<1a1> 3.
ANALOGIES OF EXPERIENCE
The principle of the Analogies of Experience is: Experience is possible only through the representation of a necessary connection of perceptions.
<1a2> Proof
Experience is empirical knowledge, i.e. knowledge which determines an object through perceptions. Thus it is a synthesis of perceptions, which is not itself contained in perception, but which contains the synthetic unity of the multiplicity of perception in one consciousness. This unity constitutes what is essential to knowledge of objects of the senses, i.e. experience, as contrasted with [B219] mere intuition, or sensation of the outer senses.
<1a3> Now it is certain that, in experience, perceptions come together only in a contingent manner, so that perception itself gives no evidence of any necessity of their connection. Nor can perception give any such evidence, since apprehension is merely a putting together of the multiplicity of empirical intuition. Apprehension contains no representation of the necessity of the connected existence of the appearances which it puts together in space and time. But since experience is knowledge of objects through perceptions, it follows that it must represent the relation between what exists in the multiplicity, not as it happens to be put together in time, but as it is objectively in time. But time itself cannot be perceived, so the existence of objects in time can be determined only through their unification in time in general, and hence only through concepts which connect them apriori. Now since apriori concepts always carry necessity with them, experience is possible only through a representation of the necessary connection of perceptions.
<1a4> The three modes of time are duration, succession, and co-existence. Therefore experience is preceded and made possible by three rules for all time-relations among appearances, in accordance with which the existence of every appearance can be determined with reference to the unity of all time.
<1a5> [B220] The universal axiom of all three Analogies depends on the necessary unity of apperception in relation to any possible empirical consciousness (or perception) at any time. Consequently, since the unity of apperception is the apriori foundation of empirical consciousness, this axiom depends on the synthetic unity of all appearances in respect of their relations in time. For the originative apperception applies to inner sense (i.e. to the totality of all representations); and more specifically, it applies apriori to the form of inner sense, which is the time-order of the multiple empirical consciousness. Now all this multiplicity must be united in the originative apperception in accordance with its time-relations. For this is required apriori by the transcendental unity of apperception, which applies to everything that is to belong to my knowledge (i.e. my unified knowledge), and hence be capable of being an object for me. This synthetic unity in the time-relation of all perceptions, which is determined apriori, is the law that all empirical determinations of time must come under rules for the determination of time in general. The Analogies of Experience, which I am now going to deal with, must be rules of this sort.
<1a6> These axioms have the peculiar characteristic that they do not concern appearances or the synthesis of their empirical intuition, but merely their existence, and their relationship to each other in respect of their existence. Now the way in which something is apprehended in appearance [B221] can be determined apriori in such a manner that the rule for its synthesis can at the same time provide this apriori intuition in every empirical example we come across — i.e. it can produce the appearance from the intuition. It is only the existence of the appearance that cannot be known apriori; and although we could advance far enough along this route to conclude that something or other must be present, we would not know it as something determinate — i.e. we would not be able to anticipate what differentiated its empirical intuition from the intuitions of other things.
<1a7> I called the first two axioms ‘mathematical’, in view of the fact that they justified the application of mathematics to appearances. They were concerned only with the possibility of appearances, and they told us how appearances could be produced in accordance with a mathematical synthesis, both in respect of their intuition, and in respect of that which is real in their perception. Hence both axioms justify the application of numerical quantities to appearances, and along with these quantities, the determination of an appearance as a quantity. So, for example, I can put together the degree of sensations of sunlight out of roughly 200,000 illuminations from the moon, and provide this degree as determined apriori — that is, I can construct it. This is why we can call the first two axioms ‘constitutive’.
<1a8> The situation must be quite different with axioms which are to bring the existence of appearances under rules apriori. For since existence cannot be constructed, [B222] they are concerned only with relations of existence, and they can deliver nothing more than merely regulative principles. Here there is no question of Axioms of Intuition or Anticipations of Perception. Rather, if we are given a perception which has a time-relation to another (even if it is undetermined), we cannot say apriori which other, or what quantity the other perception has, but only how its existence is necessarily connected with that of the first in this particular mode of time.
<1a9> In philosophy, analogies mean something very different from what they represent in mathematics. In mathematics, analogies are formulae which express the identity of two quantitative relationships. They are always constitutive, so that if two members of the proportion are given, the third will also thereby be given — i.e. it can be constructed. But in philosophy, an analogy is not the identity of two quantitative relationships, but of two qualitative ones. Here, if three members are given, I can know, and supply apriori, only the relationship with a fourth member, but not this fourth member itself. Nevertheless, I have a rule for searching for it in experience, and a criterion for identifying it there.
<1a10> So an analogy of experience is only a rule for how unity of experience is to arise from perceptions, and not for how perception itself, as empirical intuition in general, is to come about. As an axiom about objects (appearances), it has merely regulative, and not constitutive validity.
