THE CRITIQUE OF PURE REASON by Immanuel Kant (1b)

 INTRODUCTION. Of the Transcendental Faculty of judgement in General.

  If understanding in general be defined as the faculty of laws or

rules, the faculty of judgement may be termed the faculty of

subsumption under these rules; that is, of distinguishing whether this

or that does or does not stand under a given rule (casus datae legis).

General logic contains no directions or precepts for the faculty of

judgement, nor can it contain any such. For as it makes abstraction of

all content of cognition, no duty is left for it, except that of

exposing analytically the mere form of cognition in conceptions,

judgements, and conclusions, and of thereby establishing formal

rules for all exercise of the understanding. Now if this logic

wished to give some general direction how we should subsume under

these rules, that is, how we should distinguish whether this or that

did or did not stand under them, this again could not be done

otherwise than by means of a rule. But this rule, precisely because it

is a rule, requires for itself direction from the faculty of

judgement. Thus, it is evident that the understanding is capable of

being instructed by rules, but that the judgement is a peculiar

talent, which does not, and cannot require tuition, but only exercise.

This faculty is therefore the specific quality of the so-called mother

wit, the want of which no scholastic discipline can compensate.

  For although education may furnish, and, as it were, engraft upon

a limited understanding rules borrowed from other minds, yet the power

of employing these rules correctly must belong to the pupil himself;

and no rule which we can prescribe to him with this purpose is, in the

absence or deficiency of this gift of nature, secure from misuse.* A

physician therefore, a judge or a statesman, may have in his head many

admirable pathological, juridical, or political rules, in a degree

that may enable him to be a profound teacher in his particular

science, and yet in the application of these rules he may very

possibly blunder- either because he is wanting in natural judgement

(though not in understanding) and, whilst he can comprehend the

general in abstracto, cannot distinguish whether a particular case

in concreto ought to rank under the former; or because his faculty

of judgement bas not been sufficiently exercised by examples and

real practice. Indeed, the grand and only use of examples, is to

sharpen the judgement. For as regards the correctness and precision of

the insight of the understanding, examples are commonly injurious

rather than otherwise, because, as casus in terminis they seldom

adequately fulfil the conditions of the rule. Besides, they often

weaken the power of our understanding to apprehend rules or laws in

their universality, independently of particular circumstances of

experience; and hence, accustom us to employ them more as formulae

than as principles. Examples are thus the go-cart of the judgement,

which he who is naturally deficient in that faculty cannot afford to

dispense with.

  *Deficiency in judgement is properly that which is called stupidity;

and for such a failing we know no remedy. A dull or narrow-minded

person, to whom nothing is wanting but a proper degree of

understanding, may be improved by tuition, even so far as to deserve

the epithet of learned. But as such persons frequently labour under

a deficiency in the faculty of judgement, it is not uncommon to find

men extremely learned who in the application of their science betray a

lamentable degree this irremediable want.

  But although general logic cannot give directions to the faculty

of judgement, the case is very different as regards transcendental

logic, insomuch that it appears to be the especial duty of the

latter to secure and direct, by means of determinate rules, the

faculty of judgement in the employment of the pure understanding. For,

as a doctrine, that is, as an endeavour to enlarge the sphere of the

understanding in regard to pure a priori cognitions, philosophy is

worse than useless, since from all the attempts hitherto made,

little or no ground has been gained. But, as a critique, in order to

guard against the mistakes of the faculty of judgement (lapsus

judicii) in the employment of the few pure conceptions of the

understanding which we possess, although its use is in this case

purely negative, philosophy is called upon to apply all its

acuteness and penetration.

  But transcendental philosophy has this peculiarity, that besides

indicating the rule, or rather the general condition for rules,

which is given in the pure conception of the understanding, it can, at

the same time, indicate a priori the case to which the rule must be

applied. The cause of the superiority which, in this respect,

transcendental philosophy possesses above all other sciences except

mathematics, lies in this: it treats of conceptions which must

relate a priori to their objects, whose objective validity

consequently cannot be demonstrated a posteriori, and is, at the

same time, under the obligation of presenting in general but

sufficient tests, the conditions under which objects can be given in

harmony with those conceptions; otherwise they would be mere logical

forms, without content, and not pure conceptions of the understanding.

  Our transcendental doctrine of the faculty of judgement will contain

two chapters. The first will treat of the sensuous condition under

which alone pure conceptions of the understanding can be employed-

that is, of the schematism of the pure understanding. The second

will treat of those synthetical judgements which are derived a

priori from pure conceptions of the understanding under those

conditions, and which lie a priori at the foundation of all other

cognitions, that is to say, it will treat of the principles of the

pure understanding.

       TRANSCENDENTAL DOCTRINE OF THE FACULTY OF JUDGEMENT

                   OR, ANALYTIC OF PRINCIPLES.

    CHAPTER I. Of the Schematism at of the Pure Conceptions

                    of the Understanding.

  In all subsumptions of an object under a conception, the

representation of the object must be homogeneous with the

conception; in other words, the conception must contain that which

is represented in the object to be subsumed under it. For this is

the meaning of the expression: "An object is contained under a

conception." Thus the empirical conception of a plate is homogeneous

with the pure geometrical conception of a circle, inasmuch as the

roundness which is cogitated in the former is intuited in the latter.

  But pure conceptions of the understanding, when compared with

empirical intuitions, or even with sensuous intuitions in general, are

quite heterogeneous, and never can be discovered in any intuition. How

then is the subsumption of the latter under the former, and

consequently the application of the categories to phenomena,

possible?- For it is impossible to say, for example: "Causality can be

intuited through the senses and is contained in the phenomenon."- This

natural and important question forms the real cause of the necessity

of a transcendental doctrine of the faculty of judgement, with the

purpose, to wit, of showing how pure conceptions of the

understanding can be applied to phenomena. In all other sciences,

where the conceptions by which the object is thought in the general

are not so different and heterogeneous from those which represent

the object in concreto- as it is given, it is quite unnecessary to

institute any special inquiries concerning the application of the

former to the latter.

  Now it is quite clear that there must be some third thing, which

on the one side is homogeneous with the category, and with the

phenomenon on the other, and so makes the application of the former to

the latter possible. This mediating representation must be pure

(without any empirical content), and yet must on the one side be

intellectual, on the other sensuous. Such a representation is the

transcendental schema.

  The conception of the understanding contains pure synthetical

unity of the manifold in general. Time, as the formal condition of the

manifold of the internal sense, consequently of the conjunction of all

representations, contains a priori a manifold in the pure intuition.

Now a transcendental determination of time is so far homogeneous

with the category, which constitutes the unity thereof, that it is

universal and rests upon a rule a priori. On the other hand, it is

so far homogeneous with the phenomenon, inasmuch as time is

contained in every empirical representation of the manifold. Thus an

application of the category to phenomena becomes possible, by means of

the transcendental determination of time, which, as the schema of

the conceptions of the understanding, mediates the subsumption of

the latter under the former.

  After what has been proved in our deduction of the categories, no

one, it is to be hoped, can hesitate as to the proper decision of

the question, whether the employment of these pure conceptions of

the understanding ought to be merely empirical or also transcendental;

in other words, whether the categories, as conditions of a possible

experience, relate a priori solely to phenomena, or whether, as

conditions of the possibility of things in general, their

application can be extended to objects as things in themselves. For we

have there seen that conceptions are quite impossible, and utterly

without signification, unless either to them, or at least to the

elements of which they consist, an object be given; and that,

consequently, they cannot possibly apply to objects as things in

themselves without regard to the question whether and how these may be

given to us; and, further, that the only manner in which objects can

be given to us is by means of the modification of our sensibility;

and, finally, that pure a priori conceptions, in addition to the

function of the understanding in the category, must contain a priori

formal conditions of sensibility (of the internal sense, namely),

which again contain the general condition under which alone the

category can be applied to any object. This formal and pure

condition of sensibility, to which the conception of the understanding

is restricted in its employment, we shall name the schema of the

conception of the understanding, and the procedure of the

understanding with these schemata we shall call the schematism of

the pure understanding.

  The schema is, in itself, always a mere product of the

imagination. But, as the synthesis of imagination has for its aim no

single intuition, but merely unity in the determination of

sensibility, the schema is clearly distinguishable from the image.

Thus, if I place five points one after another.... this is an image of

the number five. On the other hand, if I only think a number in

general, which may be either five or a hundred, this thought is rather

the representation of a method of representing in an image a sum

(e.g., a thousand) in conformity with a conception, than the image

itself, an image which I should find some little difficulty in

reviewing, and comparing with the conception. Now this

representation of a general procedure of the imagination to present

its image to a conception, I call the schema of this conception.

  In truth, it is not images of objects, but schemata, which lie at

the foundation of our pure sensuous conceptions. No image could ever

be adequate to our conception of a triangle in general. For the

generalness of the conception it never could attain to, as this

includes under itself all triangles, whether right-angled,

acute-angled, etc., whilst the image would always be limited to a

single part of this sphere. The schema of the triangle can exist

nowhere else than in thought, and it indicates a rule of the synthesis

of the imagination in regard to pure figures in space. Still less is

an object of experience, or an image of the object, ever to the

empirical conception. On the contrary, the conception always relates

immediately to the schema of the imagination, as a rule for the

determination of our intuition, in conformity with a certain general

conception. The conception of a dog indicates a rule, according to

which my imagination can delineate the figure of a four-footed

animal in general, without being limited to any particular

individual form which experience presents to me, or indeed to any

possible image that I can represent to myself in concreto. This

schematism of our understanding in regard to phenomena and their

mere form, is an art, hidden in the depths of the human soul, whose

true modes of action we shall only with difficulty discover and

unveil. Thus much only can we say: "The image is a product of the

empirical faculty of the productive imagination- the schema of

sensuous conceptions (of figures in space, for example) is a

product, and, as it were, a monogram of the pure imagination a priori,

whereby and according to which images first become possible, which,

however, can be connected with the conception only mediately by

means of the schema which they indicate, and are in themselves never

fully adequate to it." On the other hand, the schema of a pure

conception of the understanding is something that cannot be reduced

into any image- it is nothing else than the pure synthesis expressed

by the category, conformably, to a rule of unity according to

conceptions. It is a transcendental product of the imagination, a

product which concerns the determination of the internal sense,

according to conditions of its form (time) in respect to all

representations, in so far as these representations must be

conjoined a priori in one conception, conformably to the unity of

apperception.

  Without entering upon a dry and tedious analysis of the essential

requisites of transcendental schemata of the pure conceptions of the

understanding, we shall rather proceed at once to give an

explanation of them according to the order of the categories, and in

connection therewith.

  For the external sense the pure image of all quantities

(quantorum) is space; the pure image of all objects of sense in

general, is time. But the pure schema of quantity (quantitatis) as a

conception of the understanding, is number, a representation which

comprehends the successive addition of one to one (homogeneous

quantities). Thus, number is nothing else than the unity of the

synthesis of the manifold in a homogeneous intuition, by means of my

generating time itself in my apprehension of the intuition.

  Reality, in the pure conception of the understanding, is that

which corresponds to a sensation in general; that, consequently, the

conception of which indicates a being (in time). Negation is that

the conception of which represents a not-being (in time). The

opposition of these two consists therefore in the difference of one

and the same time, as a time filled or a time empty. Now as time is

only the form of intuition, consequently of objects as phenomena, that

which in objects corresponds to sensation is the transcendental matter

of all objects as things in themselves (Sachheit, reality). Now

every sensation has a degree or quantity by which it can fill time,

that is to say, the internal sense in respect of the representation of

an object, more or less, until it vanishes into nothing (= 0 =

negatio). Thus there is a relation and connection between reality

and negation, or rather a transition from the former to the latter,

which makes every reality representable to us as a quantum; and the

schema of a reality as the quantity of something in so far as it fills

time, is exactly this continuous and uniform generation of the reality

in time, as we descend in time from the sensation which has a

certain degree, down to the vanishing thereof, or gradually ascend

from negation to the quantity thereof.

  The schema of substance is the permanence of the real in time;

that is, the representation of it as a substratum of the empirical

determination of time; a substratum which therefore remains, whilst

all else changes. (Time passes not, but in it passes the existence

of the changeable. To time, therefore, which is itself unchangeable

and permanent, corresponds that which in the phenomenon is

unchangeable in existence, that is, substance, and it is only by it

that the succession and coexistence of phenomena can be determined

in regard to time.)

