What Objective Unity of Self-consciousness is § 14
It is by means of the transcendental unity of apperception that all the manifold, given in an intuition is united into a conception of the object. On this account it is called objective, and must be distinguished from the subjective unity of consciousness, which is a determination of the internal sense, by means of which the said manifold in intuition is given empirically to be so united. Whether I can be empirically conscious of the manifold as coexistent or as successive, depends upon circumstances, or empirical conditions. Hence the empirical unity of consciousness by means of association of representations, itself relates to a phenomenal world and is wholly contingent. On the contrary, the pure form of intuition in time, merely as an intuition, which contains a given manifold, is subject to the original unity of consciousness, and that solely by means of the necessary relation of the manifold in intuition to the “I think,” consequently by means of the pure synthesis of the understanding, which lies à priori at the foundation of all empirical synthesis. The transcendental unity of apperception is alone objectively valid; the empirical which we do not consider in this essay, and which is merely a unity deduced from the former under given conditions in concreto, possesses only subjective validity. One person connects the notion conveyed in a word with one thing, another with another thing; and the unity of consciousness in that which is empirical, is, in relation to that which is given by experience, not necessarily and universally valid.
The Logical Form of all Judgements consists in the Objective Unity of Apperception of the Conceptions contained therein § 15
I could never satisfy myself with the definition which logicians give of a judgement. It is, according to them, the representation of a relation between two conceptions. I shall not dwell here on the faultiness of this definition, in that it suits only for categorical and not for hypothetical or disjunctive judgements, these latter containing a relation not of conceptions but of judgements themselves—a blunder from which many evil results have followed.[18] It is more important for our present purpose to observe, that this definition does not determine in what the said relation consists.
[18] The tedious doctrine of the four syllogistic figures concerns only categorical syllogisms; and although it is nothing more than an artifice by surreptitiously introducing immediate conclusions (consequentiae immediatae) among the premises of a pure syllogism, to give ism give rise to an appearance of more modes of drawing a conclusion than that in the first figure, the artifice would not have had much success, had not its authors succeeded in bringing categorical judgements into exclusive respect, as those to which all others must be referred—a doctrine, however, which, according to § 5, is utterly false.
But if I investigate more closely the relation of given cognitions in every judgement, and distinguish it, as belonging to the understanding, from the relation which is produced according to laws of the reproductive imagination (which has only subjective validity), I find that judgement is nothing but the mode of bringing given cognitions under the objective unit of apperception. This is plain from our use of the term of relation is in judgements, in order to distinguish the objective unity of given representations from the subjective unity. For this term indicates the relation of these representations to the original apperception, and also their necessary unity, even although the judgement is empirical, therefore contingent, as in the judgement: “All bodies are heavy.” I do not mean by this, that these representations do necessarily belong to each other in empirical intuition, but that by means of the necessary unity of appreciation they belong to each other in the synthesis of intuitions, that is to say, they belong to each other according to principles of the objective determination of all our representations, in so far as cognition can arise from them, these principles being all deduced from the main principle of the transcendental unity of apperception. In this way alone can there arise from this relation a judgement, that is, a relation which has objective validity, and is perfectly distinct from that relation of the very same representations which has only subjective validity—a relation, to wit, which is produced according to laws of association. According to these laws, I could only say: “When I hold in my hand or carry a body, I feel an impression of weight”; but I could not say: “It, the body, is heavy”; for this is tantamount to saying both these representations are conjoined in the object, that is, without distinction as to the condition of the subject, and do not merely stand together in my perception, however frequently the perceptive act may be repeated.
All Sensuous Intuitions are subject to the Categories, as Conditions under which alone the manifold Content of them can be united in one Consciousness § 16
The manifold content given in a sensuous intuition comes necessarily under the original synthetical unity of apperception, because thereby alone is the unity of intuition possible (§ 13). But that act of the understanding, by which the manifold content of given representations (whether intuitions or conceptions) is brought under one apperception, is the logical function of judgements (§ 15). All the manifold, therefore, in so far as it is given in one empirical intuition, is determined in relation to one of the logical functions of judgement, by means of which it is brought into union in one consciousness. Now the categories are nothing else than these functions of judgement so far as the manifold in a given intuition is determined in relation to them (§ 9). Consequently, the manifold in a given intuition is necessarily subject to the categories of the understanding.
