order in time, and not of the passage of time: the causal relation remains, even though no time has passed. The time between the causality of the cause and its direct effect can be vanishingly small, so that they are simultaneous. But the time-relation between the one and the other nevertheless always remains determinable. Suppose there is a bullet lying on a stuffed cushion, and pressing a hollow into it. If I consider the bullet as cause, then it is simultaneous with its effect. However, I still distinguish between the one as cause and the other as effect, by virtue of the time-relation of the dynamic connection between the two. For when I place the bullet on the cushion, the hollow follows on from the previously smooth shape of the cushion. But if, for whatever reason, [B249] the cushion has a hollow in it, a lead bullet does not follow on from the hollow.

<2a36> Therefore successiveness in time is certainly the only empirical criterion for distinguishing the effect from the causality of the cause, which precedes it. A glass is the cause which makes water in it rise higher than its horizontal level, although both appearances exist simultaneously. For as soon as I scoop water out of a larger container into the glass, something happens next, namely the alteration of the horizontal surface which the water had in the container, into the concave one which it takes on in the glass.

<2a37> This causality leads to the concept of action; that of action to the concept of power; and that of power to the concept of substance. Since my critical project is concerned only with the sources of synthetic apriori knowledge, I shall not overload it with analyses which involve merely the explanation of concepts, rather than their expansion. So I reserve the detailed exposition of these concepts for a future work to be called the System of Pure Reason — although a large proportion of such an analysis is already to be found in the existing well-known textbooks of this sort. However, there is just one concept which I cannot avoid discussing here. This is the empirical criterion for something to be a substance, in so far as it seems to reveal itself better and more easily through its activity than through the permanence of the appearance.

<2a38> [B250] Wherever there is action (and hence activity and power), there is also substance; and it is in substance alone that the seat of that fruitful source of appearances is to be looked for. So far so good. But if we are to clarify what is meant by ‘substance’ without falling into a vicious circle, it is not so easy to give an answer. How can we conclude directly from an action to the permanence of that which acts? After all, this is such an essential and distinctive criterion for something to be a substance (as phenomenon). However, after what I have already said, the answer to this question is not so difficult, even though it would be completely insoluble using the usual method of proceeding with one’s concepts purely analytically.

<2a39> ‘Action’ already denotes the relation of the subject of causality to its effect. Now every effect is an event, and hence exists in what is changeable, which indicates time through its successiveness. Consequently, the ultimate subject of the changeable is the permanent, as the substrate of everything that changes — in other words, it is substance. For according to the axiom of causality, events are always the ultimate source of all change of appearances. So they cannot belong to a subject which itself changes, because other actions and another subject would then be required to determine the change of appearances.

<2a40> Now by virtue of the above, action is a sufficient empirical criterion for proving substantiality, [B251] without my first having to check its permanence by comparing perceptions. Besides, the method of comparing perceptions would not achieve the completeness required by the greatness and strict universal validity of the concept of substance. For the ultimate subject of the causality of all coming to be and ceasing to be cannot itself come in or out of being (within the realm of appearances). This is a safe conclusion, which leads to empirical necessity and permanence in existence, and hence to the concept of a substance as appearance.

<2a41> When something happens, its mere coming into being, without reference to what it is that comes into being, is already in itself something to investigate. The one thing we must already investigate is the transition from the non-existence of a state to its existence, assuming that the state also contains no quality in the appearance. This coming into being, as I showed in the First Analogy, does not involve substance (since it does not come into being), but its state. So it is merely an alteration, and not a coming into being out of nothing.

<2a42> If this coming into being is considered as the effect of an external cause, then it is called ‘creation’. But such an event cannot be allowed among appearances, since its possibility alone would already destroy the unity of experience. On the other hand, if I consider all things, not as phenomena, but as things in themselves, and as objects [B252] of understanding alone, then, although they are substances, they can be thought of as depending for their existence on an external cause. But then our words would carry very different meanings, and they would not be applicable to appearances as possible objects of experience.

