The deduction of the pure concepts of the understanding (and with them of all theoretical knowledge a priori) consists in representing them as principles of the possibility of experience, and in representing experience as the determination of phenomena in space and time,—and, lastly, in representing that determination as depending on the principle of the original synthetical unity of apperception, as the form of the understanding, applied to space and time, as the original forms of sensibility.24
Supplement XV
All conjunction (conjunctio) is either composition (compositio) or connection (nexus). The former is the synthesis of a manifold the parts of which do not belong to each other necessarily. The two triangles, for instance, into which a square is divided by a diagonal, do by themselves not necessarily belong to each other. Such is also the synthesis of the homogeneous, in everything that can be considered mathematically, and that synthesis can be divided again into aggregation, and coalition, the former referring to extensive, the latter to intensive qualities. The latter conjunction (nexus) is the synthesis of a manifold, in so far as its elements belong to each other necessarily. Thus the accident belonging to a substance, or the effect belonging to a cause, though heterogeneous, are yet represented as a priori connected, which connection, as it is not arbitrary, I call dynamical, because it concerns the connection of the existence of the manifold. This may again be divided into the physical connection of phenomena among each other, and their metaphysical connection in the faculty of cognition a priori. (This forms a note in the 2nd Edition.)
Supplement XVI a
In the 2nd Edition the title is
I
Axioms of Intuition
Their principle is: All intuitions are extensive quantities.
Proof
All phenomena contain, so far as their form is concerned, an intuition in space and time, which forms the a priori foundation of all of them. They cannot, therefore, be apprehended, that is, received into empirical consciousness, except through the synthesis of the manifold, by which the representations of a definite space or time are produced, i.e. through the synthesis of the homogeneous, and the consciousness of the synthetical unity of that manifold (homogeneous). Now the consciousness of the manifold and homogeneous in intuition, so far as by it the representation of an object is first rendered possible, is the concept of quantity (quantum). Therefore even the perception of an object as a phenomenon is possible only through the same synthetical unity of the manifold of the given sensuous intuition, by which the unity of the composition of the manifold and homogeneous is conceived in the concept of a quantity; that is, phenomena are always quantities, and extensive quantities; because as intuitions in space and time, they must be represented through the same synthesis through which space and time in general are determined.
Supplement XVI b
II
Anticipations of Perception
Their principle is: In all phenomena the Real, which is the object of a sensation, has intensive quantity, that is, a degree.
Proof
Perception is empirical consciousness, that is, a consciousness in which there is at the same time sensation. Phenomena, as objects of perception, are not pure (merely formal) intuitions, like space and time (for space and time can never be perceived by themselves). They contain, therefore, over and above the intuition, the material for some one object in general (through which something existing in space and time is represented); that is, they contain the real of sensation, as a merely subjective representation, which gives us only the consciousness that the subject is affected, and which is referred to some object in general. Now there is a gradual transition possible from empirical to pure consciousness, till the real of it vanishes completely and there remains a merely formal consciousness (a priori) of the manifold in space and time; and, therefore, a synthesis also is possible in the production of the quantity of a sensation, from its beginning, that is, from the pure intuition = o, onwards to any quantity of it. As sensation by itself is no objective representation, and as in it the intuition of neither space nor time can be found, it follows that though not an extensive, yet some kind of quantity must belong to it (and this through the apprehension of it, in which the empirical consciousness may grow in a certain time from nothing = 0 to any amount). That quantity must be intensive, and corresponding to it, an intensive quantity, i.e. a degree of influence upon the senses, must be attributed to all objects of perception, so far as it contains sensation.
Supplement XVII
III
Analogies of Experience
Their principle is: Experience is possible only through the representation of a necessary connection of perceptions.
Proof
Experience is empirical knowledge, that is, knowledge which determines an object by means of perceptions. It is, therefore, a synthesis of perceptions, which synthesis itself is not contained in the perception, but contains the synthetical unity of the manifold of the perceptions in a consciousness, that unity constituting the essential of our knowledge of the objects of the senses, i.e. of experience (not only of intuition or of sensation of the senses). In experience perceptions come together contingently only, so that no necessity of their connection could be discovered in the perceptions themselves, apprehension being only a composition of the manifold of empirical intuition, but containing no representation of the necessity of the connected existence, in space and time, of the phenomena which it places together. Experience, on the contrary, is a knowledge of objects by perceptions, in which therefore the relation in the existence of the manifold is to be represented, not as it is put together in time, but as it is in time, objectively. Now, as time itself cannot be perceived, the determination of the existence of objects in time can take place only by their connection in time in general, that is, through concepts connecting them a priori. As these concepts always imply necessity, we are justified in saying that experience is possible only through a representation of the necessary connection of perceptions.
