No More Learning

include the predicate of weight in my conception of body in general, that, conception still indicates an object of ex
? perience, a part of the totality of experience, to which I can still add other parts ; and this I do when I recognize by ob servation that bodies are heavy. I can cognize beforehand by analysis the conception of body through the character istics of extension, impenetrability, shape, &c, all which are cogitated in this conception. But now I extend my know ledge, and looking back on experience from which I had derived this conception of body, I find weight at all times connected with the above chsracteristics, and therefore I synthetically add to my conceptions this as a predicate, and say, " all bodies are heavy. " Thus it is experience upon which rests the possibility of the synthesis of the predicate of weight with the conception of body, because both con ceptions, although the one is not contained in the other, still belong to one another (only contingently, however), as parts of a whole, namely, of experience, which is itself a synthesis of intuitions.
But to synthetical judgments a priori, such aid is entirely wanting. If I go out of and beyond the conception A, in order to recognize another B as connected with what foundation have to rest on, whereby to render the synthesis possible have here no longer the advantage of looking out in the sphere of experience for what want. Let us
take, for example, the proposition, "everything that happens has cause. " In the conception of something that happens, indeed think an existence which certnin time antecedes,
and from this can derive analytical judgments. But the conception of cause lies quite out of the above " conception, tad indicates something entirely different from that which
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? SYNTHETICAL JUDGMENTS A PRIOBI.
9
happens," and is consequently not contained in that con ception. How then am I able to assert concerning the general conception -- "that which happens " -- something entirely dif ferent from that conception, and to recognize the conception of cause although not contained in yet as belonging to and even necessarily? what here the unknown = upon which the understanding rests when believes has found, out of the conception foreign predicate which nevertheless considers to be connected with cannot be experience, because the principle adduced annexes the two represent ations, cause and effect, to the representation existence, not only with universality, which experience cannot give, but also with the expression of necessity, therefore completely prion and from pure conceptions. Upon such synthetical, that augmentative propositions, depends the whole aim of our specu lative knowledge priori for although analytical
? judgments are indeed highly important and necessary, they are so, only
to arrive at that clearness of conceptions which requisite for sure and extended synthesis, and this alone real acquisition.
V. In all theobetical sciences of season, synthetical JUDGMENTS PRIORI ABB CONTAINED AS PBISCIPLES.
Matiiematicax judgments are always synthetical. Hitherto this fact, though incontestibly true and very important in its consequences, seems to have escaped the analysts of the human mind, nay, to be in complete opposition to all their conj'c tures. For as was found that mathematical conclusions all
proceed according to the principle of contradiction (whi<. h the nature of every apodeictic certainty requires), people became persuaded that the fundamental principles of the science also were recognised and admitted in the same way. But the notion fallacious for although synthetical pro position can certainly be discerned by means of the principle of contradiction, this possible only when another syntheti cal proposition precedes, from which the latter deduced, but never of itself.
Before all, be observed, that proper mathematical propo
sitions are always judgments priori, and not empirical, be cause they carry nlong with them the conception of necessity,
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which cannot be given by experience. If this be demurred to, it matters not ; I will then limit my assertion to pure ma thematics, the very conception of which implies, that it con sists of knowledge altogether non-empirical and a priori.
We might, indeed, at first suppose that the proposition 7 + 5=12, is a merely analytical proposition, following (ac cording to the principle of contradiction), from the concep tion of a sum of seven and five. But if we regard it more narrowly, we find that our conception of the sum of seven and five contains nothing more than the uniting of both sums into one, whereby it cannot at all be cogitated what this single number is which embraces both. The conception of twelve is by no means obtained by merely cogitating the union of seven and five ; and we may analyze our conception of such a possible sum as long as we will, still we shall never dis cover in it the notion of twelve. We must go beyond these conceptions, and have recourse to an intuition which corresponds to one of the two,--our five fingers, for ex ample, or like Segner in his "Arithmetic," five points, and so by degrees, add the units contained in the five given in the intuition, to the conception of seven. For I first take the number 7, and, for the conception of 5 calling in the aid of the fingers of my hand as objects of intuition, I add the units, which I before took together to make up the number
5, gradually now by means of the material image my hand, to the number 7, and by this process, I at length see the number 12 arise. That 7 should be added to 5, I have ceriainly cogitated in my conception of a sum=7-r5, but not that this sum was equal to 12. Arithmetical propositions are therefore always synthetical, of which we may become more clearly convinced by trying large numbers. For it wih thus become quite evident, that turn and twist our conceptions as we may, it is impossible, without having recourse to intui tion, to arrive at the sum total or product by means of the mere analysis of our conceptions. Just as little is any princi ple of pure geometry analytical. " A straight line between
two points is the shortest," is a synthetical proposition. For my conception of straight, contains no notion of quantity, but is merely qualitative. The conception of the shortest is therefore wholly an addition, and by no analysis can it be ex tracted from our conception of a straight line. Intuition
? ? ? ? SYNTHETICAL JUDGMENTS A PRIORI.