Observation § 17
The manifold in an intuition, which I call mine, is represented by means of the synthesis of the understanding, as belonging to the necessary unity of self-consciousness, and this takes place by means of the category.[19] The category indicates accordingly that the empirical consciousness of a given manifold in an intuition is subject to a pure self-consciousness à priori, in the same manner as an empirical intuition is subject to a pure sensuous intuition, which is also à priori. In the above proposition, then, lies the beginning of a deduction of the pure conceptions of the understanding. Now, as the categories have their origin in the understanding alone, independently of sensibility, I must in my deduction make abstraction of the mode in which the manifold of an empirical intuition is given, in order to fix my attention exclusively on the unity which is brought by the understanding into the intuition by means of the category. In what follows (§ 22), it will be shown, from the mode in which the empirical intuition is given in the faculty of sensibility, that the unity which belongs to it is no other than that which the category (according to § 16) imposes on the manifold in a given intuition, and thus, its à priori validity in regard to all objects of sense being established, the purpose of our deduction will be fully attained.
[19] The proof of this rests on the represented unity of intuition, by means of which an object is given, and which always includes in itself a synthesis of the manifold to be intuited, and also the relation of this latter to unity of apperception.
But there is one thing in the above demonstration of which I could not make abstraction, namely, that the manifold to be intuited must be given previously to the synthesis of the understanding, and independently of it. How this takes place remains here undetermined. For if I cogitate an understanding which was itself intuitive (as, for example, a divine understanding which should not represent given objects, but by whose representation the objects themselves should be given or produced), the categories would possess no significance in relation to such a faculty of cognition. They are merely rules for an understanding, whose whole power consists in thought, that is, in the act of submitting the synthesis of the manifold which is presented to it in intuition from a very different quarter, to the unity of apperception; a faculty, therefore, which cognizes nothing per se, but only connects and arranges the material of cognition, the intuition, namely, which must be presented to it by means of the object. But to show reasons for this peculiar character of our understandings, that it produces unity of apperception à priori only by means of categories, and a certain kind and number thereof, is as impossible as to explain why we are endowed with precisely so many functions of judgement and no more, or why time and space are the only forms of our intuition.
In Cognition, its Application to Objects of Experience is the only legitimate use of the Category § 18
To think an object and to cognize an object are by no means the same thing. In cognition there are two elements: firstly, the conception, whereby an object is cogitated (the category); and, secondly, the intuition, whereby the object is given. For supposing that to the conception a corresponding intuition could not be given, it would still be a thought as regards its form, but without any object, and no cognition of anything would be possible by means of it, inasmuch as, so far as I knew, there existed and could exist nothing to which my thought could be applied. Now all intuition possible to us is sensuous; consequently, our thought of an object by means of a pure conception of the understanding, can become cognition for us only in so far as this conception is applied to objects of the senses. Sensuous intuition is either pure intuition (space and time) or empirical intuition—of that which is immediately represented in space and time by means of sensation as real. Through the determination of pure intuition we obtain à priori cognitions of objects, as in mathematics, but only as regards their form as phenomena; whether there can exist things which must be intuited in this form is not thereby established. All mathematical conceptions, therefore, are not per se cognition, except in so far as we presuppose that there exist things which can only be represented conformably to the form of our pure sensuous intuition. But things in space and time are given only in so far as they are perceptions (representations accompanied with sensation), therefore only by empirical representation. Consequently the pure conceptions of the understanding, even when they are applied to intuitions à priori (as in mathematics), produce cognition only in so far as these (and therefore the conceptions of the understanding by means of them) can be applied to empirical intuitions. Consequently the categories do not, even by means of pure intuition afford us any cognition of things; they can only do so in so far as they can be applied to empirical intuition. That is to say, the categories serve only to render empirical cognition possible. But this is what we call experience. Consequently, in cognition, their application to objects of experience is the only legitimate use of the categories.