  The schema of cause and of the causality of a thing is the real

which, when posited, is always followed by something else. It

consists, therefore, in the succession of the manifold, in so far as

that succession is subjected to a rule.

  The schema of community (reciprocity of action and reaction), or the

reciprocal causality of substances in respect of their accidents, is

the coexistence of the determinations of the one with those of the

other, according to a general rule.

  The schema of possibility is the accordance of the synthesis of

different representations with the conditions of time in general

(as, for example, opposites cannot exist together at the same time

in the same thing, but only after each other), and is therefore the

determination of the representation of a thing at any time.

  The schema of reality is existence in a determined time.

  The schema of necessity is the existence of an object in all time.

  It is clear, from all this, that the schema of the category of

quantity contains and represents the generation (synthesis) of time

itself, in the successive apprehension of an object; the schema of

quality the synthesis of sensation with the representation of time, or

the filling up of time; the schema of relation the relation of

perceptions to each other in all time (that is, according to a rule of

the determination of time): and finally, the schema of modality and

its categories, time itself, as the correlative of the determination

of an object- whether it does belong to time, and how. The schemata,

therefore, are nothing but a priori determinations of time according

to rules, and these, in regard to all possible objects, following

the arrangement of the categories, relate to the series in time, the

content in time, the order in time, and finally, to the complex or

totality in time.

  Hence it is apparent that the schematism of the understanding, by

means of the transcendental synthesis of the imagination, amounts to

nothing else than the unity of the manifold of intuition in the

internal sense, and thus indirectly to the unity of apperception, as a

function corresponding to the internal sense (a receptivity). Thus,

the schemata of the pure conceptions of the understanding are the true

and only conditions whereby our understanding receives an

application to objects, and consequently significance. Finally,

therefore, the categories are only capable of empirical use,

inasmuch as they serve merely to subject phenomena to the universal

rules of synthesis, by means of an a priori necessary unity (on

account of the necessary union of all consciousness in one original

apperception); and so to render them susceptible of a complete

connection in one experience. But within this whole of possible

experience lie all our cognitions, and in the universal relation to

this experience consists transcendental truth, which antecedes all

empirical truth, and renders the latter possible.

  It is, however, evident at first sight, that although the schemata

of sensibility are the sole agents in realizing the categories, they

do, nevertheless, also restrict them, that is, they limit the

categories by conditions which lie beyond the sphere of understanding-

namely, in sensibility. Hence the schema is properly only the

phenomenon, or the sensuous conception of an object in harmony with

the category. (Numerus est quantitas phaenomenon- sensatio realitas

phaenomenon; constans et perdurabile rerum substantia phaenomenon-

aeternitas, necessitas, phaenomena, etc.) Now, if we remove a

restrictive condition, we thereby amplify, it appears, the formerly

limited conception. In this way, the categories in their pure

signification, free from all conditions of sensibility, ought to be

valid of things as they are, and not, as the schemata represent

them, merely as they appear; and consequently the categories must have

a significance far more extended, and wholly independent of all

schemata. In truth, there does always remain to the pure conceptions

of the understanding, after abstracting every sensuous condition, a

value and significance, which is, however, merely logical. But in this

case, no object is given them, and therefore they have no meaning

sufficient to afford us a conception of an object. The notion of

substance, for example, if we leave out the sensuous determination

of permanence, would mean nothing more than a something which can be

cogitated as subject, without the possibility of becoming a

predicate to anything else. Of this representation I can make nothing,

inasmuch as it does not indicate to me what determinations the thing

possesses which must thus be valid as premier subject. Consequently,

the categories, without schemata are merely functions of the

understanding for the production of conceptions, but do not

represent any object. This significance they derive from

sensibility, which at the same time realizes the understanding and

restricts it.

   CHAPTER II. System of all Principles of the Pure Understanding.

  In the foregoing chapter we have merely considered the general

conditions under which alone the transcendental faculty of judgement

is justified in using the pure conceptions of the understanding for

synthetical judgements. Our duty at present is to exhibit in

systematic connection those judgements which the understanding

really produces a priori. For this purpose, our table of the

categories will certainly afford us the natural and safe guidance. For

it is precisely the categories whose application to possible

experience must constitute all pure a priori cognition of the

understanding; and the relation of which to sensibility will, on

that very account, present us with a complete and systematic catalogue

of all the transcendental principles of the use of the understanding.

  Principles a priori are so called, not merely because they contain

in themselves the grounds of other judgements, but also because they

themselves are not grounded in higher and more general cognitions.

This peculiarity, however, does not raise them altogether above the

need of a proof. For although there could be found no higher

cognition, and therefore no objective proof, and although such a

principle rather serves as the foundation for all cognition of the

object, this by no means hinders us from drawing a proof from the

subjective sources of the possibility of the cognition of an object.

Such a proof is necessary, moreover, because without it the

principle might be liable to the imputation of being a mere gratuitous

assertion.

  In the second place, we shall limit our investigations to those

principles which relate to the categories. For as to the principles of

transcendental aesthetic, according to which space and time are the

conditions of the possibility of things as phenomena, as also the

restriction of these principles, namely, that they cannot be applied

to objects as things in themselves- these, of course, do not fall

within the scope of our present inquiry. In like manner, the

principles of mathematical science form no part of this system,

because they are all drawn from intuition, and not from the pure

conception of the understanding. The possibility of these

principles, however, will necessarily be considered here, inasmuch

as they are synthetical judgements a priori, not indeed for the

purpose of proving their accuracy and apodeictic certainty, which is

unnecessary, but merely to render conceivable and deduce the

possibility of such evident a priori cognitions.

  But we shall have also to speak of the principle of analytical

judgements, in opposition to synthetical judgements, which is the

proper subject of our inquiries, because this very opposition will

free the theory of the latter from all ambiguity, and place it clearly

before our eyes in its true nature.

        SYSTEM OF THE PRINCIPLES OF THE PURE UNDERSTANDING.

  SECTION I. Of the Supreme Principle of all Analytical Judgements.

  Whatever may be the content of our cognition, and in whatever manner

our cognition may be related to its object, the universal, although

only negative conditions of all our judgements is that they do not

contradict themselves; otherwise these judgements are in themselves

(even without respect to the object) nothing. But although there may

exist no contradiction in our judgement, it may nevertheless connect

conceptions in such a manner that they do not correspond to the

object, or without any grounds either a priori or a posteriori for

arriving at such a judgement, and thus, without being

self-contradictory, a judgement may nevertheless be either false or

groundless.

  Now, the proposition: "No subject can have a predicate that

contradicts it," is called the principle of contradiction, and is a

universal but purely negative criterion of all truth. But it belongs

to logic alone, because it is valid of cognitions, merely as

cognitions and without respect to their content, and declares that the

contradiction entirely nullifies them. We can also, however, make a

positive use of this principle, that is, not merely to banish

falsehood and error (in so far as it rests upon contradiction), but

also for the cognition of truth. For if the judgement is analytical,

be it affirmative or negative, its truth must always be recognizable

by means of the principle of contradiction. For the contrary of that

which lies and is cogitated as conception in the cognition of the

object will be always properly negatived, but the conception itself

must always be affirmed of the object, inasmuch as the contrary

thereof would be in contradiction to the object.

  We must therefore hold the principle of contradiction to be the

universal and fully sufficient Principle of all analytical

cognition. But as a sufficient criterion of truth, it has no further

utility or authority. For the fact that no cognition can be at

variance with this principle without nullifying itself, constitutes

this principle the sine qua non, but not the determining ground of the

truth of our cognition. As our business at present is properly with

the synthetical part of our knowledge only, we shall always be on

our guard not to transgress this inviolable principle; but at the same

time not to expect from it any direct assistance in the

establishment of the truth of any synthetical proposition.

  There exists, however, a formula of this celebrated principle- a

principle merely formal and entirely without content- which contains a

synthesis that has been inadvertently and quite unnecessarily mixed up

with it. It is this: "It is impossible for a thing to be and not to be

at the same time." Not to mention the superfluousness of the

addition of the word impossible to indicate the apodeictic

certainty, which ought to be self-evident from the proposition itself,

the proposition is affected by the condition of time, and as it were

says: "A thing = A, which is something = B, cannot at the same time be

non-B." But both, B as well as non-B, may quite well exist in

succession. For example, a man who is young cannot at the same time be

old; but the same man can very well be at one time young, and at

another not young, that is, old. Now the principle of contradiction as

a merely logical proposition must not by any means limit its

application merely to relations of time, and consequently a formula

like the preceding is quite foreign to its true purpose. The

misunderstanding arises in this way. We first of all separate a

predicate of a thing from the conception of the thing, and

afterwards connect with this predicate its opposite, and hence do

not establish any contradiction with the subject, but only with its

predicate, which has been conjoined with the subject synthetically-

a contradiction, moreover, which obtains only when the first and

second predicate are affirmed in the same time. If I say: "A man who

is ignorant is not learned," the condition "at the same time" must

be added, for he who is at one time ignorant, may at another be

learned. But if I say: "No ignorant man is a learned man," the

proposition is analytical, because the characteristic ignorance is now

a constituent part of the conception of the subject; and in this

case the negative proposition is evident immediately from the

proposition of contradiction, without the necessity of adding the

condition "the same time." This is the reason why I have altered the

formula of this principle- an alteration which shows very clearly

the nature of an analytical proposition.

  SECTION II. Of the Supreme Principle of all Synthetical Judgements.

  The explanation of the possibility of synthetical judgements is a

task with which general logic has nothing to do; indeed she needs

not even be acquainted with its name. But in transcendental logic it

is the most important matter to be dealt with- indeed the only one, if

the question is of the possibility of synthetical judgements a priori,

the conditions and extent of their validity. For when this question is

fully decided, it can reach its aim with perfect ease, the

determination, to wit, of the extent and limits of the pure

understanding.

  In an analytical judgement I do not go beyond the given

conception, in order to arrive at some decision respecting it. If

the judgement is affirmative, I predicate of the conception only

that which was already cogitated in it; if negative, I merely

exclude from the conception its contrary. But in synthetical

judgements, I must go beyond the given conception, in order to

cogitate, in relation with it, something quite different from that

which was cogitated in it, a relation which is consequently never

one either of identity or contradiction, and by means of which the

truth or error of the judgement cannot be discerned merely from the

judgement itself.

  Granted, then, that we must go out beyond a given conception, in

order to compare it synthetically with another, a third thing is

necessary, in which alone the synthesis of two conceptions can

originate. Now what is this tertium quid that is to be the medium of

all synthetical judgements? It is only a complex in which all our

representations are contained, the internal sense to wit, and its form

a priori, time.

  The synthesis of our representations rests upon the imagination;

their synthetical unity (which is requisite to a judgement), upon

the unity of apperception. In this, therefore, is to be sought the

possibility of synthetical judgements, and as all three contain the

sources of a priori representations, the possibility of pure

synthetical judgements also; nay, they are necessary upon these

grounds, if we are to possess a knowledge of objects, which rests

solely upon the synthesis of representations.

  If a cognition is to have objective reality, that is, to relate to

an object, and possess sense and meaning in respect to it, it is

necessary that the object be given in some way or another. Without

this, our conceptions are empty, and we may indeed have thought by

means of them, but by such thinking we have not, in fact, cognized

anything, we have merely played with representation. To give an

object, if this expression be understood in the sense of "to

present" the object, not mediately but immediately in intuition, means

nothing else than to apply the representation of it to experience,

be that experience real or only possible. Space and time themselves,

pure as these conceptions are from all that is empirical, and

certain as it is that they are represented fully a priori in the mind,

would be completely without objective validity, and without sense

and significance, if their necessary use in the objects of

experience were not shown. Nay, the representation of them is a mere

schema, that always relates to the reproductive imagination, which

calls up the objects of experience, without which they have no

meaning. And so it is with all conceptions without distinction.