<2a43> Apriori, we do not have the least idea of how, in general, anything can be altered — that is, of how a state at one instant can be followed by a contrary one at another instant. For this we require knowledge of actual powers, which can be given only empirically — for example, motive powers, or (which comes to the same thing) appearances following one another in the particular way which constitutes motion, and which indicates such powers. But let us leave aside the content of any alteration (i.e. the state which is altered, whatever it might be), and consider its form. This form is the precondition for any alteration to take place as the coming into being of another state. Consequently, the successiveness of the states themselves (the event) can still be considered apriori in accordance with the law of causality and the preconditions of time.*

<2a44> [B253] When a substance goes from one state a to another b, the point in time of the second is different from the point in time of the first, and it follows it. Similarly, the second state, as containing what is real in appearance, is different from the first state, as not containing it. So the difference is the difference between b and zero. In other words, even if state b differs from state a only in quantity, the alteration is a coming into being of b–a, which did not exist in the previous state, and in relation to which the previous state is an =0.

<2a45> So there remains the question how a thing passes from one state a, to another state b. Between two instants there is always a time, and between two states at those instants there is always a difference, which has a quantity (since all the parts of appearances are always themselves quantities). So every transition from one state to another takes place during a time which is contained between two instants, of which the first determines the state which the thing leaves, and the second determines the state it arrives at. So both are limits of the time of an alteration, and hence of the intermediate state between two states. As such, both together belong to the whole alteration.

<2a46> Now every alteration has a cause, which exercises its causality throughout the time during which the alteration takes place. So the cause does not produce its alteration suddenly (all at once, or in an instant), but [B254] over a period of time. Consequently, just as the time grows from the initial instant a to its completion at b, similarly the quantity of reality (b–a) is produced through all the smaller degrees which are contained between the first and the last. Thus all alteration is possible only through a continuous action of causality, which, as long as it is uniform, is called a ‘moment’. The alteration does not consist of these moments, but is produced by them as their effect.

<2a47> Now this is the law of the continuity of all alteration, and its basis is as follows. Both time, and also an appearance in time, consist of parts, without there being any smallest parts. Yet the state of a thing undergoing alteration passes through all these parts, as elements, to its second state. No difference in that which is real in appearance is the smallest, just as no difference in the quantity of times is the smallest. The new state of the reality grows from the first state, in which it did not exist, through all its infinitely many degrees; and the sum of the differences between them is less than the difference between 0 and a.

<2a 48> Here I am not concerned with the possible usefulness of this proposition for scientific investigation. What does urgently demand examination is how such a proposition is possible completely apriori, since it seems to extend our knowledge of nature so much. This needs to be explained, even though it seems obvious that the proposition is true and correct, and [B255] it might be thought that this makes the question of how it is possible redundant. But there are so many unfounded claims to the extension of our knowledge through pure reason, that we must take it as a universal axiom that we should be deeply suspicious of any such claim. Even if the clearest dogmatic proof has been provided, we must not believe it, or use it as an assumption, without credentials which can provide a deduction from fundamentals.

<2a49> All increase in empirical knowledge, and every step forward made through perception, is nothing other than an extension of the determination of inner sense — i.e., it is an advance in time, whether its objects are appearances or pure intuitions. This advance in time determines everything, and it is not in itself determined by anything else. In other words, its parts exist only in time and by virtue of the synthesis of time, and they are not given before this synthesis. Consequently, every transition in perception to something which follows in time is a determination of time through the production of this perception. And just as time is always, and in all its parts, a quantity, similarly a perception is produced as a quantity, through all degrees (of which there is no smallest) from zero to its determinate degree.

<2a50> This now makes clear how it is possible to know apriori a law about the form of alterations. All that we anticipate [B256] is our own apprehension, and we must certainly be able to know its formal precondition apriori, since it itself exists in us before any given appearance.

<2a51> Thus there is a parallel between the understanding and time. Time contains the apriori sensory precondition for the possibility of a continuous advance of what exists to what follows. Similarly, the understanding, thanks to the unity of apperception, is the apriori precondition for the possibility of a continuous determination of all positions for appearances in time. It does this through the series of causes and effects. Causes inexorably bring with them the existence of their effects, and thereby make empirical knowledge of time-relations valid for all times — i.e. universally, and hence objectively valid.

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