§ 19
The foregoing proposition is of the utmost importance, for it determines the limits of the exercise of the pure conceptions of the understanding in regard to objects, just as transcendental æsthetic determined the limits of the exercise of the pure form of our sensuous intuition. Space and time, as conditions of the possibility of the presentation of objects to us, are valid no further than for objects of sense, consequently, only for experience. Beyond these limits they represent to us nothing, for they belong only to sense, and have no reality apart from it. The pure conceptions of the understanding are free from this limitation, and extend to objects of intuition in general, be the intuition like or unlike to ours, provided only it be sensuous, and not intellectual. But this extension of conceptions beyond the range of our intuition is of no advantage; for they are then mere empty conceptions of objects, as to the possibility or impossibility of the existence of which they furnish us with no means of discovery. They are mere forms of thought, without objective reality, because we have no intuition to which the synthetical unity of apperception, which alone the categories contain, could be applied, for the purpose of determining an object. Our sensuous and empirical intuition can alone give them significance and meaning.
If, then, we suppose an object of a non-sensuous intuition to be given we can in that case represent it by all those predicates which are implied in the presupposition that nothing appertaining to sensuous intuition belongs to it; for example, that it is not extended, or in space; that its duration is not time; that in it no change (the effect of the determinations in time) is to be met with, and so on. But it is no proper knowledge if I merely indicate what the intuition of the object is not, without being able to say what is contained in it, for I have not shown the possibility of an object to which my pure conception of understanding could be applicable, because I have not been able to furnish any intuition corresponding to it, but am only able to say that our intuition is not valid for it. But the most important point is this, that to a something of this kind not one category can be found applicable. Take, for example, the conception of substance, that is, something that can exist as subject, but never as mere predicate; in regard to this conception I am quite ignorant whether there can really be anything to correspond to such a determination of thought, if empirical intuition did not afford me the occasion for its application. But of this more in the sequel.
Of the Application of the Categories to Objects of the Senses in general § 20
The pure conceptions of the understanding apply to objects of intuition in general, through the understanding alone, whether the intuition be our own or some other, provided only it be sensuous, but are, for this very reason, mere forms of thought, by means of which alone no determined object can be cognized. The synthesis or conjunction of the manifold in these conceptions relates, we have said, only to the unity of apperception, and is for this reason the ground of the possibility of à priori cognition, in so far as this cognition is dependent on the understanding. This synthesis is, therefore, not merely transcendental, but also purely intellectual. But because a certain form of sensuous intuition exists in the mind à priori which rests on the receptivity of the representative faculty (sensibility), the understanding, as a spontaneity, is able to determine the internal sense by means of the diversity of given representations, conformably to the synthetical unity of apperception, and thus to cogitate the synthetical unity of the apperception of the manifold of sensuous intuition à priori, as the condition to which must necessarily be submitted all objects of human intuition. And in this manner the categories as mere forms of thought receive objective reality, that is, application to objects which are given to us in intuition, but that only as phenomena, for it is only of phenomena that we are capable of à priori intuition.
This synthesis of the manifold of sensuous intuition, which is possible and necessary à priori, may be called figurative (synthesis speciosa), in contradistinction to that which is cogitated in the mere category in regard to the manifold of an intuition in general, and is called connection or conjunction of the understanding (synthesis intellectualis). Both are transcendental, not merely because they themselves precede à priori all experience, but also because they form the basis for the possibility of other cognition à priori.