11
mast therefore here lend its aid, by means of which and thai only, our synthesis is possible.
Some few principles preposited by geometricians are, in deed, really analytical, and depend on the principle of con tradiction. They serve, however, like identical propositions, as links in the chain of method, not as principles, -- for ex ample, a=a, the whole is equal to itself, or (a+6) 7 a, the whole is greater than its part. And yet even these principles themselves, though they derive their validity from pure conceptions, are only admitted in mathematics because they can be presented in intuition. What causes us here
to believe that the predicate of such apodeictic judgments is already contained in our conception, and that
the judgment is therefore analytical, is merely the equivocal nature of the expression. We must join in thought a certain predicate to a given conception, and this necessity cleaves already to the conception. But the question not what we must join in thought to the given conception, but what we really think therein, though only obscurely, and then becomes manifest, that the predicate pertains to these conceptions, ne cessarily indeed, yet not as thought in the conception itself, out by virtue of an intuition, which must be added to the con ception.
2. The science of Natural Philosophy (Physics) contains in itself synthetical judgments priori, as principles. shall adduce two propositions. For instance, the proposition, " in all changes of the material world, the quantity of matter remains unchanged or, that, " in all communication of motion, action and re-action must always be equal. " In both of these, not only the necessity, and therefore their origin priori clear, but also that they are synthetical propo sitions. For in the conception of matter, do not cogitate
its permanency, but merely its presence in space, which fills. therefore really go out of and beyond the conception of matter, in order to think on to something priori, which did not think in it. The proposition therefore not analyti cal, but synthetical, and nevertheless conceived priori and so with regard to th<< other propositions of the pure part of natural philosophy.
3. As to Metaphysics, even we look upon merely as an attempted science, yet, from the nature of human reason, an
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indispensable one, we find that it must contain synthetical propositions & priori. It is not merely the duty of meta physics to dissect, and thereby analytically to illustrate the conceptions which we form a priori of things ; but we seek tc widen the range of our & priori knowledge. For this purpose, we must avail ourselves of such principles as add something tc the original conception --something not identical with, nor contained in and by means of synthetical judgments
priori, leave far behind us the limits of experience for example, in the proposition, " the world must have begin ning," and such like. Thus metaphysics, according to the proper aim of the science, consists merely of synthetical pro positions priori.
VI. The umrEB8AL problem of puee reasox.
? It extremely advantageous to be able to bring number of investigations under the formula of single problem. For in this manner, we not only facilitate our own labour, inas much as we define clearly to ourselves, but also render more easy for others to decide whether we have done justice to our undertaking. The proper problem of pure reason, then,
contained in the question, " How are synthetical judgments priori possible ? "
That metaphysical science has hitherto remained so va cillating state of uncertainty and contradiction, only to be attributed to the fact, that this great problem, and perhaps even the difference between analytical and synthetical judg ments, did not sooner suggest itself to philosophers. Upon the solution of this problem, or upon sufficient proof of the im possibility of synthetical knowledge priori, depends the existence or downfall of the science of metaphysics. Among
David Hume came the nearest of all to this problem yet never acquired in his mind sufficient preci sion, nor did he regard the question in its universality. On the contrary, he stopped short at the synthetical proposition ol the connection of an effect with its cause. , (principium causal- itatis), insisting that such proposition priori was impos sible. According to his conclusions, then, all that we term
philosophers,
science fancied insight of reason
metaphysical
from experience, and to
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? THE GHA1TD PBOBLEM OF PtfBE EEABOif. 13
of necessity. Against this assertion, destructive to all pure philosophy, he would have been guarded, had he had our problem before his eyes in its universality. For he would then have perceived that, according to his own argument, there likewise could not be any pure mathematical science, which assuredly cannot exist without synthetical propositions d priori, -- an absurdity from which his good understanding must have saved him.
