Kant's Critique of Pure Reason

Translation © George MacDonald Ross

All the translations as a single webpage

<p1> [Bvii] Preface to the Second Edition

This book is concerned with the sorts of knowledge which are the business of reason. You can easily tell whether or not such knowledge has developed along the sure path of a science, by considering how well it has succeeded. Suppose the outcome is as follows:

• after much preparation and preliminary work, it reaches an impasse as soon as it starts addressing its objectives;
• in order to achieve its objectives, it often has to go back, and try a different route;
• different people working on the same enterprise cannot agree on the way their common purpose is to be carried out.

If so, you can be certain that an academic discipline like this is still far from having entered upon the sure path of a science — it is merely groping around. It will already be a service to reason if we can possibly discover this path, even if we have to abandon many of its traditional objectives as futile, since they were adopted without reflection.

<p2> [Bviii] Logic has followed this sure path right from antiquity till now. This is obvious because it has never had to take a step backwards since Aristotle. You might say that it has been improved by the removal of some unnecessary subtleties, and by the clearer definition of its doctrines — but these are more questions of style, than of its certainty as a science. It is also remarkable that, to the present day, logic has not been able to take any step forward, and therefore to all appearance it seems to be closed and complete.

<p3> Some modern logicians have thought to extend it, by adding:

• psychological chapters on the various faculties of knowledge (e.g. imagination, or lateral thinking);
• metaphysical chapters on the origin of knowledge, or on the different kinds of certainty about different kinds of object (idealism, scepticism, etc.);
• anthropological chapters on prejudices (their causes and cures).

But this is due to their ignorance of the essential nature of this science. It is not an extension but a deformation of the sciences if you allow them to cross each other’s boundaries. The boundaries of logic are defined with absolute precision. It is a science [Bix] whose sole function is to provide a complete enumeration and a strict proof of the formal rules of all thought:

• whether it is apriori or empirical;
• whatever its origin;
• whatever its object;
• whatever obstacles it confronts, whether these are natural to our minds, or merely incidental.

<p4> The advantage which has made logic so successful consists simply in its limitedness, which allows it — indeed, requires it — to leave out of account all objects of knowledge, and the differences between them. So in logic, the understanding is concerned with nothing other than itself and its form. Obviously it must be far more difficult for reason to enter upon the sure path of a science, since it has to deal with objects as well as just itself. Hence logic is only a preparatory discipline — the forecourt to the sciences, so to speak. As for actual knowledge, a logic is certainly required for establishing whether it is true or false; but the knowledge itself can be acquired only through the particular sciences, in the strict and objective sense.

<p5> In so far as reason has a role to play in the sciences, something must be known in them apriori. This knowledge can relate to its object in two ways:

• either by merely [Bx] determining the object and its concept (which must be given from some other source);
• or by also making the object actual.

The first is the theoretical knowledge of reason; the second is the practical. The pure part is that in which reason determines its object completely apriori. In both cases, the pure part, however much or however little it may contain, must be dealt with first and separately. It must not be mixed up with whatever comes from other sources. It is bad financial management if you blindly spend whatever income you receive. If you later get into financial difficulties, you need to be able to distinguish which part of your expenditure is covered by your income, and which must be cut back.

<p6> Mathematics and physics are the two sciences through which reason achieves theoretical knowledge, because they must determine their objects a priori. Mathematics does this absolutely purely; physics does this at least partly purely, but also using criteria drawn from sources of knowledge other than reason itself.

<p7> Mathematics has proceeded along the sure path of a science, ever since the earliest time the history of human reason reaches back to, among that amazing race, the Greeks. However, you should not think that this was as easy for mathematics as it was for logic. In the case of logic, reason only had to deal with itself in order to hit upon that royal road [Bxi] — or rather to construct that road from its own resources. Far from being easy, I believe that for a long time mathematics was stuck at the stage of groping around, especially among the Egyptians. The change is to be ascribed to a revolution, brought about by the brain-wave of a single man. The project he thought up meant that the necessary way forward could no longer be missed, and the sure path of a science was entered upon and signposted for all time and to an infinite distance.

<p8> This revolution in our way of thinking was much more important than the discovery of the passage round the Cape of Good Hope. Yet its history, and that of the inspired person who brought it about, has not been preserved. Diogenes Laertius names the reputed discoverers of the most insignificant items of geometrical demonstration — even ones which are generally accepted as not needing any proof at all. However, the legendary account he has handed down to us shows that the memory of the revolution which was brought about by the first hint of the discovery of this new path must have seemed so important to mathematicians as to be unforgettable.