  The possibility of experience is, then, that which gives objective

reality to all our a priori cognitions. Now experience depends upon

the synthetical unity of phenomena, that is, upon a synthesis

according to conceptions of the object of phenomena in general, a

synthesis without which experience never could become knowledge, but

would be merely a rhapsody of perceptions, never fitting together into

any connected text, according to rules of a thoroughly united

(possible) consciousness, and therefore never subjected to the

transcendental and necessary unity of apperception. Experience has

therefore for a foundation, a priori principles of its form, that is

to say, general rules of unity in the synthesis of phenomena, the

objective reality of which rules, as necessary conditions even of

the possibility of experience can which rules, as necessary

conditions- even of the possibility of experience- can always be shown

in experience. But apart from this relation, a priori synthetical

propositions are absolutely impossible, because they have no third

term, that is, no pure object, in which the synthetical unity can

exhibit the objective reality of its conceptions.

  Although, then, respecting space, or the forms which productive

imagination describes therein, we do cognize much a priori in

synthetical judgements, and are really in no need of experience for

this purpose, such knowledge would nevertheless amount to nothing

but a busy trifling with a mere chimera, were not space to be

considered as the condition of the phenomena which constitute the

material of external experience. Hence those pure synthetical

judgements do relate, though but mediately, to possible experience, or

rather to the possibility of experience, and upon that alone is

founded the objective validity of their synthesis.

  While then, on the one hand, experience, as empirical synthesis,

is the only possible mode of cognition which gives reality to all

other synthesis; on the other hand, this latter synthesis, as

cognition a priori, possesses truth, that is, accordance with its

object, only in so far as it contains nothing more than what is

necessary to the synthetical unity of experience.

  Accordingly, the supreme principle of all synthetical judgements is:

"Every object is subject to the necessary conditions of the

synthetical unity of the manifold of intuition in a possible

experience."

  A priori synthetical judgements are possible when we apply the

formal conditions of the a priori intuition, the synthesis of the

imagination, and the necessary unity of that synthesis in a

transcendental apperception, to a possible cognition of experience,

and say: "The conditions of the possibility of experience in general

are at the same time conditions of the possibility of the objects of

experience, and have, for that reason, objective validity in an a

priori synthetical judgement."

     SECTION III. Systematic Representation of all Synthetical

             Principles of the Pure Understanding.

  That principles exist at all is to be ascribed solely to the pure

understanding, which is not only the faculty of rules in regard to

that which happens, but is even the source of principles according

to which everything that can be presented to us as an object is

necessarily subject to rules, because without such rules we never

could attain to cognition of an object. Even the laws of nature, if

they are contemplated as principles of the empirical use of the

understanding, possess also a characteristic of necessity, and we

may therefore at least expect them to be determined upon grounds which

are valid a priori and antecedent to all experience. But all laws of

nature, without distinction, are subject to higher principles of the

understanding, inasmuch as the former are merely applications of the

latter to particular cases of experience. These higher principles

alone therefore give the conception, which contains the necessary

condition, and, as it were, the exponent of a rule; experience, on the

other hand, gives the case which comes under the rule.

  There is no danger of our mistaking merely empirical principles

for principles of the pure understanding, or conversely; for the

character of necessity, according to conceptions which distinguish the

latter, and the absence of this in every empirical proposition, how

extensively valid soever it may be, is a perfect safeguard against

confounding them. There are, however, pure principles a priori,

which nevertheless I should not ascribe to the pure understanding- for

this reason, that they are not derived from pure conceptions, but

(although by the mediation of the understanding) from pure intuitions.

But understanding is the faculty of conceptions. Such principles

mathematical science possesses, but their application to experience,

consequently their objective validity, nay the possibility of such a

priori synthetical cognitions (the deduction thereof) rests entirely

upon the pure understanding.

  On this account, I shall not reckon among my principles those of

mathematics; though I shall include those upon the possibility and

objective validity a priori, of principles of the mathematical

science, which, consequently, are to be looked upon as the principle

of these, and which proceed from conceptions to intuition, and not

from intuition to conceptions.

  In the application of the pure conceptions of the understanding to

possible experience, the employment of their synthesis is either

mathematical or dynamical, for it is directed partly on the

intuition alone, partly on the existence of a phenomenon. But the a

priori conditions of intuition are in relation to a possible

experience absolutely necessary, those of the existence of objects

of a possible empirical intuition are in themselves contingent.

Hence the principles of the mathematical use of the categories will

possess a character of absolute necessity, that is, will be

apodeictic; those, on the other hand, of the dynamical use, the

character of an a priori necessity indeed, but only under the

condition of empirical thought in an experience, therefore only

mediately and indirectly. Consequently they will not possess that

immediate evidence which is peculiar to the former, although their

application to experience does not, for that reason, lose its truth

and certitude. But of this point we shall be better able to judge at

the conclusion of this system of principles.

  The table of the categories is naturally our guide to the table of

principles, because these are nothing else than rules for the

objective employment of the former. Accordingly, all principles of the

pure understanding are:

                                1

                              Axioms

                           of Intuition

               2                                    3

          Anticipations                          Analogies

          of Perception                        of Experience

                                4

                          Postulates of

                        Empirical Thought

                           in general

  These appellations I have chosen advisedly, in order that we might

not lose sight of the distinctions in respect of the evidence and

the employment of these principles. It will, however, soon appear

that- a fact which concerns both the evidence of these principles, and

the a priori determination of phenomena- according to the categories

of quantity and quality (if we attend merely to the form of these),

the principles of these categories are distinguishable from those of

the two others, in as much as the former are possessed of an

intuitive, but the latter of a merely discursive, though in both

instances a complete, certitude. I shall therefore call the former

mathematical, and the latter dynamical principles.* It must be

observed, however, that by these terms I mean just as little in the

one case the principles of mathematics as those of general

(physical) dynamics in the other. I have here in view merely the

principles of the pure understanding, in their application to the

internal sense (without distinction of the representations given

therein), by means of which the sciences of mathematics and dynamics

become possible. Accordingly, I have named these principles rather

with reference to their application than their content; and I shall

now proceed to consider them in the order in which they stand in the

table.

  *All combination (conjunctio) is either composition (compositio)

or connection (nexus). The former is the synthesis of a manifold,

the parts of which do not necessarily belong to each other. For

example, the two triangles into which a square is divided by a

diagonal, do not necessarily belong to each other, and of this kind is

the synthesis of the homogeneous in everything that can be

mathematically considered. This synthesis can be divided into those of

aggregation and coalition, the former of which is applied to

extensive, the latter to intensive quantities. The second sort of

combination (nexus) is the synthesis of a manifold, in so far as its

parts do belong necessarily to each other; for example, the accident

to a substance, or the effect to the cause. Consequently it is a

synthesis of that which though heterogeneous, is represented as

connected a priori. This combination- not an arbitrary one- I

entitle dynamical because it concerns the connection of the

existence of the manifold. This, again, may be divided into the

physical synthesis, of the phenomena divided among each other, and the

metaphysical synthesis, or the connection of phenomena a priori in the

faculty of cognition.

                 1. AXIOMS OF INTUITION.

     The principle of these is: All Intuitions are Extensive

                      Quantities.

                         PROOF.

  All phenomena contain, as regards their form, an intuition in

space and time, which lies a priori at the foundation of all without

exception. Phenomena, therefore, cannot be apprehended, that is,

received into empirical consciousness otherwise than through the

synthesis of a manifold, through which the representations of a

determinate space or time are generated; that is to say, through the

composition of the homogeneous and the consciousness of the

synthetical unity of this manifold (homogeneous). Now the

consciousness of a homogeneous manifold in intuition, in so far as

thereby the representation of an object is rendered possible, is the

conception of a quantity (quanti). Consequently, even the perception

of an object as phenomenon is possible only through the same

synthetical unity of the manifold of the given sensuous intuition,

through which the unity of the composition of the homogeneous manifold

in the conception of a quantity is cogitated; that is to say, all

phenomena are quantities, and extensive quantities, because as

intuitions in space or time they must be represented by means of the

same synthesis through which space and time themselves are determined.

  An extensive quantity I call that wherein the representation of

the parts renders possible (and therefore necessarily antecedes) the

representation of the whole. I cannot represent to myself any line,

however small, without drawing it in thought, that is, without

generating from a point all its parts one after another, and in this

way alone producing this intuition. Precisely the same is the case

with every, even the smallest, portion of time. I cogitate therein

only the successive progress from one moment to another, and hence, by

means of the different portions of time and the addition of them, a

determinate quantity of time is produced. As the pure intuition in all

phenomena is either time or space, so is every phenomenon in its

character of intuition an extensive quantity, inasmuch as it can

only be cognized in our apprehension by successive synthesis (from

part to part). All phenomena are, accordingly, to be considered as

aggregates, that is, as a collection of previously given parts;

which is not the case with every sort of quantities, but only with

those which are represented and apprehended by us as extensive.

  On this successive synthesis of the productive imagination, in the

generation of figures, is founded the mathematics of extension, or

geometry, with its axioms, which express the conditions of sensuous

intuition a priori, under which alone the schema of a pure

conception of external intuition can exist; for example, "be tween two

points only one straight line is possible," "two straight lines cannot

enclose a space," etc. These are the axioms which properly relate only

to quantities (quanta) as such.

  But, as regards the quantity of a thing (quantitas), that is to say,

the answer to the question: "How large is this or that object?"

although, in respect to this question, we have various propositions

synthetical and immediately certain (indemonstrabilia); we have, in

the proper sense of the term, no axioms. For example, the

propositions: "If equals be added to equals, the wholes are equal";

"If equals be taken from equals, the remainders are equal"; are

analytical, because I am immediately conscious of the identity of

the production of the one quantity with the production of the other;

whereas axioms must be a priori synthetical propositions. On the other

hand, the self-evident propositions as to the relation of numbers, are

certainly synthetical but not universal, like those of geometry, and

for this reason cannot be called axioms, but numerical formulae.

That 7 + 5 = 12 is not an analytical proposition. For neither in the

representation of seven, nor of five, nor of the composition of the

two numbers, do I cogitate the number twelve. (Whether I cogitate

the number in the addition of both, is not at present the question;

for in the case of an analytical proposition, the only point is

whether I really cogitate the predicate in the representation of the

subject.) But although the proposition is synthetical, it is

nevertheless only a singular proposition. In so far as regard is

here had merely to the synthesis of the homogeneous (the units), it

cannot take place except in one manner, although our use of these

numbers is afterwards general. If I say: "A triangle can be

constructed with three lines, any two of which taken together are

greater than the third," I exercise merely the pure function of the

productive imagination, which may draw the lines longer or shorter and

construct the angles at its pleasure. On the contrary, the number

seven is possible only in one manner, and so is likewise the number

twelve, which results from the synthesis of seven and five. Such

propositions, then, cannot be termed axioms (for in that case we

should have an infinity of these), but numerical formulae.

  This transcendental principle of the mathematics of phenomena

greatly enlarges our a priori cognition. For it is by this principle

alone that pure mathematics is rendered applicable in all its

precision to objects of experience, and without it the validity of

this application would not be so self-evident; on the contrary,

contradictions and confusions have often arisen on this very point.

Phenomena are not things in themselves. Empirical intuition is

possible only through pure intuition (of space and time);

consequently, what geometry affirms of the latter, is indisputably

valid of the former. All evasions, such as the statement that

objects of sense do not conform to the rules of construction in

space (for example, to the rule of the infinite divisibility of

lines or angles), must fall to the ground. For, if these objections

hold good, we deny to space, and with it to all mathematics, objective

validity, and no longer know wherefore, and how far, mathematics can

be applied to phenomena. The synthesis of spaces and times as the

essential form of all intuition, is that which renders possible the

apprehension of a phenomenon, and therefore every external experience,

consequently all cognition of the objects of experience; and

whatever mathematics in its pure use proves of the former, must

necessarily hold good of the latter. All objections are but the

chicaneries of an ill-instructed reason, which erroneously thinks to

liberate the objects of sense from the formal conditions of our

sensibility, and represents these, although mere phenomena, as

things in themselves, presented as such to our understanding. But in

this case, no a priori synthetical cognition of them could be

possible, consequently not through pure conceptions of space and the

science which determines these conceptions, that is to say,

geometry, would itself be impossible.

                2. ANTICIPATIONS OF PERCEPTION.

    The principle of these is: In all phenomena the Real, that

      which is an object of sensation, has Intensive Quantity,

                  that is, has a Degree.