But the figurative synthesis, when it has relation only to the originally synthetical unity of apperception, that is to the transcendental unity cogitated in the categories, must, to be distinguished from the purely intellectual conjunction, be entitled the transcendental synthesis of imagination. Imagination is the faculty of representing an object even without its presence in intuition. Now, as all our intuition is sensuous, imagination, by reason of the subjective condition under which alone it can give a corresponding intuition to the conceptions of the understanding, belongs to sensibility. But in so far as the synthesis of the imagination is an act of spontaneity, which is determinative, and not, like sense, merely determinable, and which is consequently able to determine sense à priori, according to its form, conformably to the unity of apperception, in so far is the imagination a faculty of determining sensibility à priori, and its synthesis of intuitions according to the categories must be the transcendental synthesis of the imagination. It is an operation of the understanding on sensibility, and the first application of the understanding to objects of possible intuition, and at the same time the basis for the exercise of the other functions of that faculty. As figurative, it is distinguished from the merely intellectual synthesis, which is produced by the understanding alone, without the aid of imagination. Now, in so far as imagination is spontaneity, I sometimes call it also the productive imagination, and distinguish it from the reproductive, the synthesis of which is subject entirely to empirical laws, those of association, namely, and which, therefore, contributes nothing to the explanation of the possibility of à priori cognition, and for this reason belongs not to transcendental philosophy, but to psychology.
We have now arrived at the proper place for explaining the paradox which must have struck every one in our exposition of the internal sense (§ 6), namely—how this sense represents us to our own consciousness, only as we appear to ourselves, not as we are in ourselves, because, to wit, we intuite ourselves only as we are inwardly affected. Now this appears to be contradictory, inasmuch as we thus stand in a passive relation to ourselves; and therefore in the systems of psychology, the internal sense is commonly held to be one with the faculty of apperception, while we, on the contrary, carefully distinguish them.
That which determines the internal sense is the understanding, and its original power of conjoining the manifold of intuition, that is, of bringing this under an apperception (upon which rests the possibility of the understanding itself). Now, as the human understanding is not in itself a faculty of intuition, and is unable to exercise such a power, in order to conjoin, as it were, the manifold of its own intuition, the synthesis of understanding is, considered per se, nothing but the unity of action, of which, as such, it is self-conscious, even apart from sensibility, by which, moreover, it is able to determine our internal sense in respect of the manifold which may be presented to it according to the form of sensuous intuition. Thus, under the name of a transcendental synthesis of imagination, the understanding exercises an activity upon the passive subject, whose faculty it is; and so we are right in saying that the internal sense is affected thereby. Apperception and its synthetical unity are by no means one and the same with the internal sense. The former, as the source of all our synthetical conjunction, applies, under the name of the categories, to the manifold of intuition in general, prior to all sensuous intuition of objects. The internal sense, on the contrary, contains merely the form of intuition, but without any synthetical conjunction of the manifold therein, and consequently does not contain any determined intuition, which is possible only through consciousness of the determination of the manifold by the transcendental act of the imagination (synthetical influence of the understanding on the internal sense), which I have named figurative synthesis.
This we can indeed always perceive in ourselves. We cannot cogitate a geometrical line without drawing it in thought, nor a circle without describing it, nor represent the three dimensions of space without drawing three lines from the same point perpendicular to one another. We cannot even cogitate time, unless, in drawing a straight line (which is to serve as the external figurative representation of time), we fix our attention on the act of the synthesis of the manifold, whereby we determine successively the internal sense, and thus attend also to the succession of this determination. Motion as an act of the subject (not as a determination of an object),[20] consequently the synthesis of the manifold in space, if we make abstraction of space and attend merely to the act by which we determine the internal sense according to its form, is that which produces the conception of succession. The understanding, therefore, does by no means find in the internal sense any such synthesis of the manifold, but produces it, in that it affects this sense. At the same time, how “I who think” is distinct from the “i” which intuites itself (other modes of intuition being cogitable as at least possible), and yet one and the same with this latter as the same subject; how, therefore, I am able to say: “I, as an intelligence and thinking subject, cognize myself as an object thought, so far as I am, moreover, given to myself in intuition—only, like other phenomena, not as I am in myself, and as considered by the understanding, but merely as I appear”—is a question that has in it neither more nor less difficulty than the question—“How can I be an object to myself?” or this—“How I can be an object of my own intuition and internal perceptions?” But that such must be the fact, if we admit that space is merely a pure form of the phenomena of external sense, can be clearly proved by the consideration that we cannot represent time, which is not an object of external intuition, in any other way than under the image of a line, which we draw in thought, a mode of representation without which we could not cognize the unity of its dimension, and also that we are necessitated to take our determination of periods of time, or of points of time, for all our internal perceptions from the changes which we perceive in outward things. It follows that we must arrange the determinations of the internal sense, as phenomena in time, exactly in the same manner as we arrange those of the external senses in space. And consequently, if we grant, respecting this latter, that by means of them we know objects only in so far as we are affected externally, we must also confess, with regard to the internal sense, that by means of it we intuite ourselves only as we are internally affected by ourselves; in other words, as regards internal intuition, we cognize our own subject only as phenomenon, and not as it is in itself.[21]
[20] Motion of an object in space does not belong to a pure science, consequently not to geometry; because, that a thing is movable cannot be known à priori, but only from experience. But motion, considered as the description of a space, is a pure act of the successive synthesis of the manifold in external intuition by means of productive imagination, and belongs not only to geometry, but even to transcendental philosophy.