<p9> A light dawned on the first person to demonstrate the properties of an isosceles triangle, whether it was Thales, or someone with a different name. He discovered that [Bxii] what he had to do was not to investigate what he saw in the figure, nor even to investigate the pure concept of the figure, and learn what its properties were from its concept. Instead, he had to bring out what he himself had thought into the figure apriori in accordance with concepts, and had represented to himself by constructing it. He also discovered that, in order to be certain that he knew something apriori, he must not attribute to the object of his knowledge anything which did not follow necessarily from what he himself had injected into it in accordance with its concept.

<p10> Natural science took much longer to find the highway of science. It is only about a century and half since the programme of that highly original thinker, Francis Bacon, initiated the discovery of the highway, or at least provided new encouragement to those who were already on the track of it. This can equally be described as a sudden revolution in the way we think. In what follows, I shall consider natural science only in so far as it depends on empirical principles.

<p11> Galileo rolled balls of a weight chosen by himself down an inclined plane. Torricelli made air bear a weight which he had previously calculated to be equal to that of a column of water already known to him. More recently, Stahl turned metal into calx and calx back into metal, [Bxiii] by taking something out and then putting it back again.*

When they did these things, a light dawned on all students of nature. They grasped that reason has insight only into what it produces itself on the basis of its own plan. Reason must lead the way, with principles of judgment based on unchanging laws, and it must compel nature to answer its questions. It must not let itself be strung along by nature alone, as if in a baby-walker. Random observations made without a previously thought-out plan can never hang together so as to result in a necessary law — yet this is what reason looks for and needs.

<p12> In order to be taught by nature, reason must approach it with:

• in one hand its principles, which alone can turn harmonious appearances into laws;
• in the other hand an experiment which it has devised on the basis of these principles.

However, reason should not learn from nature like a schoolchild, who merely regurgitates whatever the teacher wants, but like an authoritative judge, who compels the witnesses to answer the questions he asks them.

<p13> So even physical science owes this revolution in its way of thinking, which has proved so fruitful, to a single inspired idea. [Bxiv] This is that, when there are things which reason cannot know through its own resources, but only by learning from nature, it must not simply ascribe these things to nature, but instead it must search them out on the basis of what reason itself has put into nature. This is how natural science was first brought onto the sure path of a science, after so many centuries of mere groping around.

<p14> Metaphysics is a wholly distinct branch of the theoretical knowledge of reason, in that it rises completely above learning from experience. It depends on concepts alone, and, unlike mathematics, it does not depend on applying concepts to intuition. So in metaphysics, reason itself must be its own pupil. However, it has not yet had the good fortune to enter the sure path of a science, even though it is older than all the other disciplines, and would remain even if the rest of them together were to be completely gobbled up in the maw of an all-destroying collapse of civilisation.

<p15> In metaphysics, reason is continually brought to an impasse, even when the laws it wants to have apriori insight into (and apriori insight is what it claims) are confirmed by the most everyday experience. Time and time again we have to turn back, because we find that the path does not lead where we want. Again, there is no agreement among metaphysicians in what they assert. [Bxv] Indeed, there is so much disagreement, that metaphysics seems more like a battleground which has been specially designed for people to practise their skills in war games. In this battleground, none of the combatants have ever managed to gain the least bit of ground, or at least to hold it permanently if they have had a victory. So there can be no doubt that the method of metaphysics has up to now been no more than a groping around, and, what is worst of all, a groping around among mere concepts.

<p16> But why has metaphysics not been able to find the sure path of a science? Perhaps it is impossible. If so, then why has nature plagued our reason with an unrelenting urge to discover this path, as one of reason’s most important concerns? Even worse, what little justification we have to trust our reason, if, in one of the most important areas of our search after knowledge, it does not merely abandon us, but jollies us along with illusory hopes, and finally betrays us! Or is it that we have merely failed to find the path so far? If so, what evidence is there to justify any optimism that, if we renew the search, we will be any more successful than our predecessors?

<p17> The key feature in the success of mathematics and natural science is that they arrived at their present state through a one-off revolution. [Bxvi] I think we should take them as an example, and reflect on what was essential about the change in the way of thinking which made them so successful. At least as an experiment, we should try imitating them, in so far as they are analogous to metaphysics as systems of knowledge based on reason.

