<3a1> C

<3a2> Proof

Things are coexistent when, in empirical intuition, the perception of the one can follow the perception [B257] of the other in any order (as I showed in the Second Analogy, this cannot happen in the succession of appearances in time). Thus I can direct my perception first at the moon and then at the earth, or conversely, first at the earth and then at the moon. Since the perceptions of these objects can follow each other in any order, I say that they coexist.

<3a3> Now coexistence is the existence of the multiple at the same time. But we cannot perceive time itself, in order to establish from the fact that things are placed at the same time, that their perceptions can follow each other in any order. The synthesis of the imagination in apprehension would show each of these perceptions as in the subject when the other is not, and vice versa. However, it would not show that the objects coexisted, i.e. that when one exists, the other also exists at the same time, or that this is necessary for the perceptions to be able to follow each other in any order. So what we need is a concept of understanding of the reversible sequence of the determinations of these things which exist externally to each other at the same time. Only then can we say that the reversible sequence of perceptions is grounded in the object, and thus represent the coexistence as objective.

<3a4> Now the relation between substances, such that the ground for determinations of the one [B258] is contained in the other, is the relation of influence. And if, conversely, the ground for determinations of the second is also contained in the first, then the relation is that of community or interaction. So the coexistence of substances in space can be known in experience only on the assumption of an interaction between them. Thus this interaction is also the precondition of the possibility of things themselves as objects of experience.

<3a5> Things coexist in so far as they exist at one and the same time. But how can we know that they exist at one and the same time? When it is arbitrary what order the multiple is synthesised in, when it is apprehended — that is, it can go from A, through B, C, and D, to E, or also the other way round, from E to A. For if it were successive in time (in the order which begins with A and ends with E), it would be impossible for its apprehension in perception to begin with E, and proceed backwards to A, because A belongs to a time which has passed, and so can no longer be an object of apprehension.

<3a6> Now let us suppose that, in a multiplicity of substances as appearances, each of them was completely isolated — that is, none of them influenced the others, or received any reciprocal influences from them. I say that their coexistence would not be the object of a possible [B259] perception, and that the existence of one of them could not lead to the existence of another through any process of empirical synthesis. For if you imagine that they are separated by a completely empty space, then perception, which proceeds from one to the next in time, would certainly determine the existence of the later one by means of a subsequent perception. However, it would not be able to discriminate whether its appearance objectively followed the first, or coexisted with it.

<3a7> So, in addition to mere existence, there must be something through which A determines the position of B in time, and, conversely, B also determines the position of A in time, since only under this precondition can these substances be empirically represented as coexisting. Now the only thing which determines the position of something else in time is its cause, or the cause of its determinations. In the case of substance, only its determinations can be caused. So every substance must contain within itself, both the causality of certain determinations in the other, and the effects of the causality of the other. In other words, if their coexistence is to be known through any possible experience, they must be in dynamic community, whether directly or through intermediaries. Now, as far as objects of experience are concerned, anything which is a precondition of experience of these objects is necessary. [B260] So, in so far as substances in appearance coexist, it is necessary for all of them to be in holistic community through their interaction with each other.

<3a8> The word ‘community’ is ambiguous in our language, since it can mean both ‘coexistence’ and ‘interaction’. Here we are using it in the latter sense, as a dynamic community, without which even a spatial community could never be known empirically.

<3a9>From our experiences, we can easily see that only continuous influences in all positions in space can lead our senses from one object to another. The light pulsating between our eyes and the heavenly bodies creates an indirect community between us and them, which proves that they coexist. We cannot alter our position empirically (i.e. perceive the alteration), unless the matter all around us makes the perception of our position possible. And it is only through its reciprocal influence that matter as a whole can establish its own coexistence, and hence the coexistence of the most remote of objects (if only indirectly). Without community, every perception of appearance in space would be broken off from every other. The chain of empirical representations (i.e. experience) would have to start completely afresh with a new object, [B261] and the earlier representation could not have the least connection or time-relation with the later one.

<3a10> I shall certainly not use this as an argument against empty space. For there could always be a place entirely beyond the reach of perceptions, and therefore where there can be no empirical knowledge of things coexisting. But then it could never be an object of any possible experience for us.