[21] I do not see why so much difficulty should be found in admitting that our internal sense is affected by ourselves. Every act of attention exemplifies it. In such an act the understanding determines the internal sense by the synthetical conjunction which it cogitates, conformably to the internal intuition which corresponds to the manifold in the synthesis of the understanding. How much the mind is usually affected thereby every one will be able to perceive in himself.
§ 21
On the other hand, in the transcendental synthesis of the manifold content of representations, consequently in the synthetical unity of apperception, I am conscious of myself, not as I appear to myself, nor as I am in myself, but only that “I am.” This representation is a thought, not an intuition. Now, as in order to cognize ourselves, in addition to the act of thinking, which subjects the manifold of every possible intuition to the unity of apperception, there is necessary a determinate mode of intuition, whereby this manifold is given; although my own existence is certainly not mere phenomenon (much less mere illusion), the determination of my existence[22] Can only take place conformably to the form of the internal sense, according to the particular mode in which the manifold which I conjoin is given in internal intuition, and I have therefore no knowledge of myself as I am, but merely as I appear to myself. The consciousness of self is thus very far from a knowledge of self, in which I do not use the categories, whereby I cogitate an object, by means of the conjunction of the manifold in one apperception. In the same way as I require, for the sake of the cognition of an object distinct from myself, not only the thought of an object in general (in the category), but also an intuition by which to determine that general conception, in the same way do I require, in order to the cognition of myself, not only the consciousness of myself or the thought that I think myself, but in addition an intuition of the manifold in myself, by which to determine this thought. It is true that I exist as an intelligence which is conscious only of its faculty of conjunction or synthesis, but subjected in relation to the manifold which this intelligence has to conjoin to a limitative conjunction called the internal sense. My intelligence (that is, I) can render that conjunction or synthesis perceptible only according to the relations of time, which are quite beyond the proper sphere of the conceptions of the understanding and consequently cognize itself in respect to an intuition (which cannot possibly be intellectual, nor given by the understanding), only as it appears to itself, and not as it would cognize itself, if its intuition were intellectual.
[22] The “I think” expresses the act of determining my own existence. My existence is thus already given by the act of consciousness; but the mode in which I must determine my existence, that is, the mode in which I must place the manifold belonging to my existence, is not thereby given. For this purpose intuition of self is required, and this intuition possesses a form given à priori, namely, time, which is sensuous, and belongs to our receptivity of the determinable. Now, as I do not possess another intuition of self which gives the determining in me (of the spontaneity of which I am conscious), prior to the act of determination, in the same manner as time gives the determinable, it is clear that I am unable to determine my own existence as that of a spontaneous being, but I am only able to represent to myself the spontaneity of my thought, that is, of my determination, and my existence remains ever determinable in a purely sensuous manner, that is to say, like the existence of a phenomenon. But it is because of this spontaneity that I call myself an intelligence.