<p18> Until now, it has been assumed that all our knowledge must accommodate itself to its objects. However, on this assumption, all attempts to find out anything about the objects of our knowledge apriori through concepts have been unsuccessful — at least anything which would extend our knowledge. So let us see whether we might not make better progress towards fulfilling the objectives of metaphysics by assuming instead that objects must accommodate themselves to our knowledge. This already fits better with what we want, namely the possibility of an apriori knowledge of objects, which establishes something about them before they are given to us.

<p19> Here it is the same as with the first thoughts of Copernicus. He made little progress in explaining the motions of the heavenly bodies on the assumption that they all revolved round the observer. So he wondered if he might not make better progress if he let the observer revolve, and left the stars at rest. In metaphysics, [Bxvii] you can make a similar thought experiment about the intuition of objects. If intuition must accommodate itself to the nature of the object, I do not see how you can know anything about it apriori. But if the object (as object of the senses) accommodates itself to the nature of our faculty of intuition, then I can easily conceive that such knowledge is possible.

<p20> If these intuitions are to become knowledge, I cannot leave them as they are, but I must turn them into representations by referring them to something as their object, and determining the object through these representations. I can therefore make one of two assumptions:

• either the concepts through which I bring about this determination accommodate themselves to the object;
• or the objects, or rather (which is the same thing) the experience in which alone they can be known as given objects accommodates itself to these concepts.

If I make the first assumption, then I am back in the same difficulty as to how I can know anything about objects apriori. If I make the second assumption, I immediately see an easier way out. Experience is itself a kind of knowledge, which requires understanding; and I must therefore presuppose that the rules of understanding are in me before any objects are given to me, and hence apriori. These rules are encapsulated in apriori concepts, to which all objects of experience must [Bxviii] necessarily accommodate themselves, and with which they must be in harmony.

<p21> Then there are objects which can be thought only through reason (and indeed necessarily so), and which cannot be given in experience at all — at least not in the way that reason thinks them. It must be possible to think such objects, and the attempts at thinking them will later provide an excellent test for the validity of the new method of thinking I have adopted, namely that we can know of things apriori only what we ourselves put into them.*

• on the one hand as objects of the senses [Bxix] and of the understanding, so as to constitute experience;
• on the other hand as objects which are merely thought (perhaps as objects for a reason which has cut itself off from the world, and is striving to go beyond the limits of experience).

• as long as things are considered from this dual perspective, then the principle of pure reason is preserved intact;
• as long as things are considered from a single perspective, then the result is an unavoidable conflict of reason with itself.]

<p23> This new approach succeeds as hoped, and it promises metaphysics the sure path of a science in its first part — namely the part which deals with apriori concepts for which experience can provide appropriately corresponding objects. [Bxix] For this changed way of thinking can give a complete explanation of how apriori knowledge is possible. What is more, it can provide sufficient proofs of the laws which lie apriori at the very basis of nature (that is, nature considered as the totality of objects of experience). Both of these were impossible using the method which has prevailed up till now.

<p24> However, this deduction of our capacity for apriori knowledge in the first part of metaphysics results in a surprising outcome, which seems very damaging to the whole purpose of the second part of metaphysics. The outcome is that we can never use our capacity for apriori knowledge to go beyond the limits of possible experience — despite the fact that this is precisely the essential objective of the science of metaphysics.

<p25> [Bxx] But this constitutes precisely the experiment of cross-checking the truth of the outcome of that first assessment of our rational apriori knowledge, namely that it only applies to appearances, whereas the thing in itself, while actual for itself, remains unknown to us. For what necessarily drives us to go beyond the limits of experience and all appearances is the unconditioned, which reason necessarily and rightly demands in the thing in itself for everything which is conditioned, thus bringing to an end the series of conditions. Now if we suppose that our experiential knowledge accommodates itself to objects as things in themselves, then it emerges that the unconditioned cannot be thought at all without contradiction. On the other hand, the contradiction disappears if we suppose that our representation of things as they are given to us does not accommodate itself to them as things in themselves, but instead these objects, as appearances, accommodate themselves to our way of representing them. Consequently, the unconditioned cannot be found in things as we know them (as they are given to us), but rather in things as we do not know them (as things in themselves). So what we originally undertook merely as an experiment turns out to have been [Bxxi] established.*