                         PROOF.

  Perception is empirical consciousness, that is to say, a

consciousness which contains an element of sensation. Phenomena as

objects of perception are not pure, that is, merely formal intuitions,

like space and time, for they cannot be perceived in themselves.

They contain, then, over and above the intuition, the materials for an

object (through which is represented something existing in space or

time), that is to say, they contain the real of sensation, as a

representation merely subjective, which gives us merely the

consciousness that the subject is affected, and which we refer to some

external object. Now, a gradual transition from empirical

consciousness to pure consciousness is possible, inasmuch as the

real in this consciousness entirely vanishes, and there remains a

merely formal consciousness (a priori) of the manifold in time and

space; consequently there is possible a synthesis also of the

production of the quantity of a sensation from its commencement,

that is, from the pure intuition = 0 onwards up to a certain

quantity of the sensation. Now as sensation in itself is not an

objective representation, and in it is to be found neither the

intuition of space nor of time, it cannot possess any extensive

quantity, and yet there does belong to it a quantity (and that by

means of its apprehension, in which empirical consciousness can within

a certain time rise from nothing = 0 up to its given amount),

consequently an intensive quantity. And thus we must ascribe intensive

quantity, that is, a degree of influence on sense to all objects of

perception, in so far as this perception contains sensation.

  All cognition, by means of which I am enabled to cognize and

determine a priori what belongs to empirical cognition, may be

called an anticipation; and without doubt this is the sense in which

Epicurus employed his expression prholepsis. But as there is in

phenomena something which is never cognized a priori, which on this

account constitutes the proper difference between pure and empirical

cognition, that is to say, sensation (as the matter of perception), it

follows, that sensation is just that element in cognition which cannot

be at all anticipated. On the other hand, we might very well term

the pure determinations in space and time, as well in regard to figure

as to quantity, anticipations of phenomena, because they represent a

priori that which may always be given a posteriori in experience.

But suppose that in every sensation, as sensation in general,

without any particular sensation being thought of, there existed

something which could be cognized a priori, this would deserve to be

called anticipation in a special sense- special, because it may seem

surprising to forestall experience, in that which concerns the

matter of experience, and which we can only derive from itself. Yet

such really is the case here.

  Apprehension, by means of sensation alone, fills only one moment,

that is, if I do not take into consideration a succession of many

sensations. As that in the phenomenon, the apprehension of which is

not a successive synthesis advancing from parts to an entire

representation, sensation has therefore no extensive quantity; the

want of sensation in a moment of time would represent it as empty,

consequently = O. That which in the empirical intuition corresponds to

sensation is reality (realitas phaenomenon); that which corresponds to

the absence of it, negation = O. Now every sensation is capable of a

diminution, so that it can decrease, and thus gradually disappear.

Therefore, between reality in a phenomenon and negation, there

exists a continuous concatenation of many possible intermediate

sensations, the difference of which from each other is always

smaller than that between the given sensation and zero, or complete

negation. That is to say, the real in a phenomenon has always a

quantity, which however is not discoverable in apprehension,

inasmuch as apprehension take place by means of mere sensation in

one instant, and not by the successive synthesis of many sensations,

and therefore does not progress from parts to the whole. Consequently,

it has a quantity, but not an extensive quantity.

  Now that quantity which is apprehended only as unity, and in which

plurality can be represented only by approximation to negation = O,

I term intensive quantity. Consequently, reality in a phenomenon has

intensive quantity, that is, a degree. if we consider this reality

as cause (be it of sensation or of another reality in the

phenomenon, for example, a change), we call the degree of reality in

its character of cause a momentum, for example, the momentum of

weight; and for this reason, that the degree only indicates that

quantity the apprehension of which is not successive, but

instantaneous. This, however, I touch upon only in passing, for with

causality I have at present nothing to do.

  Accordingly, every sensation, consequently every reality in

phenomena, however small it may be, has a degree, that is, an

intensive quantity, which may always be lessened, and between

reality and negation there exists a continuous connection of

possible realities, and possible smaller perceptions. Every colour-

for example, red- has a degree, which, be it ever so small, is never

the smallest, and so is it always with heat, the momentum of weight,

etc.

  This property of quantities, according to which no part of them is

the smallest possible (no part simple), is called their continuity.

Space and time are quanta continua, because no part of them can be

given, without enclosing it within boundaries (points and moments),

consequently, this given part is itself a space or a time. Space,

therefore, consists only of spaces, and time of times. Points and

moments are only boundaries, that is, the mere places or positions

of their limitation. But places always presuppose intuitions which are

to limit or determine them; and we cannot conceive either space or

time composed of constituent parts which are given before space or

time. Such quantities may also be called flowing, because synthesis

(of the productive imagination) in the production of these

quantities is a progression in time, the continuity of which we are

accustomed to indicate by the expression flowing.

  All phenomena, then, are continuous quantities, in respect both to

intuition and mere perception (sensation, and with it reality). In the

former case they are extensive quantities; in the latter, intensive.

When the synthesis of the manifold of a phenomenon is interrupted,

there results merely an aggregate of several phenomena, and not

properly a phenomenon as a quantity, which is not produced by the mere

continuation of the productive synthesis of a certain kind, but by the

repetition of a synthesis always ceasing. For example, if I call

thirteen dollars a sum or quantity of money, I employ the term quite

correctly, inasmuch as I understand by thirteen dollars the value of a

mark in standard silver, which is, to be sure, a continuous

quantity, in which no part is the smallest, but every part might

constitute a piece of money, which would contain material for still

smaller pieces. If, however, by the words thirteen dollars I

understand so many coins (be their value in silver what it may), it

would be quite erroneous to use the expression a quantity of

dollars; on the contrary, I must call them aggregate, that is, a

number of coins. And as in every number we must have unity as the

foundation, so a phenomenon taken as unity is a quantity, and as

such always a continuous quantity (quantum continuum).

  Now, seeing all phenomena, whether considered as extensive or

intensive, are continuous quantities, the proposition: "All change

(transition of a thing from one state into another) is continuous,"

might be proved here easily, and with mathematical evidence, were it

not that the causality of a change lies, entirely beyond the bounds of

a transcendental philosophy, and presupposes empirical principles. For

of the possibility of a cause which changes the condition of things,

that is, which determines them to the contrary to a certain given

state, the understanding gives us a priori no knowledge; not merely

because it has no insight into the possibility of it (for such insight

is absent in several a priori cognitions), but because the notion of

change concerns only certain determinations of phenomena, which

experience alone can acquaint us with, while their cause lies in the

unchangeable. But seeing that we have nothing which we could here

employ but the pure fundamental conceptions of all possible

experience, among which of course nothing empirical can be admitted,

we dare not, without injuring the unity of our system, anticipate

general physical science, which is built upon certain fundamental

experiences.

  Nevertheless, we are in no want of proofs of the great influence

which the principle above developed exercises in the anticipation of

perceptions, and even in supplying the want of them, so far as to

shield us against the false conclusions which otherwise we might

rashly draw.

  If all reality in perception has a degree, between which and

negation there is an endless sequence of ever smaller degrees, and if,

nevertheless, every sense must have a determinate degree of

receptivity for sensations; no perception, and consequently no

experience is possible, which can prove, either immediately or

mediately, an entire absence of all reality in a phenomenon; in

other words, it is impossible ever to draw from experience a proof

of the existence of empty space or of empty time. For in the first

place, an entire absence of reality in a sensuous intuition cannot

of course be an object of perception; secondly, such absence cannot be

deduced from the contemplation of any single phenomenon, and the

difference of the degrees in its reality; nor ought it ever to be

admitted in explanation of any phenomenon. For if even the complete

intuition of a determinate space or time is thoroughly real, that

is, if no part thereof is empty, yet because every reality has its

degree, which, with the extensive quantity of the phenomenon

unchanged, can diminish through endless gradations down to nothing

(the void), there must be infinitely graduated degrees, with which

space or time is filled, and the intensive quantity in different

phenomena may be smaller or greater, although the extensive quantity

of the intuition remains equal and unaltered.

  We shall give an example of this. Almost all natural philosophers,

remarking a great difference in the quantity of the matter of

different kinds in bodies with the same volume (partly on account of

the momentum of gravity or weight, partly on account of the momentum

of resistance to other bodies in motion), conclude unanimously that

this volume (extensive quantity of the phenomenon) must be void in all

bodies, although in different proportion. But who would suspect that

these for the most part mathematical and mechanical inquirers into

nature should ground this conclusion solely on a metaphysical

hypothesis- a sort of hypothesis which they profess to disparage and

avoid? Yet this they do, in assuming that the real in space (I must

not here call it impenetrability or weight, because these are

empirical conceptions) is always identical, and can only be

distinguished according to its extensive quantity, that is,

multiplicity. Now to this presupposition, for which they can have no

ground in experience, and which consequently is merely metaphysical, I

oppose a transcendental demonstration, which it is true will not

explain the difference in the filling up of spaces, but which

nevertheless completely does away with the supposed necessity of the

above-mentioned presupposition that we cannot explain the said

difference otherwise than by the hypothesis of empty spaces. This

demonstration, moreover, has the merit of setting the understanding at

liberty to conceive this distinction in a different manner, if the

explanation of the fact requires any such hypothesis. For we

perceive that although two equal spaces may be completely filled by

matters altogether different, so that in neither of them is there left

a single point wherein matter is not present, nevertheless, every

reality has its degree (of resistance or of weight), which, without

diminution of the extensive quantity, can become less and less ad

infinitum, before it passes into nothingness and disappears. Thus an

expansion which fills a space- for example, caloric, or any other

reality in the phenomenal world- can decrease in its degrees to

infinity, yet without leaving the smallest part of the space empty; on

the contrary, filling it with those lesser degrees as completely as

another phenomenon could with greater. My intention here is by no

means to maintain that this is really the case with the difference

of matters, in regard to their specific gravity; I wish only to prove,

from a principle of the pure understanding, that the nature of our

perceptions makes such a mode of explanation possible, and that it

is erroneous to regard the real in a phenomenon as equal quoad its

degree, and different only quoad its aggregation and extensive

quantity, and this, too, on the pretended authority of an a priori

principle of the understanding.

  Nevertheless, this principle of the anticipation of perception

must somewhat startle an inquirer whom initiation into

transcendental philosophy has rendered cautious. We must naturally

entertain some doubt whether or not the understanding can enounce

any such synthetical proposition as that respecting the degree of

all reality in phenomena, and consequently the possibility of the

internal difference of sensation itself- abstraction being made of its

empirical quality. Thus it is a question not unworthy of solution:

"How the understanding can pronounce synthetically and a priori

respecting phenomena, and thus anticipate these, even in that which is

peculiarly and merely empirical, that, namely, which concerns

sensation itself?"

  The quality of sensation is in all cases merely empirical, and

cannot be represented a priori (for example, colours, taste, etc.).

But the real- that which corresponds to sensation- in opposition to

negation = O, only represents something the conception of which in

itself contains a being (ein seyn), and signifies nothing but the

synthesis in an empirical consciousness. That is to say, the empirical

consciousness in the internal sense can be raised from 0 to every

higher degree, so that the very same extensive quantity of

intuition, an illuminated surface, for example, excites as great a

sensation as an aggregate of many other surfaces less illuminated.

We can therefore make complete abstraction of the extensive quantity

of a phenomenon, and represent to ourselves in the mere sensation in a

certain momentum, a synthesis of homogeneous ascension from 0 up to

the given empirical consciousness, All sensations therefore as such

are given only a posteriori, but this property thereof, namely, that

they have a degree, can be known a priori. It is worthy of remark,

that in respect to quantities in general, we can cognize a priori only

a single quality, namely, continuity; but in respect to all quality

(the real in phenomena), we cannot cognize a priori anything more than

the intensive quantity thereof, namely, that they have a degree. All

else is left to experience.

                  3. ANALOGIES OF EXPERIENCE.

    The principle of these is: Experience is possible only

     through the representation of a necessary connection

                      of Perceptions.

                           PROOF.