Transcendental Deduction of the universally possible employment in experience of the Pure Conceptions of the Understanding § 22
In the metaphysical deduction, the à priori origin of categories was proved by their complete accordance with the general logical of thought; in the transcendental deduction was exhibited the possibility of the categories as à priori cognitions of objects of an intuition in general (§ 16 and 17).At present we are about to explain the possibility of cognizing, à priori, by means of the categories, all objects which can possibly be presented to our senses, not, indeed, according to the form of their intuition, but according to the laws of their conjunction or synthesis, and thus, as it were, of prescribing laws to nature and even of rendering nature possible. For if the categories were inadequate to this task, it would not be evident to us why everything that is presented to our senses must be subject to those laws which have an à priori origin in the understanding itself.
I premise that by the term synthesis of apprehension I understand the combination of the manifold in an empirical intuition, whereby perception, that is, empirical consciousness of the intuition (as phenomenon), is possible.
We have à priori forms of the external and internal sensuous intuition in the representations of space and time, and to these must the synthesis of apprehension of the manifold in a phenomenon be always comformable, because the synthesis itself can only take place according to these forms. But space and time are not merely forms of sensuous intuition, but intuitions themselves (which contain a manifold), and therefore contain à priori the determination of the unity of this manifold.[23] (See the Transcendent Æsthetic.) Therefore is unity of the synthesis of the manifold without or within us, consequently also a conjunction to which all that is to be represented as determined in space or time must correspond, given à priori along with (not in) these intuitions, as the condition of the synthesis of all apprehension of them. But this synthetical unity can be no other than that of the conjunction of the manifold of a given intuition in general, in a primitive act of consciousness, according to the categories, but applied to our sensuous intuition. Consequently all synthesis, whereby alone is even perception possible, is subject to the categories. And, as experience is cognition by means of conjoined perceptions, the categories are conditions of the possibility of experience and are therefore valid à priori for all objects of experience.
[23] Space represented as an object (as geometry really requires it to be) contains more than the mere form of the intuition; namely, a combination of the manifold given according to the form of sensibility into a representation that can be intuited; so that the form of the intuition gives us merely the manifold, but the formal intuition gives unity of representation. In the æsthetic, I regarded this unity as belonging entirely to sensibility, for the purpose of indicating that it antecedes all conceptions, although it presupposes a synthesis which does not belong to sense, through which alone, however, all our conceptions of space and time are possible. For as by means of this unity alone (the understanding determining the sensibility) space and time are given as intuitions, it follows that the unity of this intuition à priori belongs to space and time, and not to the conception of the understanding (§ 20).
When, then, for example, I make the empirical intuition of a house by apprehension of the manifold contained therein into a perception, the necessary unity of space and of my external sensuous intuition lies at the foundation of this act, and I, as it were, draw the form of the house conformably to this synthetical unity of the manifold in space. But this very synthetical unity remains, even when I abstract the form of space, and has its seat in the understanding, and is in fact the category of the synthesis of the homogeneous in an intuition; that is to say, the category of quantity, to which the aforesaid synthesis of apprehension, that is, the perception, must be completely conformable.[24]
[24] In this manner it is proved, that the synthesis of apprehension, which is empirical, must necessarily be conformable to the synthesis of apperception, which is intellectual, and contained à priori in the category. It is one and the same spontaneity which at one time, under the name of imagination, at another under that of understanding, produces conjunction in the manifold of intuition.
To take another example, when I perceive the freezing of water, I apprehend two states (fluidity and solidity), which, as such, stand toward each other mutually in a relation of time. But in the time, which I place as an internal intuition, at the foundation of this phenomenon, I represent to myself synthetical unity of the manifold, without which the aforesaid relation could not be given in an intuition as determined (in regard to the succession of time). Now this synthetical unity, as the à priori condition under which I conjoin the manifold of an intuition, is, if I make abstraction of the permanent form of my internal intuition (that is to say, of time), the category of cause, by means of which, when applied to my sensibility, I determine everything that occurs according to relations of time. Consequently apprehension in such an event, and the event itself, as far as regards the possibility of its perception, stands under the conception of the relation of cause and effect: and so in all other cases.