<1a11> [B223] The same is also true of the Postulates of Empirical Thought in General, which are collectively concerned with:
They are only regulative axioms, and they differ from the mathematical ones, which are constitutive. The difference does not lie in their certainty, which is established apriori in both cases; but in the way in which they are evident — i.e. only the mathematical ones are intuitively, and hence demonstrably evident.
<1a12> Here I must stress a point which I have already made about the other synthetic axioms. This is that these Analogies have their sole significance and validity, not as axioms of the transcendental use of the understanding, but only of their empirical use; and hence it is only as such that they can be proved. Consequently, appearances cannot be subsumed under the categories as such, but only under their schemata.
<1a13> For if the objects which these axioms are to apply to were things in themselves, then it would be quite impossible to have any synthetic apriori knowledge of them. But they are nothing other than appearances, and complete knowledge of them (which must always be the ultimate goal of apriori axioms) depends solely on the possibility of experience. Consequently, the axioms can have as their aim nothing other than the preconditions for the unity of empirical [B224] knowledge in the synthesis of appearances. But this unity is thought only in the schema of the pure concept of the understanding. The category contains the function of its unity, as of a synthesis in general, and the function is not restricted by any sensory precondition.
<1a14> So these axioms justify us in unifying appearances only by an analogy with the logical and universal unity of concepts. We do indeed use the category in the axiom itself; but in its implementation (its application to appearances), it is replaced by its schema, as the key to its use — or rather, we set the schema alongside the category as a restricting precondition, and call it a formula of the category.
<1a15> A
First Analogy
The Axiom of the Permanence of Substance
In every change of appearances, substance is permanent, and its quantum in nature is neither increased nor diminished.
<1a16> Proof
All appearances are in time; and in it alone can either coexistence or succession be represented, with time as their substrate (as the permanent form of inner intuition). All [B225] change of appearances must be thought in time; but time itself remains, and does not change. For it is that in which succession or coexistence can be represented merely as determinations of time.
<1a17> Now time in itself cannot be perceived. Consequently, the substrate which represents time in general must be found in the objects of perception, i.e. in appearances. It is in this substrate that all change or coexistence can be perceived, through the relation of appearances to the substrate when they are apprehended. But the substrate of all that is real (i.e. every property of the existence of things) is substance; and everything which belongs to existence can be thought only as a determination of substance. Now, all time-relations between appearances can be determined only by relation to the permanent. Consequently, the permanent is substance in appearance — that is, the real in appearance which, as the substrate of all change, always remains the same. So since it cannot change as to its existence, it is also the case that its quantum in nature can be neither increased nor diminished.
<1a18> Our apprehension of the multiplicity of appearance is always successive, and is therefore always changing. So through apprehension alone, we can never determine whether this multiplicity, as object of experience, is coexistent or successive. In order to determine this, we need some underlying basis which always exists — in other words, something lasting and permanent, of which all [B226] change and coexistence are nothing other than so many ways in which the permanent exists, or so many modes of time. Thus time-relations are possible only in the permanent, since the only time-relations are simultaneity and succession. That is, the permanent is the substrate of the empirical representation of time itself, and no time-determination is possible without it.
<1a19> Permanence universally reveals time as the enduring correlate of all existence of appearances, of all change, and of all co-existence. For time itself is not subject to change, but only appearances in time. Similarly, coexistence is not a mode of time itself, since no parts of time are simultaneous, but all are successive. If we wanted to ascribe succession to time itself, we would have to imagine yet another time in which this succession was possible.
<1a20> It is only through the permanent that existence in different successive parts of the time series acquires a quantity, which is called duration. For in mere succession alone, existence is always passing away and coming into being, and never has the least quantity. So without the permanent, there is no time-relation.
<1a21> Now time in itself cannot be perceived. So the permanent in appearances is the substrate of all time-determination, and hence also the precondition for the possibility of all synthetic unity of perceptions, i.e. of experience. [B227] And in this permanent thing, all existence and all change in time can be considered only as a mode of the existence of that which lasts and is permanent. Thus in all appearances, the permanent is the object itself, i.e. the substance (of the phenomena). But everything which changes, or can change, belongs only to the way in which this substance or substances exist, and hence to their determinations.
<1a22> I find that throughout history, not only philosophers but also ordinary people have presupposed this permanence as a substrate of all change in appearances, and have always taken it as indubitable. The only difference is that philosophers express themselves more precisely on this issue, by saying that in all alterations in the world, the substance remains, and only the accidents change. However, I have never come across so much as an attempt at a proof of this so obviously a synthetic proposition. Indeed, it only rarely occupies the place it deserves at the summit of the laws of nature which are pure and established completely apriori.