  Experience is an empirical cognition; that is to say, a cognition

which determines an object by means of perceptions. It is therefore

a synthesis of perceptions, a synthesis which is not itself

contained in perception, but which contains the synthetical unity of

the manifold of perception in a consciousness; and this unity

constitutes the essential of our cognition of objects of the senses,

that is, of experience (not merely of intuition or sensation). Now

in experience our perceptions come together contingently, so that no

character of necessity in their connection appears, or can appear from

the perceptions themselves, because apprehension is only a placing

together of the manifold of empirical intuition, and no representation

of a necessity in the connected existence of the phenomena which

apprehension brings together, is to be discovered therein. But as

experience is a cognition of objects by means of perceptions, it

follows that the relation of the existence of the existence of the

manifold must be represented in experience not as it is put together

in time, but as it is objectively in time. And as time itself cannot

be perceived, the determination of the existence of objects in time

can only take place by means of their connection in time in general,

consequently only by means of a priori connecting conceptions. Now

as these conceptions always possess the character of necessity,

experience is possible only by means of a representation of the

necessary connection of perception.

  The three modi of time are permanence, succession, and

coexistence. Accordingly, there are three rules of all relations of

time in phenomena, according to which the existence of every

phenomenon is determined in respect of the unity of all time, and

these antecede all experience and render it possible.

  The general principle of all three analogies rests on the

necessary unity of apperception in relation to all possible

empirical consciousness (perception) at every time, consequently, as

this unity lies a priori at the foundation of all mental operations,

the principle rests on the synthetical unity of all phenomena

according to their relation in time. For the original apperception

relates to our internal sense (the complex of all representations),

and indeed relates a priori to its form, that is to say, the

relation of the manifold empirical consciousness in time. Now this

manifold must be combined in original apperception according to

relations of time- a necessity imposed by the a priori

transcendental unity of apperception, to which is subjected all that

can belong to my (i.e., my own) cognition, and therefore all that

can become an object for me. This synthetical and a priori

determined unity in relation of perceptions in time is therefore the

rule: "All empirical determinations of time must be subject to rules

of the general determination of time"; and the analogies of

experience, of which we are now about to treat, must be rules of

this nature.

  These principles have this peculiarity, that they do not concern

phenomena, and the synthesis of the empirical intuition thereof, but

merely the existence of phenomena and their relation to each other

in regard to this existence. Now the mode in which we apprehend a

thing in a phenomenon can be determined a priori in such a manner that

the rule of its synthesis can give, that is to say, can produce this a

priori intuition in every empirical example. But the existence of

phenomena cannot be known a priori, and although we could arrive by

this path at a conclusion of the fact of some existence, we could

not cognize that existence determinately, that is to say, we should be

incapable of anticipating in what respect the empirical intuition of

it would be distinguishable from that of others.

  The two principles above mentioned, which I called mathematical,

in consideration of the fact of their authorizing the application of

mathematic phenomena, relate to these phenomena only in regard to

their possibility, and instruct us how phenomena, as far as regards

their intuition or the real in their perception, can be generated

according to the rules of a mathematical synthesis. Consequently,

numerical quantities, and with them the determination of a

phenomenon as a quantity, can be employed in the one case as well as

in the other. Thus, for example, out of 200,000 illuminations by the

moon, I might compose and give a priori, that is construct, the degree

of our sensations of the sunlight. We may therefore entitle these

two principles constitutive.

  The case is very different with those principles whose province it

is to subject the existence of phenomena to rules a priori. For as

existence does not admit of being constructed, it is clear that they

must only concern the relations of existence and be merely

regulative principles. In this case, therefore, neither axioms nor

anticipations are to be thought of. Thus, if a perception is given us,

in a certain relation of time to other (although undetermined)

perceptions, we cannot then say a priori, what and how great (in

quantity) the other perception necessarily connected with the former

is, but only how it is connected, quoad its existence, in this given

modus of time. Analogies in philosophy mean something very different

from that which they represent in mathematics. In the latter they

are formulae, which enounce the equality of two relations of quantity,

and are always constitutive, so that if two terms of the proportion

are given, the third is also given, that is, can be constructed by the

aid of these formulae. But in philosophy, analogy is not the

equality of two quantitative but of two qualitative relations. In this

case, from three given terms, I can give a priori and cognize the

relation to a fourth member, but not this fourth term itself, although

I certainly possess a rule to guide me in the search for this fourth

term in experience, and a mark to assist me in discovering it. An

analogy of experience is therefore only a rule according to which

unity of experience must arise out of perceptions in respect to

objects (phenomena) not as a constitutive, but merely as a

regulative principle. The same holds good also of the postulates of

empirical thought in general, which relate to the synthesis of mere

intuition (which concerns the form of phenomena), the synthesis of

perception (which concerns the matter of phenomena), and the synthesis

of experience (which concerns the relation of these perceptions).

For they are only regulative principles, and clearly distinguishable

from the mathematical, which are constitutive, not indeed in regard to

the certainty which both possess a priori, but in the mode of evidence

thereof, consequently also in the manner of demonstration.

  But what has been observed of all synthetical propositions, and must

be particularly remarked in this place, is this, that these

analogies possess significance and validity, not as principles of

the transcendental, but only as principles of the empirical use of the

understanding, and their truth can therefore be proved only as such,

and that consequently the phenomena must not be subjoined directly

under the categories, but only under their schemata. For if the

objects to which those principles must be applied were things in

themselves, it would be quite impossible to cognize aught concerning

them synthetically a priori. But they are nothing but phenomena; a

complete knowledge of which- a knowledge to which all principles a

priori must at last relate- is the only possible experience. It

follows that these principles can have nothing else for their aim than

the conditions of the empirical cognition in the unity of synthesis of

phenomena. But this synthesis is cogitated only in the schema of the

pure conception of the understanding, of whose unity, as that of a

synthesis in general, the category contains the function

unrestricted by any sensuous condition. These principles will

therefore authorize us to connect phenomena according to an analogy,

with the logical and universal unity of conceptions, and

consequently to employ the categories in the principles themselves;

but in the application of them to experience, we shall use only

their schemata, as the key to their proper application, instead of the

categories, or rather the latter as restricting conditions, under

the title of "formulae" of the former.

                     A. FIRST ANALOGY.

           Principle of the Permanence of Substance.

   In all changes of phenomena, substance is permanent, and the

   quantum thereof in nature is neither increased nor diminished.

                          PROOF.

  All phenomena exist in time, wherein alone as substratum, that is,

as the permanent form of the internal intuition, coexistence and

succession can be represented. Consequently time, in which all changes

of phenomena must be cogitated, remains and changes not, because it is

that in which succession and coexistence can be represented only as

determinations thereof. Now, time in itself cannot be an object of

perception. It follows that in objects of perception, that is, in

phenomena, there must be found a substratum which represents time in

general, and in which all change or coexistence can be perceived by

means of the relation of phenomena to it. But the substratum of all

reality, that is, of all that pertains to the existence of things,

is substance; all that pertains to existence can be cogitated only

as a determination of substance. Consequently, the permanent, in

relation to which alone can all relations of time in phenomena be

determined, is substance in the world of phenomena, that is, the

real in phenomena, that which, as the substratum of all change,

remains ever the same. Accordingly, as this cannot change in

existence, its quantity in nature can neither be increased nor

diminished.

  Our apprehension of the manifold in a phenomenon is always

successive, is Consequently always changing. By it alone we could,

therefore, never determine whether this manifold, as an object of

experience, is coexistent or successive, unless it had for a

foundation something fixed and permanent, of the existence of which

all succession and coexistence are nothing but so many modes (modi

of time). Only in the permanent, then, are relations of time

possible (for simultaneity and succession are the only relations in

time); that is to say, the permanent is the substratum of our

empirical representation of time itself, in which alone all

determination of time is possible. Permanence is, in fact, just

another expression for time, as the abiding correlate of all existence

of phenomena, and of all change, and of all coexistence. For change

does not affect time itself, but only the phenomena in time (just as

coexistence cannot be regarded as a modus of time itself, seeing

that in time no parts are coexistent, but all successive). If we

were to attribute succession to time itself, we should be obliged to

cogitate another time, in which this succession would be possible.

It is only by means of the permanent that existence in different parts

of the successive series of time receives a quantity, which we entitle

duration. For in mere succession, existence is perpetually vanishing

and recommencing, and therefore never has even the least quantity.

Without the permanent, then, no relation in time is possible. Now,

time in itself is not an object of perception; consequently the

permanent in phenomena must be regarded as the substratum of all

determination of time, and consequently also as the condition of the

possibility of all synthetical unity of perceptions, that is, of

experience; and all existence and all change in time can only be

regarded as a mode in the existence of that which abides unchangeably.

Therefore, in all phenomena, the permanent is the object in itself,

that is, the substance (phenomenon); but all that changes or can

change belongs only to the mode of the existence of this substance

or substances, consequently to its determinations.

  I find that in all ages not only the philosopher, but even the

common understanding, has preposited this permanence as a substratum

of all change in phenomena; indeed, I am compelled to believe that

they will always accept this as an indubitable fact. Only the

philosopher expresses himself in a more precise and definite manner,

when he says: "In all changes in the world, the substance remains, and

the accidents alone are changeable." But of this decidedly synthetical

proposition, I nowhere meet with even an attempt at proof; nay, it

very rarely has the good fortune to stand, as it deserves to do, at

the head of the pure and entirely a priori laws of nature. In truth,

the statement that substance is permanent, is tautological. For this

very permanence is the ground on which we apply the category of

substance to the phenomenon; and we should have been obliged to

prove that in all phenomena there is something permanent, of the

existence of which the changeable is nothing but a determination.

But because a proof of this nature cannot be dogmatical, that is,

cannot be drawn from conceptions, inasmuch as it concerns a

synthetical proposition a priori, and as philosophers never

reflected that such propositions are valid only in relation to

possible experience, and therefore cannot be proved except by means of

a deduction of the possibility of experience, it is no wonder that

while it has served as the foundation of all experience (for we feel

the need of it in empirical cognition), it has never been supported by

proof.

  A philosopher was asked: "What is the weight of smoke?" He answered:

"Subtract from the weight of the burnt wood the weight of the

remaining ashes, and you will have the weight of the smoke." Thus he

presumed it to be incontrovertible that even in fire the matter

(substance) does not perish, but that only the form of it undergoes

a change. In like manner was the saying: "From nothing comes nothing,"

only another inference from the principle or permanence, or rather

of the ever-abiding existence of the true subject in phenomena. For if

that in the phenomenon which we call substance is to be the proper

substratum of all determination of time, it follows that all existence

in past as well as in future time, must be determinable by means of it

alone. Hence we are entitled to apply the term substance to a

phenomenon, only because we suppose its existence in all time, a

notion which the word permanence does not fully express, as it seems

rather to be referable to future time. However, the internal necessity

perpetually to be, is inseparably connected with the necessity

always to have been, and so the expression may stand as it is.

"Gigni de nihilo nihil; in nihilum nil posse reverti,"* are two

propositions which the ancients never parted, and which people

nowadays sometimes mistakenly disjoin, because they imagine that the

propositions apply to objects as things in themselves, and that the

former might be inimical to the dependence (even in respect of its

substance also) of the world upon a supreme cause. But this

apprehension is entirely needless, for the question in this case is

only of phenomena in the sphere of experience, the unity of which

never could be possible, if we admitted the possibility that new

things (in respect of their substance) should arise. For in that case,

we should lose altogether that which alone can represent the unity

of time, to wit, the identity of the substratum, as that through which

alone all change possesses complete and thorough unity. This

permanence is, however, nothing but the manner in which we represent

to ourselves the existence of things in the phenomenal world.

  *[Persius, Satirae, iii.83-84. "Nothing can be produced from

nothing; nothing can be returned into nothing."]

  The determinations of a substance, which are only particular modes

of its existence, are called accidents. They are always real,

because they concern the existence of substance (negations are only

determinations, which express the non-existence of something in the

substance). Now, if to this real in the substance we ascribe a

particular existence (for example, to motion as an accident of

matter), this existence is called inherence, in contradistinction to

the existence of substance, which we call subsistence. But hence arise

many misconceptions, and it would be a more accurate and just mode

of expression to designate the accident only as the mode in which

the existence of a substance is positively determined. Meanwhile, by

reason of the conditions of the logical exercise of our understanding,

it is impossible to avoid separating, as it were, that which in the

existence of a substance is subject to change, whilst the substance

remains, and regarding it in relation to that which is properly

permanent and radical. On this account, this category of substance

stands under the title of relation, rather because it is the condition

thereof than because it contains in itself any relation.