In the solution of the above problem is at the same time comprehended the possibility of the use of pure reason in the foundation and construction of all sciences which contain theoretical knowledge & priori of objects, that is to say, the answer to the following questions :
? How is pure mathematical science possible ?
How is pure natural science possible ?
Respecting these sciences, as they do certainly exist, it may
with propriety be asked, how they are possible ? --for that they must be possible, is shewn by the fact of their really existing. * But as to metaphysics, the miserable progress it has hitherto made, and the fact that of no one system yet brought forward, as far as regards its true aim, can it be said that this science really exists, leaves any one at liberty to doubt with reason the very possibility of its existence.
Yet, in a certain sense,' this kind of knowledge must un questionably be looked upon as given; in other words, meta physics must be considered as really existing, if not as a science, nevertheless as a natural disposition of the human mind (metaphyska naturalis). For human reason, without any instigations imputable to the mere vanity of great know ledge, unceasingly progresses, urged on by its own feeling of need, towards such questions as cannot be answered by any em pirical application of reason, or principles derived therefrom ; and so there has ever really existed in every man some system
* As to the existence of pure natural science, or physics, perhaps many may still express doubts. But we have only to look at the different pro positions which are commonly treated of at the commencement of proper (empirical) physical science --those, for example, relating to the perma nence of the same quautity of matter, the vit inertia, the equality of action and reaction. &c. --to be soou convinced that ttiey form e science of pure physics {phyrica pur a, or rationalis), which well deserves to ha separately exposed as a special science, in its whole extent, whether thai be (rr<<n' or confined.
? ? ? u INTBODtJCTIOlT.
of metaphysics. It will always exist, so soon as reason awake* to the exercise of its power of speculation. And now the question arises -- How is metaphysics, as a natural disposition, possible ? In other words, how, from the nature of universal human reason, do those questions arise which pure reason proposes to itself, and which it is impelled by its own feeling
af need to answer as well as it can ?
But as in all the attempts hitherto made to answer the ques
tions which reason is prompted by its very nature to propose to itself, for example, whether the world had a beginning, or has existed from eternity, it has always met with unavoidable contradictions, we must not rest satisfied with the mere natu ral disposition of the mind to metaphysics, that with the existence of the faculty of pure reason, whence, indeed, some sort of metaphysical system always arises; but must be possible to arrive at certainty in regard to the question whether we know or do not know the things of which metaphysics treats. We must be able to arrive at decision on the subjects of its questions, or on the ability or inability of reason to form'
any judgment respecting them and therefore either to extend with confidence the bounds of our pure reason, or to set strictly defined and safe limits to its action. This last ques tion, which arises out of the above universal problem, would properly run thus How metaphysics possible as science
Thus, the critique of reason leads at last, naturally and necessarily, to science and, on the other hand, the dogma tical use of reason without criticism leads to groundless asser tions, against which others equally specious can always be set, thus ending unavoidably in scepticism.
Besides, this science cannot be of great and formidable prolixity, because has not to do with objects of reason, the variety of which inexhaustible, but merely with reason her self and her problems problems whieh arise out of her own bosom, and are not proposed to her the nature of outward 'things, but her own nature. And when once reason has previously become able completely to understand her own
power in regard to objects which she meets with in experience, will be easy to determine securely the extent and limits of
her attempted application to objects beyond the confines
? experience. mini, therefore, We may anJ
regard
the hitherto attempts
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made; to establish metaphysical science dogmatically as non existent. For what of analysis, that mere dissection of
contained in one or other, not the aim of, but only preparation for metaphysics proper, which has for its object the extension, by means of synthesis, of our a priori knowledge. And for this purpose, mere analysis of course useless, because only shews what contained in these conceptions, but not how we arrive, a priori, at them; and this her duty to shew, in order to be able afterwards to determine their valid use in regard to all objects of expe rience, to all knowledge general. But little self-denial, indeed, needed to give up these pretensions, seeing the undeniable, and in the dogmatic mode of procedure, in evitable contradictions of Reason with herself, have long since ruined the reputation of every system of metaphysics that has appeared up to this time. will require more firmness to remain undeterred by difficulty from within, and opposition from without, from endeavouring, method quite opposed to all those hitherto followed, to further the growth and fruitfulness of science indispensable to human reason -- science from which every branch has borne may be cut away, but whose roots remain indestructible.