Supplement XVIII
A. First Analogy
Principle of the Permanence of Substance
In all changes of phenomena the substance is permanent, and its quantum is neither increased nor diminished in nature.
Proof
All phenomena exist in time, and in it alone, as the substratum (as permanent form of the internal intuition), can simultaneousness as well as succession be represented. Time, therefore, in which all change of phenomena is to be thought, does not change, for it is that in which simultaneousness and succession can be represented only as determinations of it. As time by itself cannot be perceived, it follows that the substratum which represents time in general, and in which all change or simultaneousness can be perceived in apprehension, through the relation of phenomena to it, must exist in the objects of perception, that is, in the phenomena. Now the substratum of all that is real, that is, of all that belongs to the existence of things, is the substance, and all that belongs to existence can be conceived only as a determination of it. Consequently the permanent, in reference to which alone all temporal relations of phenomena can be determined, is the substance in phenomena, that is, what is real in them, and, as the substratum of all change, remains always the same. As therefore substance cannot change in existence, we were justified in saying that its quantum can neither be increased nor diminished in nature.
Supplement XIX
B. Second Analogy
Principle of the Succession of Time, according to the Law of Causality
All changes take place according to the law of connection between cause and effect.
Proof
(It has been shown by the preceding principle, that all phenomena in the succession of time are changes only, i.e. a successive being and not-being of the determinations of the substance, which is permanent, and consequently that the being of the substance itself, which follows upon its not-being, and its not-being, which follows on its being,—in other words, that an arising or perishing of
the substance itself is inadmissible. The same principle might also have been expressed thus: all change (succession) of phenomena consists in modification only, for arising and perishing are no modifications of the substance, because the concept of modification presupposes the same subject as existing with two opposite determinations, and therefore as permanent. After this preliminary remark, we shall proceed to the proof.)
I perceive that phenomena succeed each other, that is, that there is a state of things at one time the opposite of which existed at a previous time. I am therefore really connecting two perceptions in time. That connection is not a work of the senses only and of intuition, but is here the product of a synthetical power of the faculty of imagination, which determines the internal sense with reference to relation in time. Imagination, however, can connect those two states in two ways, so that either the one or the other precedes in time: for time cannot be perceived by itself, nor can we determine in the object empirically and with reference to time, what precedes and what follows. I am, therefore, conscious only that my imagination places the one before, the other after, and not, that in the object the one state comes before the other. In other words, the objective relation of phenomena following upon each other remains undetermined by mere perception. In order that this may be known as determined, it is necessary to conceive the relation between the two states in such a way that it should be determined thereby with necessity, which of the two should be taken as coming first, and which as second, and not conversely. Such a concept, involving a necessity of synthetical unity, can be a pure concept of the understanding only, which is not supplied by experience, and this is, in this case, the concept of the relation of cause and effect, the former determining the latter in time as the consequence, the cause not being something that might be antecedent in imagination only, or might not be perceived at all. Experience itself, therefore, that is, an empirical knowledge of phenomena, is possible only by our subjecting the succession of phenomena, and with it all change, to the law of causality, and phenomena themselves, as objects of experience, are consequently possible according to the same law only.
Supplement XX
C. Third Analogy
Principle of Coexistence, according to the Law of Reciprocity or Community
All substances, so far as they can be perceived as coexistent in space, are always affecting each other reciprocally.
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, as was shown in the second principle, is impossible in the temporal succession of phenomena. Thus I may first observe the moon and afterwards the earth, or, conversely also, first the earth and afterwards the moon, and because the perceptions of these objects can follow each other in both ways, I say that they are coexistent. Now coexistence is the existence of the manifold in the same time. Time itself, however, cannot be perceived, so that we might learn from the fact that things exist in the same time that their perceptions can follow each other reciprocally. The synthesis of imagination in apprehension would, therefore, give us each of these perceptions as existing in the subject, when the other is absent, and vice versa: it would never tell us that the objects are coexistent, that is, that if the one is there, the other also must be there in the same time, and this by necessity, so that the perceptions may follow each other reciprocally. Hence we require a concept of understanding of the reciprocal sequence of determinations of things existing at the same time, but outside each other, in order to be able to say, that the reciprocal sequence of the perceptions is founded in the object, and thus to represent their coexistence as objective. The relation of substances, however, of which the first has determinations the ground of which is contained in the other, is the relation of influence, and if, conversely also, the first contains the ground of determinations in the latter, the relation is that of community or reciprocity. Hence the coexistence of substances in space cannot be known in experience otherwise but under the supposition of reciprocal action: and this is therefore the condition also of the possibility of things themselves as objects of experience.