<p27> So speculative reason has been denied any progress in this realm which lies beyond the senses. It now remains to explore whether the knowledge of practical reason might not include data for determining the transcendent rational concept of the unconditioned. This way it might fulfil the desire of metaphysics to get beyond the bounds of all possible experience, by means of apriori knowledge which is possible for us — though only in the practical function of reason. Through the above method, speculative reason has at least made a space for such an extension of our knowledge, even though it has had to leave it completely empty. So we are still at liberty — indeed, we are urged by reason itself — to fill this space if we can, by means of the [Bxxii] practical data of reason.*

<p29> The job of this critique of pure speculative reason is the experiment of turning the traditional procedure of metaphysics upside down. In this way, I shall undertake a complete revolution in metaphysics, following the example of the geometrician and the natural scientist. The Critique is a treatise on method, not a systematic exposition of the science of metaphysics itself. However, it establishes a complete outline of this science, both as to its limits, and as to [Bxxiii] its whole internal structure.

<p30> It is peculiar to pure speculative reason that it can and should establish a complete preliminary outline for a system of metaphysics. It has two means of doing this:

• it can survey its own power to choose the different ways in which objects are thought;
• it can also provide a complete list of the varied ways in which it can pose problems for itself.

The first is possible because, in apriori knowledge, nothing can be attributed to the object which the thinking subject does not derive from itself. The second is possible because, as far as the principles of knowledge are concerned, pure speculative reason is a completely separate and self-subsistent unity. As in an organism, every part exists for the sake of all the others, and all for the sake of each individual. No principle can be accepted as certain in just one connection, unless its holistic connectedness with the whole sphere of pure reason has also been investigated.

<p31> Consequently, metaphysics also has another rare advantage, not enjoyed by any other rational science which has to do with objects. (It is shared by logic — but logic is concerned only with the form of thought in general.) The advantage is that, if this Critique brings metaphysics onto the sure path of a science, then it can have complete coverage of all the knowledge that falls within its territory. [Bxxiv] Metaphysics is concerned merely with principles, and with the limitations to their application which are determined by the principles themselves. So it can bring its work to completion, and bequeath it to posterity as a fixed asset which will never be increased. In fact, as a foundational science, it has a duty to be complete, and it must be possible to say of it: ‘Consider nothing done, as long as anything remains to be done.’

<p32> But, you will ask, what sort of treasure is this that I am thinking of bequeathing to posterity? What is the worth of a metaphysics which has been purified by such criticism, and thereby established for all time? On a quick glance at this work, you might think that it had merely a negative use, telling us never to risk taking speculative reason beyond the bounds of experience. And this is in fact its first use. But this use becomes positive as soon as you realise that the axioms with which speculative reason ventures beyond its limits do not in fact extend the use of reason, but, if you consider things more closely, inevitably have the effect of restricting it. This is because the axioms essentially belong to sensibility, and they actually threaten to expand the limits of sensibility [Bxxv] to include everything, and thus completely supplant the practical use of pure reason.

<p33> Hence a critique which limits the speculative use of reason is to that extent indeed negative. But in that it thereby removes an obstacle which limits, or even threatens to obliterate the practical use of reason, it is in fact of positive and very important use. This is provided you are convinced that there is an absolutely necessary use of pure reason (namely the moral), in which it inevitably extends itself beyond the limits of sensibility. It needs no assistance from speculative reason to do this; yet it must be secure from its opposition, so that reason does not fall into contraction with itself. To deny that this function of the Critique is a positive use would be like saying that the police are of no positive use, because their main job is only to prevent the violence which citizens fear from each other, so that each can carry on their business in peace and safety.

<p34> In the analytic part of the Critique, I shall show:

• that space and time are only forms of sensory intuition, and hence no more than preconditions of the existence of things as appearances;
• further, that we can have no concepts of the understanding, and hence no basic requirements for the knowledge of things, except in so far as [Bxxvi] intuition corresponding to these concepts can be given;
• and consequently that we can have no knowledge of any object as a thing in itself, but only in so far as it is an object of sensory intuition, i.e. as an appearance.

<p35> From this it obviously follows that all speculative knowledge of reason (even if it is only possible knowledge) is limited to mere objects of experience. However, it must always be borne in mind — and this is something important to note — that even though we cannot know these objects as things in themselves, yet we must at least be able to think them as things in themselves.*

<p37> For otherwise there would follow the absurd proposition that there was [Bxxvii] an appearance without that which appeared.