<1a23> In fact, the proposition that substance is permanent is tautological, since permanence is the only basis on which we can apply the category of substance to appearance. But one would first have to prove that in all appearances there is something permanent, in which anything changeable is nothing other than a determination of its existence. However, such a proof can never be constructed [B228] dogmatically (i.e. from concepts), because the proposition in question is synthetic apriori. It never occurred to anyone that propositions of this sort are valid only in relation to possible experience, and hence also that they can be proved only through a deduction of the possibility of experience. So it is no wonder that it has never been proved, even though it has been the foundation for all experience, since the need for it is felt in any empirical knowledge.
<1a24> A philosopher was asked: ‘How much does smoke weigh?’ He replied: ‘Subtract the weight of the remaining ash from the weight of the wood that was burned, and then you will have the weight of the smoke.’ He thus assumed as undeniable that, even in fire, the matter (substance) does not disappear, but only its form undergoes a change.
<1a25> Similarly, the old saying that ‘nothing comes from nothing’ was only another corollary of the axiom of permanence — or rather, of the ever-continuing existence of the essential subject in appearances. For if that in appearance which is called ‘substance’ is to be the essential substrate of all time-determination, then every past and future existence must be determinable by reference to it alone, and nothing else. Hence the only reason why we can call an appearance a ‘substance’ is because we presuppose its existence throughout time. The word [B229] ‘permanence’ isn’t quite right, since it refers more to future time. Nevertheless it will do, since the inner necessity to continue to exist is inseparable from the necessity to have always existed in the past.
<1a26> ‘Nothing comes from nothing, and nothing can return to nothing’ were two propositions which the scholastics joined together inseparably. Nowadays they are sometimes separated, due to the mistaken belief that they refer to things in themselves. It was feared that the first was inconsistent with the dependence of the world on a supreme cause, especially as far as its substance is concerned. However, this worry is unnecessary, since here we are dealing only with appearances in the world of experience. The unity of appearances would never be possible if we allowed new things (in the sense of new substances) to come into existence. In that case, we would lose the only thing which can represent the unity of time, namely the identity of the substrate through which alone all change has holistic unity. Yet this permanence is nothing other than the way in which we represent to ourselves the existence of things in appearance.
<1a27> The determinations of a substance, which are nothing other than its particular ways of existing, are called accidents. They are always real, because they involve the existence of a substance. (Negations are merely determinations which express the non-being of something in a substance.) Now that which is real [B230] in a substance is sometimes treated as having a separate existence — for example, motion, as an accident of matter. In such cases, the existence of the accident is called ‘inherence’, in order to distinguish it from the existence of the substance, which is called ‘subsistence’. But this gives rise to many confusions, and it is more precise and correct to adhere to the terminology in which an accident is the way in which the existence of a substance is positively determined.
<1a28> Nevertheless, the preconditions for the logical use of our understanding mean that we cannot avoid separating out that in the existence of a substance which can change while the substance stays the same, and to treat it as standing in relation to that in its existence which is essentially permanent and fundamental. This is why the category of substance comes under the heading of Relation — though more as the precondition of relations than as itself containing a relation.
<2a29> Now this permanence is also the ground for correcting the concept of alteration. Coming into being and going out of being are not alterations of what comes in or out of being. Alteration is when one and the same object exists first in one way, and then in another way. Hence everything which alters continues to exist, and only its state changes. So change applies only to determinations, which can come in or out of being. Consequently we can say (in a way which sounds paradoxical) that only the permanent (i.e. substance) alters; [B231] and that the variable does not undergo alteration, but change, in that some determinations go out of being, and others come into being.
<1a30> Hence alteration can be perceived only in substances. Essentially, it is impossible to perceive coming in or out of being, except in so far as it is merely a determination of the permanent. This is because it is the permanent which makes possible the representation of the transition from one state to another, and from not-being to being. So these transitions can be known empirically only as changing determinations of that which is permanent.
<1a31> Suppose that something begins to exist out of the blue; then you must have a point in time at which it did not exist. But what can you fix this point in time to, unless to something which is already there? For a preceding empty time is not an object of perception. But if you fix what comes into being to things which already exist, and continue to exist until it comes into being, then what comes into being is only a determination of what already exists as that which is permanent. It is the same with ceasing to exist — for it presupposes the empirical representation of a time when there is no longer an appearance.
<1a32> Substances (in appearance) are the substrates of all time-determinations. If some of them came into being and others went out of being, the sole precondition of the empirical unity of time would disappear. [B232] Appearances would then relate to two distinct time streams, in which their existence would flow along parallel paths — which is absurd. For there is only one time, in which no different times can be simultaneous, and all must be successive.
<1a33> So permanence is a necessary precondition, under which alone appearances can be determined as things or objects in any possible experience. As for the question of what the empirical criterion for this necessary permanence is, and the related question of the substantiality of appearances, there will be later opportunities for me to make the necessary points.