Categories are conceptions which prescribe laws à priori to phenomena, consequently to nature as the complex of all phenomena (natura materialiter spectata). And now the question arises—inasmuch as these categories are not derived from nature, and do not regulate themselves according to her as their model (for in that case they would be empirical)—how it is conceivable that nature must regulate herself according to them, in other words, how the categories can determine à priori the synthesis of the manifold of nature, and yet not derive their origin from her. The following is the solution of this enigma.
It is not in the least more difficult to conceive how the laws of the phenomena of nature must harmonize with the understanding and with its à priori form—that is, its faculty of conjoining the manifold—than it is to understand how the phenomena themselves must correspond with the à priori form of our sensuous intuition. For laws do not exist in the phenomena any more than the phenomena exist as things in themselves. Laws do not exist except by relation to the subject in which the phenomena inhere, in so far as it possesses understanding, just as phenomena have no existence except by relation to the same existing subject in so far as it has senses. To things as things in themselves, conformability to law must necessarily belong independently of an understanding to cognize them. But phenomena are only representations of things which are utterly unknown in respect to what they are in themselves. But as mere representations, they stand under no law of conjunction except that which the conjoining faculty prescribes. Now that which conjoins the manifold of sensuous intuition is imagination, a mental act to which understanding contributes unity of intellectual synthesis, and sensibility, manifoldness of apprehension. Now as all possible perception depends on the synthesis of apprehension, and this empirical synthesis itself on the transcendental, consequently on the categories, it is evident that all possible perceptions, and therefore everything that can attain to empirical consciousness, that is, all phenomena of nature, must, as regards their conjunction, be subject to the categories. And nature (considered merely as nature in general) is dependent on them, as the original ground of her necessary conformability to law (as natura formaliter spectata). But the pure faculty (of the understanding) of prescribing laws à priori to phenomena by means of mere categories, is not competent to enounce other or more laws than those on which a nature in general, as a conformability to law of phenomena of space and time, depends. Particular laws, inasmuch as they concern empirically determined phenomena, cannot be entirely deduced from pure laws, although they all stand under them. Experience must be superadded in order to know these particular laws; but in regard to experience in general, and everything that can be cognized as an object thereof, these à priori laws are our only rule and guide.
Result of this Deduction of the Conceptions of the Understanding § 23
We cannot think any object except by means of the categories; we cannot cognize any thought except by means of intuitions corresponding to these conceptions. Now all our intuitions are sensuous, and our cognition, in so far as the object of it is given, is empirical. But empirical cognition is experience; consequently no à priori cognition is possible for us, except of objects of possible experience.[25]
[25] Lest my readers should stumble at this assertion, and the conclusions that may be too rashly drawn from it, I must remind them that the categories in the act of thought are by no means limited by the conditions of our sensuous intuition, but have an unbounded sphere of action. It is only the cognition of the object of thought, the determining of the object, which requires intuition. In the absence of intuition, our thought of an object may still have true and useful consequences in regard to the exercise of reason by the subject. But as this exercise of reason is not always directed on the determination of the object, in other words, on cognition thereof, but also on the determination of the subject and its volition, I do not intend to treat of it in this place.
But this cognition, which is limited to objects of experience, is not for that reason derived entirely, from, experience, but—and this is asserted of the pure intuitions and the pure conceptions of the understanding—there are, unquestionably, elements of cognition, which exist in the mind à priori. Now there are only two ways in which a necessary harmony of experience with the conceptions of its objects can be cogitated. Either experience makes these conceptions possible, or the conceptions make experience possible. The former of these statements will not hold good with respect to the categories (nor in regard to pure sensuous intuition), for they are à priori conceptions, and therefore independent of experience. The assertion of an empirical origin would attribute to them a sort of generatio aequivoca. Consequently, nothing remains but to adopt the second alternative (which presents us with a system, as it were, of the epigenesis of pure reason), namely, that on the part of the understanding the categories do contain the grounds of the possibility of all experience. But with respect to the questions how they make experience possible, and what are the principles of the possibility thereof with which they present us in their application to phenomena, the following section on the transcendental exercise of the faculty of judgement will inform the reader.