VII. Idea and division of a pabticitlab science, ttnden THE NAME OF A CRITIQUE OF PuBE REASON.
From all that has been said, there results the idea of par ticular science, which may be called the Critique of Pvre Reason. For reason the faculty which furnishes us with the principles of knowledge priori. Hence, pure reason
the faculty which contains the principles of cognizing any thing absolutely priori. An Organon of pure reason would be a compendium of those principles according to which alone all pure cognitions priori can be obtained. The completely extended application of such an organon would afford us system of pure reason. As this, however, de manding great deal, and yet doubtful whether any extension of our knowledge be here possible, or so, in what cases we can regard science of the mere criticism of pure reason, its sources and limits, as the propcedeutie to ? yBtem of pure reason. Such science must not be called Doctrine, but only Criticie of pure Reason and iu use,
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? l<< INTRODUCTION
in regard to speculation, would be only negative, hot to en large the bounds of, but to purify our reason, and to shield it against error, --which alone is no little gain. I apply the term transcendental to all knowledge which is not so much occu pied with objects as with the mode of our cognition of these objects, so far as this mode of cognition is possible a priori. A system of such conceptions would be called Transcendental Philosophy. But this, again, is still beyond the bounds of our present essay. For as such a science must contain a complete exposition not only of our synthetical a priori, but of our analytical & priori knowledge, it is of too wide a range for our present purpose, because we do not require to carry our analysis any farther than is necessary to understand, in their full extent, the principles of synthesis a priori, with which alone we have to do. This investigation, which we cannot properly call a doctrine, but only a transcendental critique, because it aims not at the enlargement, but at the correction and guidance of our knowledge, and is to serve as a touchstone of the worth or worthlessness of all know ledge a priori, is the sole object of our present essay. Such a critique is consequently, as far as possible, a preparation for an organon ; and if this new organon should be found to fail, at least for a canon of pure reason, according to which the complete system of the philosophy of pure reason, whether it extend or limit the bounds of that reason, might one day be set forth both analytically and synthetically. For that this is possible, nay, that such a system is not of so great extent as to preclude the hope of its ever being com
is evident. For we have not here to do with the nature of outward objects, which is infinite, but solely with the mind, which judges of the nature of objects, and, again, with the mind only in respect of its cognition & priori. And the object of our investigations, as it is not to be sought without, but altogether within ourselves, cannot remain con cealed, and in all probability is limited enough to be com pletely surveyed and fairly estimated, according to its worth or worthlessness. Still less let the reader here expect a critique of books and systems of pure reason ; our present object is exclusively a critique of the faculty of pure reason itself. Only when we make this critique our foundation, do we possess a pure touchstone for estimating the philosophical
? pleted,
? ? ? IDEA OF A UKITMiDl
OF PUKE HEA. SOIT. 17
value of ancient and modern writings on this subject; and without this criterion, the incompetent historian or judge decides upon and corrects the groundless assertions of others with his own, which have themselves just as little foundation.
Transcendental philosophy is the idea of a science, for
which the Critique of Pure Reason must sketch the whole
plan architectonically, that from principles, with full
guarantee for the validity and stability of all the parts which
enter into the building. the system of all the principles
of pure reason. If this Critique itself does not assume the
title of transcendental philosophy, only because, to be
complete system, ought to contain full analysis of all
human knowledge a priori. Our critique must, indeed, lay
before us complete enumeration of all the radical concep
tions which constitute the said pure knowledge. But from
the complete analysis of these conceptions themselves, as
also from complete investigation of those derived from
them, abstains with reason partly because would he
deviating from the end in view to occupy itself with this
analysis, since this process not attended with the difficulty
and insecurity to be found in the synthesis, to which our
critique entirely devoted, and partly because would be
inconsistent with the unity of our plan to burden this essay
with the vindication of the completeness of such an analysis
and deduction, with which, after all, we have at present
nothing to do. This completeness of the analysis of these radical conceptions, as well as of the deduction from the
? a priori which may be given the analysis, we can, however, easily attain, provided only that we are in pos session of all these radical conceptions, which are to serve as principles of the synthesis, and that in respect of tills main purpose nothing wanting.
To the Critique of Pure Reason, therefore, belongs all that constitutes transcendental philosophy and the complete idea of transcendental philosophy, but still not the science itself oecause only proceeds so far with the analysis as necessary to the power of judging completely of our syn thetical knowledge a priori.