<3a11> The following may be helpful as a further explanation. Since, in our minds, all appearances are contained in a possible experience, they must belong to a community of apperception (in the sense of a coexisting one). In so far as their objects are to be represented as coexisting in connection with each other, they must determine each other’s position at a particular time, and thereby constitute a whole. If this subjective community is to be based on an objective foundation (i.e. apply to appearances as substances), then the perception of the one must make possible the perception of the other as its foundation, and vice versa. This is not so that the successiveness which always characterises perceptions (as apprehensions) will be attributed to the objects, but so that the objects can be represented as coexisting. But this is a reciprocal influence, i.e. a real community of substances (in the sense of an interacting one), without which the empirical relationship of coexistence can have no place in experience. In so far as appearances are separate from each other [B262] yet connected with each other, this interaction turns them into a real compound whole; and compound wholes of this sort are possible in many ways. Hence the three dynamical relations, which are the source of all the rest, are those of inherence, consequence, and composition.

* * *

<3a12> So these are the three Analogies of Experience. They are nothing other than axioms of the determination of the existence of appearances in time in respect of all its three modes, namely:

• relation to time itself as a quantity (the quantity of existence, i.e. duration);
• relation in time as a series (succession); and finally
• relation, also in time, as a totality of all existence (coexistence).

This unity of time-determination is dynamical through and through. In other words, time is not treated as something in which experience directly determines the position of everything that exists. This is impossible, because absolute time is not an object of perception which could hold appearances together. Rather, the position of all appearances in time is determined by the rule of the understanding through which alone their existence can acquire synthetic unity in respect of time-relations. Thus their position is determined apriori, and it is valid for all and every time.

<3a13> [B263] By ‘nature’ (in the empirical sense) I mean the interconnection of appearances, with respect to their existence, through necessary rules, i.e. through laws. Thus there are certain laws, and apriori ones at that, which initially make a nature of any sort possible. On the other hand, empirical laws can exist and be discovered only through experience, and indeed only in compliance with those original laws which initially make experience itself possible. So in essence, what my Analogies do is to plot the unity of nature in the interconnection of all appearances along certain parameters, which represent nothing other than the relation of time (as including all existence) to the unity of apperception, which can be realised only in synthesis according to rules. So taken together, the Analogies say that all appearances belong to, and must belong to a single nature, because without this apriori unity, there could be no unity of experience, and hence no determination of the objects in it.

<3a14> Something needs to be said about the method I have used to prove these transcendental laws of nature, and about their special character. What I have to say is at the same time very important as a necessary guide for any other attempt to prove propositions which not merely belong to the understanding, but are also synthetic apriori.

<3a15> I might have tried to prove the Analogies dogmatically (i.e. from concepts). That is, I might have argued as follows:

• everything that exists is to be found only in [B264] that which is permanent;
• every event presupposes something in the previous state from which it follows in accordance with a rule; and finally
• in every coexistent multiplicity, the states coexist in relation to each other in accordance with a rule (they are in community).

If I had done so, all my efforts would have been in vain. For you cannot get from one object and its existence to the existence or mode of existing of another object, merely by means of concepts of these things, however you care to analyse them.

<3a16> So what is missing? The third item required is the possibility of experience, as a type of knowledge in which it must ultimately be possible for all objects to be given to us, if the representation of them is to have objective reality for us. The essential form of this third item consists in the synthetic unity of apperception of all appearances. In it we discovered apriori preconditions for the holistic and necessary time-determination of everything existent in appearance, without which even the empirical determination of time would be impossible. We also discovered rules for the apriori synthetic unity by means of which we can anticipate experience.

<3a17> Up till now, philosophers have lacked this method, and have suffered from the delusion that it is possible to use a dogmatic method to prove synthetic propositions which the empirical use of the understanding recommends as its principles. This is why it happened that a proof of the principle of sufficient reason was so often attempted, but always in vain. [B265] No-one ever so much as thought of the other two Analogies, even though they were always used without being recognised for what they were.* This was because of the lack of the guiding-thread of the categories, which alone can reveal and make obvious every deficiency of the understanding, whether in concepts or in axioms.