It is quite possible that someone may propose a species of preformation-system of pure reason—a middle way between the two—to wit, that the categories are neither innate and first à priori principles of cognition, nor derived from experience, but are merely subjective aptitudes for thought implanted in us contemporaneously with our existence, which were so ordered and disposed by our Creator, that their exercise perfectly harmonizes with the laws of nature which regulate experience. Now, not to mention that with such an hypothesis it is impossible to say at what point we must stop in the employment of predetermined aptitudes, the fact that the categories would in this case entirely lose that character of necessity which is essentially involved in the very conception of them, is a conclusive objection to it. The conception of cause, for example, which expresses the necessity of an effect under a presupposed condition, would be false, if it rested only upon such an arbitrary subjective necessity of uniting certain empirical representations according to such a rule of relation. I could not then say—“The effect is connected with its cause in the object (that is, necessarily),” but only, “I am so constituted that I can think this representation as so connected, and not otherwise.” Now this is just what the sceptic wants. For in this case, all our knowledge, depending on the supposed objective validity of our judgement, is nothing but mere illusion; nor would there be wanting people who would deny any such subjective necessity in respect to themselves, though they must feel it. At all events, we could not dispute with any one on that which merely depends on the manner in which his subject is organized.
Short view of the above Deduction.
The foregoing deduction is an exposition of the pure conceptions of the understanding (and with them of all theoretical à priori cognition), as principles of the possibility of experience, but of experience as the determination of all phenomena in space and time in general—of experience, finally, from the principle of the original synthetical unity of apperception, as the form of the understanding in relation to time and space as original forms of sensibility.
I consider the division by paragraphs to be necessary only up to this point, because we had to treat of the elementary conceptions. As we now proceed to the exposition of the employment of these, I shall not designate the chapters in this manner any further.
BOOK II. Analytic of Principles
General logic is constructed upon a plan which coincides exactly with the division of the higher faculties of cognition. These are, understanding, judgement, and reason. This science, accordingly, treats in its analytic of conceptions, judgements, and conclusions in exact correspondence with the functions and order of those mental powers which we include generally under the generic denomination of understanding.
As this merely formal logic makes abstraction of all content of cognition, whether pure or empirical, and occupies itself with the mere form of thought (discursive cognition), it must contain in its analytic a canon for reason. For the form of reason has its law, which, without taking into consideration the particular nature of the cognition about which it is employed, can be discovered à priori, by the simple analysis of the action of reason into its momenta.
Transcendental logic, limited as it is to a determinate content, that of pure à priori cognitions, to wit, cannot imitate general logic in this division. For it is evident that the transcendental employment of reason is not objectively valid, and therefore does not belong to the logic of truth (that is, to analytic), but as a logic of illusion, occupies a particular department in the scholastic system under the name of transcendental dialectic.
Understanding and judgement accordingly possess in transcendental logic a canon of objectively valid, and therefore true exercise, and are comprehended in the analytical department of that logic. But reason, in her endeavours to arrive by à priori means at some true statement concerning objects and to extend cognition beyond the bounds of possible experience, is altogether dialectic, and her illusory assertions cannot be constructed into a canon such as an analytic ought to contain.
Accordingly, the analytic of principles will be merely a canon for the faculty of judgement, for the instruction of this faculty in its application to phenomena of the pure conceptions of the understanding, which contain the necessary condition for the establishment of à priori laws. On this account, although the subject of the following chapters is the especial principles of understanding, I shall make use of the term Doctrine of the faculty of judgement, in order to define more particularly my present purpose.
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.[26] 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 has 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.
[26] 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 à 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 à 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 à priori to their objects, whose objective validity consequently cannot be demonstrated à 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 à priori from pure conceptions of the understanding under those conditions, and which lie à 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 à 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 à 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 à 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 à priori conceptions, in addition to the function of the understanding in the category, must contain à 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 à 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 à 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 à 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 à 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 à 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 à 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 à 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 æsthetic, 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 à 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 à 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 à priori or à 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.