The principal thing we must attend to, in the division of the parts of science like this, that no conceptions must tnter which contain aught empirical other words, that
conceptions
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INTROUUCTION.
the knowledge i prion" must be completely pure. Hence, although the highest principles and fundamental conceptions of morality are certainly cognitions & priori, yet they do not belong to transcendental philosophy ; because, though they certainly do not lay the conceptions of pain, pleasure, desires, inclinations, &c. , (which are all of empirical origin) at the foundation of its precepts, yet still into the conception of duty, --as an obstacle to be overcome, or as an incitement which should not be made into a motive, --these empirical conceptions must necessarily enter, in the constiuction of a system of pure morality. Transcendental philosophy is con sequently a philosophy of the pure and merely speculative reason. For all that is practical, so far as it contains mo tives, relates to feelings, and these belong to empirical sources of cognition.
If we wish to divide this science from the universal point of view of a science in general, it ought to comprehend, first, a Doctrine of the Elements, and, secondly, a Doctrine of tht Method of pure reason. Each of these main divisions will have its subdivisions, the separate reasons for which we cannot here particularise. Only so much seems necessary, by way of introduction or premonition, that there are two sources of human knowledge (which probably spring from a common, but to us unknown root), namely, sense and under standing. By the former, objects are given to us ; by the latter, thought. So far as the faculty of sense may contain representations h priori, which form the conditions under which objects are given, in so far it belongs to transcendental
? The transcendental doctrine of sense must form the first part of our science of elements, because the con ditions under which alone the objects of human knowledge are givea, must precede those under which they are thought.
philosophy.
? ? ? ? OF PURE REASON.
TRANSCENDENTAL DOCTRINE OF ELEMENTS.
CRITIQUE
? ? ? TRANSCENDENTAL DOCTRINE OF ELEMENTS. PART FIRST.
TRANSCENDENTAL ESTHETIC.
? 1. Introductory.
In whatsoever mode, or by whatsoever means, our know ledge may relate to objects, it is at least quite clear, that the only manner in which it immediately relates to them, is by means of an intuition.
To this as the indispensable ground work, all thought points. But an intuition can take place >>nly in so far as the object is given to us. This, again, is only possible, to man at least, on condition that the object affect the mind in a certain manner. The capacity for receiving re presentations (receptivity) through the mode in which we are affected by objects, is called sensibility. By means of sensi bility, therefore, objects are given to us, and it alone furnishes us with intuitions ; by the understanding they are thought, and from it arise conceptions. But all thought must directly, ' r indirectly, by means of certain signs, relate ultimately to intuitions ; consequently, with us, to sensibility, because in no other way can an object be given to us.
The effect of an object upon the faculty of representation, sc far as we are affected by the said object, is sensation. That sort of intuition which relates to an object by means of sensa tion, is called an empirical intuition. The undetermined ob
ject of an empirical intuition, is called phenomenon. Thnt which in the phenomenon corresponds to the sensation, I term its matter ; but that which effects that the content of the pheno menon can be arranged under certain relations, I call its form. But that in which our sensations are merely arranged, and by which they are susceptible of assuming a certain form, can not be itself sensation. It is then, the matter of all pbeno- mena that is given to us h posteriori ; the form must lie ready i priori for them in the mind and consequently can be re garded separately from all sensation.
? ? ? ? 22 TRANSCENDENTAL JS8THETI0.
I call all representations pure, in the transcendental n lean ing of the word, wherein nothing is met with that belongs to sensation. And accordingly we find existing in the mind << priori, the pure form of sensuous intuitions in general, in which all the manifold content of the phenomenal world ii nrranged and viewed under certain relations. This pure form of sensibility I shall call pure intuition. Thus, if I take away from our representation of a body, all that the under standing thinks as belonging to as substance, force, divisi bility, &c. , and also whatever belongs to sensation, as impe netrability, hardness, colour, &c. yet there still something left us from this empirical intuition, namely, extension and shape. These belong to pure intuition, which exists priori
in the mind, as mere form of sensibility, and without any real object of the senses or any sensation.
The science of all the principles of sensibility priori, call Transcendental JEsthetic. * There must, then, be such science, forming the first part of the transcendental doctrine of elements, in contradistinction to that part which contains the principles of pure thought, and which called transcen dental logic.