  Now, upon this notion of permanence rests the proper notion of the

conception change. Origin and extinction are not changes of that which

originates or becomes extinct. Change is but a mode of existence,

which follows on another mode of existence of the same object; hence

all that changes is permanent, and only the condition thereof changes.

Now since this mutation affects only determinations, which can have

a beginning or an end, we may say, employing an expression which seems

somewhat paradoxical: "Only the permanent (substance) is subject to

change; the mutable suffers no change, but rather alternation, that

is, when certain determinations cease, others begin."

  Change, when, cannot be perceived by us except in substances, and

origin or extinction in an absolute sense, that does not concern

merely a determination of the permanent, cannot be a possible

perception, for it is this very notion of the permanent which

renders possible the representation of a transition from one state

into another, and from non-being to being, which, consequently, can be

empirically cognized only as alternating determinations of that

which is permanent. Grant that a thing absolutely begins to be; we

must then have a point of time in which it was not. But how and by

what can we fix and determine this point of time, unless by that which

already exists? For a void time- preceding- is not an object of

perception; but if we connect this beginning with objects which

existed previously, and which continue to exist till the object in

question in question begins to be, then the latter can only be a

determination of the former as the permanent. The same holds good of

the notion of extinction, for this presupposes the empirical

representation of a time, in which a phenomenon no longer exists.

  Substances (in the world of phenomena) are the substratum of all

determinations of time. The beginning of some, and the ceasing to be

of other substances, would utterly do away with the only condition

of the empirical unity of time; and in that case phenomena would

relate to two different times, in which, side by side, existence would

pass; which is absurd. For there is only one time in which all

different times must be placed, not as coexistent, but as successive.

  Accordingly, permanence is a necessary condition under which alone

phenomena, as things or objects, are determinable in a possible

experience. But as regards the empirical criterion of this necessary

permanence, and with it of the substantiality of phenomena, we shall

find sufficient opportunity to speak in the sequel.

                   B. SECOND ANALOGY.

      Principle of the Succession of Time According

                to the Law of Causality.

     All changes take place according to the law of the

              connection of Cause and Effect.

                         PROOF.

  (That all phenomena in the succession of time are only changes, that

is, a successive being and non-being of the determinations of

substance, which is permanent; consequently that a being of

substance itself which follows on the non-being thereof, or a

non-being of substance which follows on the being thereof, in other

words, that the origin or extinction of substance itself, is

impossible- all this has been fully established in treating of the

foregoing principle. This principle might have been expressed as

follows: "All alteration (succession) of phenomena is merely

change"; for the changes of substance are not origin or extinction,

because the conception of change presupposes the same subject as

existing with two opposite determinations, and consequently as

permanent. After this premonition, we shall proceed to the proof.)

  I perceive that phenomena succeed one another, that is to say, a

state of things exists at one time, the opposite of which existed in a

former state. In this case, then, I really connect together two

perceptions in time. Now connection is not an operation of mere

sense and intuition, but is the product of a synthetical faculty of

imagination, which determines the internal sense in respect of a

relation of time. But imagination can connect these two states in

two ways, so that either the one or the other may antecede in time;

for time in itself cannot be an object of perception, and what in an

object precedes and what follows cannot be empirically determined in

relation to it. I am only conscious, then, that my imagination

places one state before and the other after; not that the one state

antecedes the other in the object. In other words, the objective

relation of the successive phenomena remains quite undetermined by

means of mere perception. Now in order that this relation may be

cognized as determined, the relation between the two states must be so

cogitated that it is thereby determined as necessary, which of them

must be placed before and which after, and not conversely. But the

conception which carries with it a necessity of synthetical unity, can

be none other than a pure conception of the understanding which does

not lie in mere perception; and in this case it is the conception of

"the relation of cause and effect," the former of which determines the

latter in time, as its necessary consequence, and not as something

which might possibly antecede (or which might in some cases not be

perceived to follow). It follows that it is only because we subject

the sequence of phenomena, and consequently all change, to the law

of causality, that experience itself, that is, empirical cognition

of phenomena, becomes possible; and consequently, that phenomena

themselves, as objects of experience, are possible only by virtue of

this law.

  Our apprehension of the manifold of phenomena is always

successive. The representations of parts succeed one another.

Whether they succeed one another in the object also, is a second point

for reflection, which was not contained in the former. Now we may

certainly give the name of object to everything, even to every

representation, so far as we are conscious thereof; but what this word

may mean in the case of phenomena, not merely in so far as they (as

representations) are objects, but only in so far as they indicate an

object, is a question requiring deeper consideration. In so far as

they, regarded merely as representations, are at the same time objects

of consciousness, they are not to be distinguished from

apprehension, that is, reception into the synthesis of imagination,

and we must therefore say: "The manifold of phenomena is always

produced successively in the mind." If phenomena were things in

themselves, no man would be able to conjecture from the succession

of our representations how this manifold is connected in the object;

for we have to do only with our representations. How things may be

in themselves, without regard to the representations through which

they affect us, is utterly beyond the sphere of our cognition. Now

although phenomena are not things in themselves, and are

nevertheless the only thing given to us to be cognized, it is my

duty to show what sort of connection in time belongs to the manifold

in phenomena themselves, while the representation of this manifold

in apprehension is always successive. For example, the apprehension of

the manifold in the phenomenon of a house which stands before me, is

successive. Now comes the question whether the manifold of this

house is in itself successive- which no one will be at all willing

to grant. But, so soon as I raise my conception of an object to the

transcendental signification thereof, I find that the house is not a

thing in itself, but only a phenomenon, that is, a representation, the

transcendental object of which remains utterly unknown. What then am I

to understand by the question: "How can the manifold be connected in

the phenomenon itself- not considered as a thing in itself, but merely

as a phenomenon?" Here that which lies in my successive apprehension

is regarded as representation, whilst the phenomenon which is given

me, notwithstanding that it is nothing more than a complex of these

representations, is regarded as the object thereof, with which my

conception, drawn from the representations of apprehension, must

harmonize. It is very soon seen that, as accordance of the cognition

with its object constitutes truth, the question now before us can only

relate to the formal conditions of empirical truth; and that the

phenomenon, in opposition to the representations of apprehension,

can only be distinguished therefrom as the object of them, if it is

subject to a rule which distinguishes it from every other

apprehension, and which renders necessary a mode of connection of

the manifold. That in the phenomenon which contains the condition of

this necessary rule of apprehension, is the object.

  Let us now proceed to our task. That something happens, that is to

say, that something or some state exists which before was not,

cannot be empirically perceived, unless a phenomenon precedes, which

does not contain in itself this state. For a reality which should

follow upon a void time, in other words, a beginning, which no state

of things precedes, can just as little be apprehended as the void time

itself. Every apprehension of an event is therefore a perception which

follows upon another perception. But as this is the case with all

synthesis of apprehension, as I have shown above in the example of a

house, my apprehension of an event is not yet sufficiently

distinguished from other apprehensions. But I remark also that if in a

phenomenon which contains an occurrence, I call the antecedent state

of my perception, A, and the following state, B, the perception B

can only follow A in apprehension, and the perception A cannot

follow B, but only precede it. For example, I see a ship float down

the stream of a river. My perception of its place lower down follows

upon my perception of its place higher up the course of the river, and

it is impossible that, in the apprehension of this phenomenon, the

vessel should be perceived first below and afterwards higher up the

stream. Here, therefore, the order in the sequence of perceptions in

apprehension is determined; and by this order apprehension is

regulated. In the former example, my perceptions in the apprehension

of a house might begin at the roof and end at the foundation, or

vice versa; or I might apprehend the manifold in this empirical

intuition, by going from left to right, and from right to left.

Accordingly, in the series of these perceptions, there was no

determined order, which necessitated my beginning at a certain

point, in order empirically to connect the manifold. But this rule

is always to be met with in the perception of that which happens,

and it makes the order of the successive perceptions in the

apprehension of such a phenomenon necessary.

  I must, therefore, in the present case, deduce the subjective

sequence of apprehension from the objective sequence of phenomena, for

otherwise the former is quite undetermined, and one phenomenon is

not distinguishable from another. The former alone proves nothing as

to the connection of the manifold in an object, for it is quite

arbitrary. The latter must consist in the order of the manifold in a

phenomenon, according to which order the apprehension of one thing

(that which happens) follows that of another thing (which precedes),

in conformity with a rule. In this way alone can I be authorized to

say of the phenomenon itself, and not merely of my own apprehension,

that a certain order or sequence is to be found therein. That is, in

other words, I cannot arrange my apprehension otherwise than in this

order.

  In conformity with this rule, then, it is necessary that in that

which antecedes an event there be found the condition of a rule,

according to which in this event follows always and necessarily; but I

cannot reverse this and go back from the event, and determine (by

apprehension) that which antecedes it. For no phenomenon goes back

from the succeeding point of time to the preceding point, although

it does certainly relate to a preceding point of time; from a given

time, on the other hand, there is always a necessary progression to

the determined succeeding time. Therefore, because there certainly

is something that follows, I must of necessity connect it with

something else, which antecedes, and upon which it follows, in

conformity with a rule, that is necessarily, so that the event, as

conditioned, affords certain indication of a condition, and this

condition determines the event.

  Let us suppose that nothing precedes an event, upon which this event

must follow in conformity with a rule. All sequence of perception

would then exist only in apprehension, that is to say, would be merely

subjective, and it could not thereby be objectively determined what

thing ought to precede, and what ought to follow in perception. In

such a case, we should have nothing but a play of representations,

which would possess no application to any object. That is to say, it

would not be possible through perception to distinguish one phenomenon

from another, as regards relations of time; because the succession

in the act of apprehension would always be of the same sort, and

therefore there would be nothing in the phenomenon to determine the

succession, and to render a certain sequence objectively necessary.

And, in this case, I cannot say that two states in a phenomenon follow

one upon the other, but only that one apprehension follows upon

another. But this is merely subjective, and does not determine an

object, and consequently cannot be held to be cognition of an

object- not even in the phenomenal world.

  Accordingly, when we know in experience that something happens, we

always presuppose that something precedes, whereupon it follows in

conformity with a rule. For otherwise I could not say of the object

that it follows; because the mere succession in my apprehension, if it

be not determined by a rule in relation to something preceding, does

not authorize succession in the object. Only, therefore, in

reference to a rule, according to which phenomena are determined in

their sequence, that is, as they happen, by the preceding state, can I

make my subjective synthesis (of apprehension) objective, and it is

only under this presupposition that even the experience of an event is

possible.

  No doubt it appears as if this were in thorough contradiction to all

the notions which people have hitherto entertained in regard to the

procedure of the human understanding. According to these opinions,

it is by means of the perception and comparison of similar

consequences following upon certain antecedent phenomena that the

understanding is led to the discovery of a rule, according to which

certain events always follow certain phenomena, and it is only by this

process that we attain to the conception of cause. Upon such a

basis, it is clear that this conception must be merely empirical,

and the rule which it furnishes us with- "Everything that happens must

have a cause"- would be just as contingent as experience itself. The

universality and necessity of the rule or law would be perfectly

spurious attributes of it. Indeed, it could not possess universal

validity, inasmuch as it would not in this case be a priori, but

founded on deduction. But the same is the case with this law as with

other pure a priori representations (e.g., space and time), which we

can draw in perfect clearness and completeness from experience, only

because we had already placed them therein, and by that means, and

by that alone, had rendered experience possible. Indeed, the logical

clearness of this representation of a rule, determining the series

of events, is possible only when we have made use thereof in

experience. Nevertheless, the recognition of this rule, as a condition

of the synthetical unity of phenomena in time, was the ground of

experience itself and consequently preceded it a priori.

  It is now our duty to show by an example that we never, even in

experience, attribute to an object the notion of succession or

effect (of an event- that is, the happening of something that did

not exist before), and distinguish it from the subjective succession

of apprehension, unless when a rule lies at the foundation, which

compels us to observe this order of perception in preference to any

other, and that, indeed, it is this necessity which first renders

possible the representation of a succession in the object.