<p38> My Critique has shown that it is necessary to distinguish between things as objects of experience, and the very same things as things in themselves. Now let us see what follows if we suppose that this distinction had not been made. On this supposition, absolutely everything would be an efficient cause governed by the axiom of causality, and subject to the determinism of mechanistic nature. Thus I would not, without falling into a manifest contradiction, be able to say of one and the same being, for example the human soul, that its will is free, and yet at the same time subject to the determinism of nature — i.e. not free. This is because I have used the word ‘soul’ in exactly the same sense in both propositions, namely as a thing in general, i.e. as a thing in itself. Without a prior critique, I could not have used it in any other way.

<p39> In the Critique, I have argued that ‘object’ must be taken in two senses, namely as an appearance, and as a thing in itself. And in the Deduction of the Concepts of the Understanding, I have argued that the axiom of causality applies to things only in the first sense, namely in so far as they are objects of experience; but the same things taken in the second sense are not subject to the axiom. If I am right, then there is no contradiction in thinking of one and the same will [Bxxviii] as necessarily subject to the law of nature, and to that extent not free, in the realm of appearance (in its observable actions); and on the other hand, in thinking of it as not subject to that law, and hence as free, in so far as it belongs to a thing in itself.

<p40> Now I cannot know my soul considered as a thing in itself through any speculative reason, still less through empirical observation. Consequently, I cannot know freedom as the property of a being to which I ascribe effects in the world of the senses. This is because I would have to know such a being as determined in respect of its existence, but not as determined in time (and it is impossible for it to be determined in time, since I cannot ground my concept of it in any intuition). All the same, I can think freedom, in that the representation of it at least contains no internal contradiction — provided we have in place my critical distinction between the two modes of representation (the sensory and the intellectual), and the consequential limitation of the concepts of the understanding, as also of the axioms which flow from them.

<p41> Let us assume that morality presupposes freedom (in the strongest sense) as a property of our will, since morality depends on basic practical axioms embedded in our reason as its apriori premises. These axioms would be utterly impossible if freedom were not presupposed. [Bxxix] But if it were the case that speculative reason had proved that freedom could not be thought, then our first assumption (namely that the precondition for morality is fulfilled) must necessarily give way to the dictates of speculative reason, since the opposite of what is proved by speculative reason contains a manifest contradiction. Consequently, freedom would have to be replaced by the mechanism of nature, and morality would have to go with it, since the opposite of morality contains no contradiction unless freedom is presupposed.

<p42> All I need for morality is that: the concept of freedom should not:

• be self-contradictory (if so, I can at least think it, and it is unnecessary for me to have any deeper insight into it);
• prevent one and the same act from coming under the mechanism of nature, taken in a different context.

Consequently, ethics and natural science each have their own distinct spheres. This would not have been the case if criticism had not previously taught us that we are inevitably ignorant of things in themselves, and that anything of which we can have theoretical knowledge is limited to mere appearances.

<p43> Precisely the same account of the positive usefulness of the critical axioms of pure reason can be given in the case of God, and of the simple nature of our soul. But I shall omit these for the sake of brevity.

<p44> [Bxxx] God, freedom and immortality are things I cannot assume for the sake of the necessary practical use of my reason, unless at the same time I deprive speculative reason of its claim to transcendent insights. In order to achieve its insights, speculative reason would have to use axioms which in fact apply only to objects of possible experience. If these axioms are applied to that which cannot be an object of experience, then in effect the object of experience is always turned into an appearance, and any extension of pure reason in its practical function will be declared impossible.

<p45> I have therefore had to deny knowledge, in order to make room for faith. The dogmatism of metaphysics is the prejudice that progress can be made in metaphysics without a critique of pure reason. This is the true source of all the unbelief which fights against morality, and which is always very dogmatic.

<p46> So, even though it cannot be difficult to hand down to posterity the legacy of a systematic metaphysics constructed in accordance with the Critique of Pure Reason, it is a gift which should not be despised. You need merely compare the cultivation of reason along the sure path of a science in general, with its groundless fumbling and unreflective [Bxxxi] wandering around in the absence of a critique.

<p47> Another benefit is that students with a thirst for knowledge will occupy their time more profitably. In the usual dogmatic philosophy, they are given too much encouragement, and at too early a stage, to quibble confidently about things they don’t understand, and into which neither they nor anyone else in the whole wide world will ever have any insight. They are even encouraged to try and invent new thoughts and opinions, and thus to neglect their study of well-grounded sciences.