In the science of transcendental esthetic accordingly, we shall first isolate sensibility or the sensuous faculty, by sepa rating from all that annexed to its perceptions by the conceptions of understanding, so that nothing be left but em pirical intuition. In the next place we shall take away from this intuition all that belongs to sensation, so that nothing may remain but pure intuition, and the mere form of phaj-
* The Germans are the only people who at present use this word to indicate what others call the critique of taste. At the foundation of this term lies the disappointed hope, which the eminent analyst, Baum- garten, conceived, of subjecting the criticism of the beautiful to principles of reason, and so of elevating its rules into science. But his endeavours were vain. For the said rules or criteria are, in respect to their chief sources, merely empirical, consequently never can serve as determinate laws priori, by which our judgment in matters of taste to be directed.
rather our judgment which forms the proper test as to the correct ness of the principles. On this account advisable to give up the use of the term as designating the critique of taste, and to apply solely to that doctrine, which true scieLce,-- the science of the laws of sensibility -- and thus come nearer to the language and the sense of the ancients in their well-known division of the objects of cognition into m'oSi;ra icai vonra or to share with speculative philosophy, and emilloj partly in tran scendental. uartlY in psvcholnsicr. l signification.
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? JlETAPHrSIOAL EXPOSITION OF 8PACB, 2. ')
nomsna, which is all that the sensibility can afford a priori. From this investigation it will be found that there are two ore forms of sensuous intuition, as principles of knowledge
priori, namely, space and time. To the consideration of these we shall now proceed.
SECTION I. OF SPACE.
? 2. Metaphysical Exposition of this Conception.
Bx means of the external sense (a property of the mind), we represent to ourselves objects as without us, and these all in space. Therein alone are their shape, dimensions, and rela tions to each other determined or determinable. The internal sense, by means of which the mind contemplates itself or its internal state, gives, indeed, no intuition of the soul as an object ; yet there is nevertheless a determinate form, under which alone the contemplation of our internal state is pos sible, bo that all which relates to the inward determinations of the mind is represented in relations of time. Of time we cannot have any external intuition, any more than we can have an internal intuition of space. What then are time and space ? Are they real existences I Or, are they merely relations or de terminations of things, such however, as would equally belong to these things in themselves, though they should never become objects of intuition ; or, are they such as belong only to the form of intuition, and consequently to the subjective consti tution of the mind, without which these predicates of time and space could not be attached to any object ? In order to become informed on these points, we shall first give an expo sition of the conception of space. By exposition, I mean the
clear, though not detailed, representation of that which belongs to a conception ; and an exposition is metaphysical, when it contains that which represents the conception as given a priori.
1. Space is not a conception which has been derived from outward experiences. For, in order that certain sen sations may relate to something without me, (that to something which occupies different part of space from that
which am) in like manner, in order that may represent them not merely as without of and near to each other, but also in separate places, the representation of space must alreudj
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exist as a foundation. Consequently, the representation of space cannot be borrowed from the relations of external phe
nomena through experience ; but, on the contrary, this ex ternal experience is itself only possible through the said ante cedent representation.
2. Space then is a necessary representation & priori, which serves for the foundation of all external intuitions. We never can imagine or make a representation to ourselves of the non existence of space, though we may easily enough think that no objects are found in it. It must, therefore, be considered as the condition of the possibility of phenomena, and by no means as a determination dependent on them, and is a repre sentation & priori, which necessarily supplies the basis for external phenomena.
3. Space is no discursive, or as we say, general conception of the relations of things, but a pure intuition. For in the first place, we can only represent to ourselves one space, and when we talk of divers spaces, we mean only parts of one and the same space. Moreover these parts cannot antecede this one all-embracing space, as the component parts from which the aggregate can be made up, but can be cogitated only as existing in it. Space is essentially one, and multiplicity in
consequently the general notion of spaces, of this or that space, depends solely upon limitations. Hence follows that an priori intuition (which not empirical), lies at the root of nil our conceptions of space. Thus, moreover, the principles of geometry, -- for example, that " in triangle, two sides together are greater than the third," are never deduced from general conceptions of line and triangle, but from in tuition, and this priori, with apodeictic certainty.