  We have representations within us, of which also we can be

conscious. But, however widely extended, however accurate and

thoroughgoing this consciousness may be, these representations are

still nothing more than representations, that is, internal

determinations of the mind in this or that relation of time. Now how

happens it that to these representations we should set an object, or

that, in addition to their subjective reality, as modifications, we

should still further attribute to them a certain unknown objective

reality? It is clear that objective significancy cannot consist in a

relation to another representation (of that which we desire to term

object), for in that case the question again arises: "How does this

other representation go out of itself, and obtain objective

significancy over and above the subjective, which is proper to it,

as a determination of a state of mind?" If we try to discover what

sort of new property the relation to an object gives to our subjective

representations, and what new importance they thereby receive, we

shall find that this relation has no other effect than that of

rendering necessary the connection of our representations in a certain

manner, and of subjecting them to a rule; and that conversely, it is

only because a certain order is necessary in the relations of time

of our representations, that objective significancy is ascribed to

them.

  In the synthesis of phenomena, the manifold of our representations

is always successive. Now hereby is not represented an object, for

by means of this succession, which is common to all apprehension, no

one thing is distinguished from another. But so soon as I perceive

or assume that in this succession there is a relation to a state

antecedent, from which the representation follows in accordance with a

rule, so soon do I represent something as an event, or as a thing that

happens; in other words, I cognize an object to which I must assign

a certain determinate position in time, which cannot be altered,

because of the preceding state in the object. When, therefore, I

perceive that something happens, there is contained in this

representation, in the first place, the fact, that something

antecedes; because, it. is only in relation to this that the

phenomenon obtains its proper relation of time, in other words, exists

after an antecedent time, in which it did not exist. But it can

receive its determined place in time only by the presupposition that

something existed in the foregoing state, upon which it follows

inevitably and always, that is, in conformity with a rule. From all

this it is evident that, in the first place, I cannot reverse the

order of succession, and make that which happens precede that upon

which it follows; and that, in the second place, if the antecedent

state be posited, a certain determinate event inevitably and

necessarily follows. Hence it follows that there exists a certain

order in our representations, whereby the present gives a sure

indication of some previously existing state, as a correlate, though

still undetermined, of the existing event which is given- a

correlate which itself relates to the event as its consequence,

conditions it, and connects it necessarily with itself in the series

of time.

  If then it be admitted as a necessary law of sensibility, and

consequently a formal condition of all perception, that the

preceding necessarily determines the succeeding time (inasmuch as I

cannot arrive at the succeeding except through the preceding), it must

likewise be an indispensable law of empirical representation of the

series of time that the phenomena of the past determine all

phenomena in the succeeding time, and that the latter, as events,

cannot take place, except in so far as the former determine their

existence in time, that is to say, establish it according to a rule.

For it is of course only in phenomena that we can empirically

cognize this continuity in the connection of times.

  For all experience and for the possibility of experience,

understanding is indispensable, and the first step which it takes in

this sphere is not to render the representation of objects clear,

but to render the representation of an object in general, possible. It

does this by applying the order of time to phenomena, and their

existence. In other words, it assigns to each phenomenon, as a

consequence, a place in relation to preceding phenomena, determined

a priori in time, without which it could not harmonize with time

itself, which determines a place a priori to all its parts. This

determination of place cannot be derived from the relation of

phenomena to absolute time (for it is not an object of perception);

but, on the contrary, phenomena must reciprocally determine the places

in time of one another, and render these necessary in the order of

time. In other words, whatever follows or happens, must follow in

conformity with a universal rule upon that which was contained in

the foregoing state. Hence arises a series of phenomena, which, by

means of the understanding, produces and renders necessary exactly the

same order and continuous connection in the series of our possible

perceptions, as is found a priori in the form of internal intuition

(time), in which all our perceptions must have place.

  That something happens, then, is a perception which belongs to a

possible experience, which becomes real only because I look upon the

phenomenon as determined in regard to its place in time,

consequently as an object, which can always be found by means of a

rule in the connected series of my perceptions. But this rule of the

determination of a thing according to succession in time is as

follows: "In what precedes may be found the condition, under which

an event always (that is, necessarily) follows." From all this it is

obvious that the principle of cause and effect is the principle of

possible experience, that is, of objective cognition of phenomena,

in regard to their relations in the succession of time.

  The proof of this fundamental proposition rests entirely on the

following momenta of argument. To all empirical cognition belongs

the synthesis of the manifold by the imagination, a synthesis which is

always successive, that is, in which the representations therein

always follow one another. But the order of succession in

imagination is not determined, and the series of successive

representations may be taken retrogressively as well as progressively.

But if this synthesis is a synthesis of apprehension (of the

manifold of a given phenomenon),then the order is determined in the

object, or to speak more accurately, there is therein an order of

successive synthesis which determines an object, and according to

which something necessarily precedes, and when this is posited,

something else necessarily follows. If, then, my perception is to

contain the cognition of an event, that is, of something which

really happens, it must be an empirical judgement, wherein we think

that the succession is determined; that is, it presupposes another

phenomenon, upon which this event follows necessarily, or in

conformity with a rule. If, on the contrary, when I posited the

antecedent, the event did not necessarily follow, I should be

obliged to consider it merely as a subjective play of my

imagination, and if in this I represented to myself anything as

objective, I must look upon it as a mere dream. Thus, the relation

of phenomena (as possible perceptions), according to which that

which happens is, as to its existence, necessarily determined in

time by something which antecedes, in conformity with a rule- in other

words, the relation of cause and effect- is the condition of the

objective validity of our empirical judgements in regard to the

sequence of perceptions, consequently of their empirical truth, and

therefore of experience. The principle of the relation of causality in

the succession of phenomena is therefore valid for all objects of

experience, because it is itself the ground of the possibility of

experience.

  Here, however, a difficulty arises, which must be resolved. The

principle of the connection of causality among phenomena is limited in

our formula to the succession thereof, although in practice we find

that the principle applies also when the phenomena exist together in

the same time, and that cause and effect may be simultaneous. For

example, there is heat in a room, which does not exist in the open

air. I look about for the cause, and find it to be the fire, Now the

fire as the cause is simultaneous with its effect, the heat of the

room. In this case, then, there is no succession as regards time,

between cause and effect, but they are simultaneous; and still the law

holds good. The greater part of operating causes in nature are

simultaneous with their effects, and the succession in time of the

latter is produced only because the cause cannot achieve the total

of its effect in one moment. But at the moment when the effect first

arises, it is always simultaneous with the causality of its cause,

because, if the cause had but a moment before ceased to be, the effect

could not have arisen. Here it must be specially remembered that we

must consider the order of time and not the lapse thereof. The

relation remains, even though no time has elapsed. The time between

the causality of the cause and its immediate effect may entirely

vanish, and the cause and effect be thus simultaneous, but the

relation of the one to the other remains always determinable according

to time. If, for example, I consider a leaden ball, which lies upon

a cushion and makes a hollow in it, as a cause, then it is

simultaneous with the effect. But I distinguish the two through the

relation of time of the dynamical connection of both. For if I lay the

ball upon the cushion, then the hollow follows upon the before

smooth surface; but supposing the cushion has, from some cause or

another, a hollow, there does not thereupon follow a leaden ball.

  Thus, the law of succession of time is in all instances the only

empirical criterion of effect in relation to the causality of the

antecedent cause. The glass is the cause of the rising of the water

above its horizontal surface, although the two phenomena are

contemporaneous. For, as soon as I draw some water with the glass from

a larger vessel, an effect follows thereupon, namely, the change of

the horizontal state which the water had in the large vessel into a

concave, which it assumes in the glass.

  This conception of causality leads us to the conception of action;

that of action, to the conception of force; and through it, to the

conception of substance. As I do not wish this critical essay, the

sole purpose of which is to treat of the sources of our synthetical

cognition a priori, to be crowded with analyses which merely

explain, but do not enlarge the sphere of our conceptions, I reserve

the detailed explanation of the above conceptions for a future

system of pure reason. Such an analysis, indeed, executed with great

particularity, may already be found in well-known works on this

subject. But I cannot at present refrain from making a few remarks

on the empirical criterion of a substance, in so far as it seems to be

more evident and more easily recognized through the conception of

action than through that of the permanence of a phenomenon.

  Where action (consequently activity and force) exists, substance

also must exist, and in it alone must be sought the seat of that

fruitful source of phenomena. Very well. But if we are called upon

to explain what we mean by substance, and wish to avoid the vice of

reasoning in a circle, the answer is by no means so easy. How shall we

conclude immediately from the action to the permanence of that which

acts, this being nevertheless an essential and peculiar criterion of

substance (phenomenon)? But after what has been said above, the

solution of this question becomes easy enough, although by the

common mode of procedure- merely analysing our conceptions- it would

be quite impossible. The conception of action indicates the relation

of the subject of causality to the effect. Now because all effect

consists in that which happens, therefore in the changeable, the

last subject thereof is the permanent, as the substratum of all that

changes, that is, substance. For according to the principle of

causality, actions are always the first ground of all change in

phenomena and, consequently, cannot be a property of a subject which

itself changes, because if this were the case, other actions and

another subject would be necessary to determine this change. From

all this it results that action alone, as an empirical criterion, is a

sufficient proof of the presence of substantiality, without any

necessity on my part of endeavouring to discover the permanence of

substance by a comparison. Besides, by this mode of induction we could

not attain to the completeness which the magnitude and strict

universality of the conception requires. For that the primary

subject of the causality of all arising and passing away, all origin

and extinction, cannot itself (in the sphere of phenomena) arise and

pass away, is a sound and safe conclusion, a conclusion which leads us

to the conception of empirical necessity and permanence in

existence, and consequently to the conception of a substance as

phenomenon.

  When something happens, the mere fact of the occurrence, without

regard to that which occurs, is an object requiring investigation. The

transition from the non-being of a state into the existence of it,

supposing that this state contains no quality which previously existed

in the phenomenon, is a fact of itself demanding inquiry. Such an

event, as has been shown in No. A, does not concern substance (for

substance does not thus originate), but its condition or state. It

is therefore only change, and not origin from nothing. If this

origin be regarded as the effect of a foreign cause, it is termed

creation, which cannot be admitted as an event among phenomena,

because the very possibility of it would annihilate the unity of

experience. If, however, I regard all things not as phenomena, but

as things in themselves and objects of understanding alone, they,

although substances, may be considered as dependent, in respect of

their existence, on a foreign cause. But this would require a very

different meaning in the words, a meaning which could not apply to

phenomena as objects of possible experience.

  How a thing can be changed, how it is possible that upon one state

existing in one point of time, an opposite state should follow in

another point of time- of this we have not the smallest conception a

priori. There is requisite for this the knowledge of real powers,

which can only be given empirically; for example, knowledge of

moving forces, or, in other words, of certain successive phenomena (as

movements) which indicate the presence of such forces. But the form of

every change, the condition under which alone it can take place as the

coming into existence of another state (be the content of the

change, that is, the state which is changed, what it may), and

consequently the succession of the states themselves can very well

be considered a priori, in relation to the law of causality and the

conditions of time.*

  *It must be remarked that I do not speak of the change of certain

relations, but of the change of the state. Thus, when a body moves

in a uniform manner, it does not change its state (of motion); but

only when all motion increases or decreases.

  When a substance passes from one state, a, into another state, b,

the point of time in which the latter exists is different from, and

subsequent to that in which the former existed. In like manner, the

second state, as reality (in the phenomenon), differs from the

first, in which the reality of the second did not exist, as b from

zero. That is to say, if the state, b, differs from the state, a, only

in respect to quantity, the change is a coming into existence of b -

a, which in the former state did not exist, and in relation to which

that state is = O.

  Now the question arises how a thing passes from one state = a,

into another state = b. Between two moments there is always a

certain time, and between two states existing in these moments there

is always a difference having a certain quantity (for all parts of

phenomena are in their turn quantities). Consequently, every

transition from one state into another is always effected in a time

contained between two moments, of which the first determines the state

which leaves, and the second determines the state into the thing

passes. the thing leaves, and the second determines the state into

which the thing Both moments, then, are limitations of the time of a

change, consequently of the intermediate state between both, and as

such they belong to the total of the change. Now every change has a

cause, which evidences its causality in the whole time during which

the charge takes place. The cause, therefore, does not produce the

change all at once or in one moment, but in a time, so that, as the

time gradually increases from the commencing instant, a, to its

completion at b, in like manner also, the quantity of the reality

(b - a) is generated through the lesser degrees which are contained

between the first and last. All change is therefore possible only

through a continuous action of the causality, which, in so far as it

is uniform, we call a momentum. The change does not consist of these

momenta, but is generated or produced by them as their effect.