<p48> But the greatest advantage of all which you should take into account, is that all objections against morality and religion will be silenced for ever. And the critical philosophy achieves this in the Socratic way, namely by the clearest proof of the ignorance of the opponent. For there always has been, and always will be some sort of metaphysics or other in the world; and it brings with it a dialectic of pure reason, because dialectic is natural to reason. Therefore it is the primary and most important task of philosophy to purge metaphysics of all the pernicious influence of dialectic for once and for all, by putting a stop to errors at source.

<p49> This important change in the relations between the sciences means that speculative reason must lose territory which it once imagined it possessed. However, everything remains in the same advantageous state as it always was in respect of universal [Bxxxii] human concerns, and the usefulness which the world has hitherto gained from the teachings of pure reason. The loss affects only the monopoly of university philosophy, and it has no effect at all on the interests of humanity. I ask the most inflexible dogmatist whether any of the following proofs emanating from the universities could ever have penetrated to the general public, or had the slightest influence on its convictions:

1. the proof of the continued existence of our soul after death, drawn from the simplicity of its substance;
2. the proof of the freedom of the will, as against universal mechanism, drawn from the subtle but ineffectual distinction between subjective and objective practical necessity;
3. the proof of the existence of God drawn from the concept of a supremely real being (or that of the contingency of the changeable, and of the necessity of a first mover).

<p50> This has not happened, and can never be expected to happen, because the understanding of ordinary people is unsuited to such subtle speculation. The above convictions are widespread among the general public; but in so far as they rest on rational grounds at all, these grounds must be completely independent of the speculative proofs, as follows:

1. the hope of a future life depends on the natural disposition, obvious in all human beings, never to be satisfied with what is limited in time, since this would cut short the fulfilment of their destiny;
2. [Bxxxiii] the consciousness of freedom depends simply on a clear awareness of duties, set against all bodily desires;
3. the belief in a wise and great creator of the world depends solely on the wonderful order, beauty, and providence evident everywhere in nature.

<p51> These grounds for conviction remain undisturbed. Indeed, they are reinforced by the fact that schools of philosophy are now told that they have no higher or more extensive insight into any point concerning the universal human condition, than is available to ordinary mortals, who deserve our highest respect. Schools of philosophy should therefore limit themselves to the cultivation of these grounds of proof alone, since they can be understood by everyone, and are sufficient from the moral point of view. The change affects only the arrogant claims of philosophy schools, which would prefer to be accepted as the sole possessors and guardians of such truths — as they are rightly held to be in many other areas. As sole guardians, they would share with the general public only the use of these truths, but they would keep the key to them for themselves. ‘Even though he is as ignorant as I am, he wants to be thought to be the only person who knows’.

<p52> Nevertheless, [Bxxxiv] a more modest claim is still reserved for speculative philosophers. They will always remain the sole trustees of a science which benefits the general public without their knowing it, namely the critique of reason. It can never become popular; but there is no need for it to be so. Ordinary people are no more willing to fill their heads with fine-spun arguments for useful truths, than the equally subtle objections against them are likely ever to enter their minds. By contrast, academics inevitably find themselves involved in both, just like everyone who aspires to speculation. It is therefore the duty of schools of philosophy to conduct a fundamental investigation into the rights of speculative reason, so as to prevent, for once and for all, the scandal which would break out sooner or later, when even ordinary people became aware of the disputes which metaphysicians (and hence eventually the clergy as well) inevitably get involved in, through lack of a critical philosophy. The outcome of these disputes is that metaphysicians themselves thereby demonstrate the falsehood of their own teachings. Only the critical philosophy can cut out the root of materialism, fatalism, atheism, free-thinking unbelief, fanaticism, and superstition. These can be harmful to everyone; but it also eliminates idealism and scepticism, which are a danger mainly to philosophy schools, and hardly likely to infect the general public.

<p53> If governments [Bxxxv] think fit to concern themselves with what happens in universities, they would show a wise concern for the sciences as well for humankind by favouring the freedom of such a critique, since it alone can put the cultivation of reason on a firm footing. Instead, they support the ridiculous despotism of schools of philosophy, which raise a loud cry about the danger to society whenever their cobwebs are torn apart — even though the general public has never paid any attention to them, and so could never feel their loss.