4. Spnce represented as an infinite given quantity. Now every conception must indeed be considered . u representa tion which contained in an infinite multitude of different
possible representations, which, therefore, comprises these under itself but no conception, as such, can be so conceived, as contained within itself an infinite multitude of representations. Nevertheless, space so conceived of, for all parts of space ire equally capable of being produced to infinity. Conse quently, the original representation of space an intuition a priori, and not conception
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TBAN8CENDENTAL
EXPOSITION OF SPACE.
i 3. Transcendental exposition of the conception of Space.
By a transcendental exposition, I mean the explanation of a conception, as a principle, whence can be discerned the possi bility of other synthetical a priori cognitions. For this pur pose, it is requisite, firstly, that such cognitions do really flow from the given conception ; and, secondly, that the said cog nitions are only possible under the presupposition of a given mode of explaining this conception.
Geometry is a science which determines the properties of space synthetically, and yet & priori. What, then, must be our representation of space, in order that such a cognition of it may be possible ? It must be originally intuition, for from a mere conception, no propositions can be deduced which go out beyond the conception,* and yet this happens in geometry.
But this intuition must be found in the mind ipriori, that before any perception of objects, consequently must be pure, not empirical, intuition. For geometrical prin ciples are always apodeictic, that united with the conscious ness of their necessity, as, '* Space has only three dimen sions. " But propositions of this kind cannot be empirical judgments, nor conclusions from them. (Introd. II. ) Now, how can an external intuition anterior to objects themselves, and in which our conception of objects can be determined a priori, exist in the human mind? Obviously not otherwise than in so far as has its seat in the subject only, as the formal capacity of the subject'sbeing affected objects, and thereby of obtaining immediate representation, that intuition con sequently, only as the form, the external sense general.
Thus only means of our explanation that the pos sibility of geometry, as synthetical science priori, becomes comprehensible. Every mode of explanation which does not shew us this possibility, although in appearance may be similar to ours, can with the utmost certainty be distinguished from by these marks.
4. Conclusion* from the foregoing conceptions.
(a) Space does not represent any property of objects as
? That is, the analysis of conception only gives you what contained and does not add to your knowledg: of the object of wliich j-1u
have concqtion, but merely evolve* it. -- TV.
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? 26 THANSCENDENTAL -F. STHETIC.
things in themselves, nor does it represent them in their rela tions to each other ; in other words, space does not represent to us any determination of objects such as attaches to the ob jects themselves, and would remain, even though all subjective conditions of the intuition were abstracted. For neither abso lute nor relative determinations of objects can be intuited prior to the existence of the things to which they belong, and therefore not b) priori.
(b) Space is nothing else than the form of all phenomena of the external sense, that the subjective condition of the sensi bility, under which alone external intuition possible. Now, oecause the receptivity or capacity of the subject to be affected
objects necessarily antecedes all intuitions of these objects, easdy understood how the form of all phenomena can be
given in the mind previous to all actual perceptions, there fore priori, and how as pure intuition, in which all objects must be determined, can contain principles of the relations of these objects prior to all experience.
therefore from the human point of view only that we
can speak of space, extended objects, &c. If we depart from the subjective condition, under which alone we can obtain external intuition, or, in other words, by means of which we are affected by objects, the representation of space has nc meaning whatsoever. This predicate [of space] only appli cable to things in so far as they appear to us, that are objects of sensibility. The constant form of this receptivity, which we call sensibility, necessary condition of all rela tions in which objects can be intuited as existing without us, and when abstraction of these objects made, pure intuition, to which we give the name of space. clear that we can not make the special conditions of sensibility into conditions of the possibility of things, but only of the possibility of their existence as far as they are phenomena. And so we may correctly say that space contains all which can appear to us externally, but not all things considered as things them selves, be they intuited or not, or by whatsoever subject one will. As co the intuitions of other thinking beings, we can not judge whether they are or are not bound by the same conditions which limit our own intuition, and which for us are universally valid. If we join the limitation of judgment to the conception of the subject, then the judgment will po<<
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sess unconditioned validity. For example, the proposition, "All objects are beside each other in space," is valid only under the limitation that these things are taken as objects of our sensuous intuition. But if I join the condition to the con ception, and say, " all things, as external phenomena, are be side each other in space," then the rule is valid universally, and without any limitation. Our expositions, consequently, teach the reality e. the objective validity) of space in re gard of all which can be presented to us externally as object, and at the same time also the ideality of space in regard to objects when they are considered means cf reason as things in themselves, that without reference to the constitution of our sensibility. We maintain, therefore, the empirical reality of space in regard to all possible external experience, although we must admit its transcendental ideality in other words, that nothing, so soon as we withdraw the condition upon
which the possibility of all experience depends, and look upon space as something that belongs to things in themselves.