Supplement XXI
An important protest, however, against these rules for proving existence mediately is brought forward by Idealism, and this is therefore the proper place for its refutation.
Refutation of Idealism
Idealism (I mean material idealism) is the theory which declares the existence of objects in space, without us, as either doubtful only and not demonstrable, or as false and impossible. The former is the problematical idealism of Descartes, who declares one empirical assertion only to be undoubted, namely, that of I am; the latter is the dogmatical idealism of Berkeley, who declares space and all things to which it belongs as an inseparable condition, as something impossible in itself, and, therefore, the things in space as mere imaginations. Dogmatic idealism is inevitable, if we look upon space as a property belonging to things by themselves, for in that case space and all of which it is a condition, would be a non-entity. The ground on which that idealism rests has been removed by us in the transcendental Æsthetic. Problematical idealism, which asserts nothing, but only pleads our inability of proving any existence except our own by means of immediate experience, is reasonable and in accordance with a sound philosophical mode of thought, which allows of no decisive judgment, before a sufficient proof has been found. The required proof will have to demonstrate that we may have not only an imagination, but also an experience of external things, and this it seems can hardly be effected in any other way except by proving that even our internal experience, which Descartes considers as undoubted, is possible only under the supposition of external experience.
Theorem
The simple, but empirically determined Consciousness of my own existence, proves the Existence of objects in space outside myself.
Proof
I am conscious of my own existence as determined in time, and all determination in time presupposes something permanent in the perception.25 That permanent, however, cannot be an intuition within me, because all the causes which determine my existence, so far as they can be found within me, are representations, and as such require themselves something permanent, different from them, in reference to which their change, and therefore my existence in time in which they change, may be determined. The perception of this permanent, therefore, is possible only through a thing outside me, and not through the mere representation of a thing outside me, and the determination of my existence in time is, consequently, possible only by the existence of real things, which I perceive outside me. Now, as the consciousness in time is necessarily connected with the consciousness of the possibility of that determination of time, it is also necessarily connected with the existence of things outside me, as the condition of the determination of time. In other words, the consciousness of my own existence is, at the same time, an immediate consciousness of the existence of other things.
Note 1.—It will have been perceived that in the foregoing proof the trick played by idealism has been turned against it, and with greater justice. Idealism assumed that the only immediate experience is the internal, and that from it we can no more than infer external things, though in an untrustworthy manner only, as always happens if from given effects we infer definite causes: it being quite possible that the cause of the representations, which are ascribed by us, it may be wrongly, to external things, may lie within ourselves. We, however, have proved that external experience is really immediate,26 and that only by means of it, though not the consciousness of our own existence, yet its determination in time, that is, internal experience, becomes possible. No doubt the representation of I am, which expresses the consciousness that can accompany all thought, is that which im mediately includes the existence of a subject: but it does not yet include a knowledge of it, and therefore no empirical knowledge, that is, experience. For that we require, besides the thought of something existing, intuition also, and in this case internal i
ntuition in respect to which, that is, to time, the subject must be determined. For that purpose external objects are absolutely necessary, so that internal experience itself is possible, mediately only, and through external experience.
Note 2.—This view is fully confirmed by the empirical use of our faculty of knowledge, as applied to the determination of time. Not only are we unable to perceive any determination of time, except through a change in external relations (motion) with reference to what is permanent in space (for instance, the movement of the sun with respect to terrestrial objects), but we really have nothing permanent to which we could refer the concept of a substance, as an intuition, except matter only: and even its permanence is not derived from external experience, but presupposed a priori as a necessary condition of all determination of time, and therefore also of27 the determination of the internal sense with respect to our own existence through the existence of external things. The consciousness of myself, in the representation of the ego, is not an intuition, but a merely intellectual representation of the spontaneity of a thinking subject. Hence that ego has not the slightest predicate derived from intuition, which predicate, as permanent, might serve as the correlate of the determination of time in the internal sense: such as is, for instance, impermeability in matter, as an empirical intuition.
Note 3.—Because the existence of external objects is required for the possibility of a definite consciousness of ourselves, it does not follow that every intuitional representation of external things involves, at the same time, their existence; for such a representation may well be the mere effect of the faculty of imagination (in dreams as well as in madness); but it can be such an effect only through the reproduction of former external perceptions, which, as we have shown, is impossible without the reality of external objects. What we wanted to prove here was only that internal experience in general is possible only through external experience in general. Whether this or that supposed experience be purely imaginary, must be settled according to its own particular determinations, and through a comparison with the criteria of all real experience.
Critique of Pure Reason Page 73