  Such is the law of the continuity of all change, the ground of which

is that neither time itself nor any phenomenon in time consists of

parts which are the smallest possible, but that, notwithstanding,

the state of a thing passes in the process of a change through all

these parts, as elements, to its second state. There is no smallest

degree of reality in a phenomenon, just as there is no smallest degree

in the quantity of time; and so the new state of reality grows up

out of the former state, through all the infinite degrees thereof, the

differences of which one from another, taken all together, are less

than the difference between o and a.

  It is not our business to inquire here into the utility of this

principle in the investigation of nature. But how such a

proposition, which appears so greatly to extend our knowledge of

nature, is possible completely a priori, is indeed a question which

deserves investigation, although the first view seems to demonstrate

the truth and reality of the principle, and the question, how it is

possible, may be considered superfluous. For there are so many

groundless pretensions to the enlargement of our knowledge by pure

reason that we must take it as a general rule to be mistrustful of all

such, and without a thoroughgoing and radical deduction, to believe

nothing of the sort even on the clearest dogmatical evidence.

  Every addition to our empirical knowledge, and every advance made in

the exercise of our perception, is nothing more than an extension of

the determination of the internal sense, that is to say, a progression

in time, be objects themselves what they may, phenomena, or pure

intuitions. This progression in time determines everything, and is

itself determined by nothing else. That is to say, the parts of the

progression exist only in time, and by means of the synthesis thereof,

and are not given antecedently to it. For this reason, every

transition in perception to anything which follows upon another in

time, is a determination of time by means of the production of this

perception. And as this determination of time is, always and in all

its parts, a quantity, the perception produced is to be considered

as a quantity which proceeds through all its degrees- no one of

which is the smallest possible- from zero up to its determined degree.

From this we perceive the possibility of cognizing a priori a law of

changes- a law, however, which concerns their form merely. We merely

anticipate our own apprehension, the formal condition of which,

inasmuch as it is itself to be found in the mind antecedently to all

given phenomena, must certainly be capable of being cognized a priori.

  Thus, as time contains the sensuous condition a priori of the

possibility of a continuous progression of that which exists to that

which follows it, the understanding, by virtue of the unity of

apperception, contains the condition a priori of the possibility of

a continuous determination of the position in time of all phenomena,

and this by means of the series of causes and effects, the former of

which necessitate the sequence of the latter, and thereby render

universally and for all time, and by consequence, objectively, valid

the empirical cognition of the relations of time.

                   C. THIRD ANALOGY.

      Principle of Coexistence, According to the Law

               of Reciprocity or Community.

   All substances, in so far as they can be perceived in space

    at the same time, exist in a state of complete reciprocity

                     of action.

                        PROOF.

  Things are coexistent, when in empirical intuition the perception of

the one can follow upon the perception of the other, and vice versa-

which cannot occur in the succession of phenomena, as we have shown in

the explanation of the second principle. Thus I can perceive the

moon and then the earth, or conversely, first the earth and then the

moon; and for the reason that my perceptions of these objects can

reciprocally follow each other, I say, they exist contemporaneously.

Now coexistence is the existence of the manifold in the same time. But

time itself is not an object of perception; and therefore we cannot

conclude from the fact that things are placed in the same time, the

other fact, that the perception of these things can follow each

other reciprocally. The synthesis of the imagination in apprehension

would only present to us each of these perceptions as present in the

subject when the other is not present, and contrariwise; but would not

show that the objects are coexistent, that is to say, that, if the one

exists, the other also exists in the same time, and that this is

necessarily so, in order that the perceptions may be capable of

following each other reciprocally. It follows that a conception of the

understanding or category of the reciprocal sequence of the

determinations of phenomena (existing, as they do, apart from each

other, and yet contemporaneously), is requisite to justify us in

saying that the reciprocal succession of perceptions has its

foundation in the object, and to enable us to represent coexistence as

objective. But that relation of substances in which the one contains

determinations the ground of which is in the other substance, is the

relation of influence. And, when this influence is reciprocal, it is

the relation of community or reciprocity. Consequently the coexistence

of substances in space cannot be cognized in experience otherwise than

under the precondition of their reciprocal action. This is therefore

the condition of the possibility of things themselves as objects of

experience.

  Things are coexistent, in so far as they exist in one and the same

time. But how can we know that they exist in one and the same time?

Only by observing that the order in the synthesis of apprehension of

the manifold is arbitrary and a matter of indifference, that is to

say, that it can proceed from A, through B, C, D, to E, or

contrariwise from E to A. For if they were successive in time (and

in the order, let us suppose, which begins with A), it is quite

impossible for the apprehension in perception to begin with E and go

backwards to A, inasmuch as A belongs to past time and, therefore,

cannot be an object of apprehension.

  Let us assume that in a number of substances considered as phenomena

each is completely isolated, that is, that no one acts upon another.

Then I say that the coexistence of these cannot be an object of

possible perception and that the existence of one cannot, by any

mode of empirical synthesis, lead us to the existence of another.

For we imagine them in this case to be separated by a completely

void space, and thus perception, which proceeds from the one to the

other in time, would indeed determine their existence by means of a

following perception, but would be quite unable to distinguish whether

the one phenomenon follows objectively upon the first, or is

coexistent with it.

  Besides the mere fact of existence, then, there must be something by

means of which A determines the position of B in time and, conversely,

B the position of A; because only under this condition can

substances be empirically represented as existing contemporaneously.

Now that alone determines the position of another thing in time

which is the cause of it or of its determinations. Consequently

every substance (inasmuch as it can have succession predicated of it

only in respect of its determinations) must contain the causality of

certain determinations in another substance, and at the same time

the effects of the causality of the other in itself. That is to say,

substances must stand (mediately or immediately) in dynamical

community with each other, if coexistence is to be cognized in any

possible experience. But, in regard to objects of experience, that

is absolutely necessary without which the experience of these

objects would itself be impossible. Consequently it is absolutely

necessary that all substances in the world of phenomena, in so far

as they are coexistent, stand in a relation of complete community of

reciprocal action to each other.

  The word community has in our language* two meanings, and contains

the two notions conveyed in the Latin communio and commercium. We

employ it in this place in the latter sense- that of a dynamical

community, without which even the community of place (communio spatii)

could not be empirically cognized. In our experiences it is easy to

observe that it is only the continuous influences in all parts of

space that can conduct our senses from one object to another; that the

light which plays between our eyes and the heavenly bodies produces

a mediating community between them and us, and thereby evidences their

coexistence with us; that we cannot empirically change our position

(perceive this change), unless the existence of matter throughout

the whole of space rendered possible the perception of the positions

we occupy; and that this perception can prove the contemporaneous

existence of these places only through their reciprocal influence, and

thereby also the coexistence of even the most remote objects- although

in this case the proof is only mediate. Without community, every

perception (of a phenomenon in space) is separated from every other

and isolated, and the chain of empirical representations, that is,

of experience, must, with the appearance of a new object, begin

entirely de novo, without the least connection with preceding

representations, and without standing towards these even in the

relation of time. My intention here is by no means to combat the

notion of empty space; for it may exist where our perceptions cannot

exist, inasmuch as they cannot reach thereto, and where, therefore, no

empirical perception of coexistence takes place. But in this case it

is not an object of possible experience.

  *German.

  The following remarks may be useful in the way of explanation. In

the mind, all phenomena, as contents of a possible experience, must

exist in community (communio) of apperception or consciousness, and in

so far as it is requisite that objects be represented as coexistent

and connected, in so far must they reciprocally determine the position

in time of each other and thereby constitute a whole. If this

subjective community is to rest upon an objective basis, or to be

applied to substances as phenomena, the perception of one substance

must render possible the perception of another, and conversely. For

otherwise succession, which is always found in perceptions as

apprehensions, would be predicated of external objects, and their

representation of their coexistence be thus impossible. But this is

a reciprocal influence, that is to say, a real community

(commercium) of substances, without which therefore the empirical

relation of coexistence would be a notion beyond the reach of our

minds. By virtue of this commercium, phenomena, in so far as they

are apart from, and nevertheless in connection with each other,

constitute a compositum reale. Such composita are possible in many

different ways. The three dynamical relations then, from which all

others spring, are those of inherence, consequence, and composition.

  These, then, are the three analogies of experience. They are nothing

more than principles of the determination of the existence of

phenomena in time, according to the three modi of this

determination; to wit, the relation to time itself as a quantity

(the quantity of existence, that is, duration), the relation in time

as a series or succession, finally, the relation in time as the

complex of all existence (simultaneity). This unity of determination

in regard to time is thoroughly dynamical; that is to say, time is not

considered as that in which experience determines immediately to every

existence its position; for this is impossible, inasmuch as absolute

time is not an object of perception, by means of which phenomena can

be connected with each other. On the contrary, the rule of the

understanding, through which alone the existence of phenomena can

receive synthetical unity as regards relations of time, determines for

every phenomenon its position in time, and consequently a priori,

and with validity for all and every time.

  By nature, in the empirical sense of the word, we understand the

totality of phenomena connected, in respect of their existence,

according to necessary rules, that is, laws. There are therefore

certain laws (which are moreover a priori) which make nature possible;

and all empirical laws can exist only by means of experience, and by

virtue of those primitive laws through which experience itself becomes

possible. The purpose of the analogies is therefore to represent to us

the unity of nature in the connection of all phenomena under certain

exponents, the only business of which is to express the relation of

time (in so far as it contains all existence in itself) to the unity

of apperception, which can exist in synthesis only according to rules.

The combined expression of all is this: "All phenomena exist in one

nature, and must so exist, inasmuch as without this a priori unity, no

unity of experience, and consequently no determination of objects in

experience, is possible."

  As regards the mode of proof which we have employed in treating of

these transcendental laws of nature, and the peculiar character of

we must make one remark, which will at the same time be important as a

guide in every other attempt to demonstrate the truth of

intellectual and likewise synthetical propositions a priori. Had we

endeavoured to prove these analogies dogmatically, that is, from

conceptions; that is to say, had we employed this method in attempting

to show that everything which exists, exists only in that which is

permanent- that every thing or event presupposes the existence of

something in a preceding state, upon which it follows in conformity

with a rule- lastly, that in the manifold, which is coexistent, the

states coexist in connection with each other according to a rule-

all our labour would have been utterly in vain. For more conceptions

of things, analyse them as we may, cannot enable us to conclude from

the existence of one object to the existence of another. What other

course was left for us to pursue? This only, to demonstrate the

possibility of experience as a cognition in which at last all

objects must be capable of being presented to us, if the

representation of them is to possess any objective reality. Now in

this third, this mediating term, the essential form of which

consists in the synthetical unity of the apperception of all

phenomena, we found a priori conditions of the universal and necessary

determination as to time of all existences in the world of

phenomena, without which the empirical determination thereof as to

time would itself be impossible, and we also discovered rules of

synthetical unity a priori, by means of which we could anticipate

experience. For want of this method, and from the fancy that it was

possible to discover a dogmatical proof of the synthetical

propositions which are requisite in the empirical employment of the

understanding, has it happened that a proof of the principle of

sufficient reason has been so often attempted, and always in vain. The

other two analogies nobody has ever thought of, although they have

always been silently employed by the mind,* because the guiding thread

furnished by the categories was wanting, the guide which alone can

enable us to discover every hiatus, both in the system of

conceptions and of principles.

  *The unity of the universe, in which all phenomena to be

connected, is evidently a mere consequence of the admitted principle

of the community of all substances which are coexistent. For were

substances isolated, they could not as parts constitute a whole, and

were their connection (reciprocal action of the manifold) not

necessary from the very fact of coexistence, we could not conclude

from the fact of the latter as a merely ideal relation to the former

as a real one. We have, however, shown in its place that community

is the proper ground of the possibility of an empirical cognition of

coexistence, and that we may therefore properly reason from the latter

to the former as its condition.