But, with the exception of space, there no representation, subjective and referring to something external to us, which could be called objective prion. For there are no other
subjective representations from which we can deduce syn thetical propositions priori, as we can from the intuition of space. (See 3. ) Therefore, to speak accurately, no ideality whatever belongs to these, although they agree in this respect with the representation of space, that they belong merely to the subjective nature of the mode of sensuous perception such mode, for example, as that of sight, of hearing, and of feeling, by means of the sensations of colour, sound, and heat, but which, because they are only sensations, and not intuitions, do not of themselves give us the cognition of any object, least of all, an a priori cognition. My purpose, in the above remark, merely this to guard any one against illus-
trating the asserted ideality of space by examples quite insuffi
cient, for example, by colour, taste, &c. for these must be con
templated not as properties of things, but only as changes in the subject, changes which may be different in different men. For
such case, that which originally mere phenomenon, rose, for example, taken by the empirical understanding for
thing in itself, though to every different eye, in respect of its colour, may appear different. On the contrary, -tbo
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transcendental conception of pbsenomena admonition, that, genera! , nothing which thing in itself, and that space not
space critical intuited apace form which be
longs as property to things but that objects are quite unknown to us in themselves, and what we call outward ob jects, are nothing else but mere representations of our sensi bility, whose form space, but whose real correlate, the tiling in itself, not known by means of these representa tions, nor ever can be, but respecting which, in experience, no inquiry ever made.
SECTION II. OF TIME.
5. Metaphysical exposition this conception.
Time not an empirical conception. For neither co existence nor succession would be perceived us, the re
? of time did not exist <<s foundation
Without this presupposition we could not represent to our selves that things exist together at one and the same time, or at different times, that contemporaneously, or succession.
2. Time necessary representation, lying at the found ation of all our intuitions. With regard to phenomena general, we cannot think away time from them, and represent them to ourselves as out of and unconnected with time, bul we can quite well represent to ourselves time void of pheno mena. Time therefore given priori. In alone aL reality of phenomena possible. These may all be annihilated in thought, but time itself, as the universal condition of their possibility, cannot be so annulled.
3. On this necessity priori, also founded the possibility of apodeictic principles of the relations of time, or axioms of time in general, such as, " Time has only one dimension," " Different times are not co-existent but successive," (as dif ferent spaces are not successive but co-existent). ' These principles cannot be derived from experience, for would give neither strict universality, nor apodeictic certainty. We should Dnly be able to say, " so common experience teaches us," but not must be so. They are valid as rules, through which,
general, experience possible; and they instruct us respect ing experience, and not means of it.
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? TRANSCENDENTAL EXPOSITION OF TIME. 1! 9
4. Time is not a discursive, or as it is called, general con ception, but a pure form of the sensuous intuition. Different times are merely parts of one and the same time. But the representation which can only be given by a single object is an intuition. Besides, the proposition that different times can not be co-existent, could not be derived from a general con ception. For this proposition is synthetical, and therefore cannot spring out of conceptions alone. It is therefore con tained immediately in the intuition and representation of time.
5. The infinity of time signifies nothing more than that every determined quantity of time is possible only through limitations of one time lying at the foundation. Consequently, the original representation, time, must be given as unlimited. But as the determinate representation of the parts of time and of every quantity of an object can only be obtained by limitation, the complete representation of time must not be furnished by means of conceptions, for these contain only partial representations. Conceptions, on the contrary, must have immediate intuition for their basis.
? 6. Transcendental exposition of the conception of lime.
I may here refer to what is said above (? 5, 3), where, for the sake of brevity, I have placed under the head of metaphy sical exposition, that which is properly transcendental. Here I shall add that the conception of change, and with it the conception of motion, as change of place, is possible only through and in the representation of time ; that if this re presentation were not an intuition (internal) h priori, no con ception, of whatever kind, could render comprehensible the possibility of change, in other words, of a conjunction of contra dictorily opposed predicates in one and the same object, for ex ample, the presence of a thing in a place and the non-presence of the same thing in the same place. It is only in time, that it is possible to meet with two contradictorily opposed deter
minations in one thing, that after each other.