<p54> The critical philosophy is not opposed to the dogmatic procedure of reason in the pure knowledge it has as a science, since science must always be dogmatic, in the sense of strictly proving things apriori on the basis of firm principles. Rather, it is opposed to dogmatism, by which I mean the presumption that it is possible to make progress with nothing but pure knowledge derived from philosophical concepts in accordance with principles. Reason has long been accustomed to doing this, but without asking by what means or by what right it has acquired these concepts and principles. So dogmatism is the dogmatic procedure of pure reason, but without a previous critique of its own powers.

<p55> Opposition to dogmatism should not be taken as condoning superficial waffle, supposedly in the interest of ordinary people; [Bxxxvi] nor should it be taken as condoning scepticism, which gives short shrift to the whole of metaphysics. Rather, criticism is a preliminary activity necessary for the advancement of a metaphysics which is well-founded as a science. Such a metaphysics must necessarily be pursued dogmatically, and in the most strictly systematic way — hence it is suitable for teaching at university, and not for popular consumption. For it cannot abandon the requirement which it has promised to fulfil, namely that it must conduct its business completely apriori, and hence to the complete satisfaction of pure reason.

<p56> In the future, when I carry out the plan prescribed in the Critique (that is, when I write a System of Metaphysics), I shall have to follow the strict method of the famous Wolff, the greatest of all dogmatic philosophers. Wolff showed by his example how the path of a science is to be taken — an example through which he founded the German spirit of thoroughness, which is not yet extinct. His method consisted in the orderly establishment of principles, the clear definition of concepts, the attempt at strictness of proof, and the avoidance of rash inferential leaps. This is why he was supremely qualified to turn metaphysics round from its present state onto the sure path of a science, if only it had occurred to him to prepare the ground first through a critique of the relevant mental faculty, namely pure reason [Bxxxvii] itself. The blame for this omission lies not so much with Wolff himself, as with the dogmatic style of thinking characteristic of his age — so the philosophers of that period, as well as of earlier periods, have no reason to reproach each other for it. Those who reject both Wolff’s method and the procedure of the critique of pure reason can have nothing else in mind than to shake off the fetters of science altogether, and to turn work into play, certainty into opinion, and love of wisdom (philosophy) into love of self-glorification (philodoxy).

<p57> As for this second edition, I have naturally taken the opportunity to remove as many difficulties and obscurities as possible. These could have given rise to various misinterpretations which even clever thinkers have fallen into in passing judgment on the book — and perhaps I was partly to blame. I have found nothing to change in the propositions themselves or in the grounds of their proofs, nor in the form or completeness of the plan. One reason for this is the long time I spent testing them before publishing the book. The other reason is the essential characteristic of the subject-matter itself. A pure speculative reason is by nature an organism, in which the whole exists for the sake of every part, and [Bxxxviii] every individual part exists for the sake of the whole. Consequently, even the slightest weakness, whether it is a positive mistake (an error) or an omission, must inevitably show up when speculative reason is put to use.

<p58> I hope that this system will continue to maintain its unalterability in future. It is not pride that justifies my confidence in this, but simply the obviousness of the outcome of my experiment. It makes no difference if you start out from the least significant element to the whole of pure reason, or if you go in the reverse direction from the whole to every part. For even the whole is given in itself through the ultimate goal of pure reason in its practical aspect. Consequently, any attempt to alter even the smallest part at once introduces contradictions, not simply to the system, but to human reason in general.

<p59> It is only in the manner of expression that much remains to be done, and here I have tried to make improvements in this edition. These should remove:

• the misunderstanding of the Aesthetic, especially in the concept of time;
• the obscurity of the deduction of the concepts of the understanding;
• the supposed lack of sufficient obviousness in the proof of the axioms of the pure understanding;
• and finally, the misinterpretation of the paralogisms which I have attributed to rational psychology.

My alterations to the manner of expression extend only this far (namely only to the end of the first chapter of the Transcendental [Bxxxix] Dialectic), and no further.*

<p66> [Bxl] Time was too short, and I had not come across any misunderstandings on the part of competent and impartial [Bxli] critics in relation to the rest of the work. Although I would not presume to name these critics with the praise they deserve, [Bxlii] the attention I have paid to their comments will be evident to them in the relevant passages.

<p67> However, the improvements I have made bring with them a small loss for the reader, which I could not avoid without making the book too long. This is that I have had to leave out or shorten various passages, which, while not in any way essential for the completeness of the whole, may yet be missed by many readers, since they could otherwise have been useful for some alternative purpose. I did so in order to make space for what I hope is now a more comprehensible exposition, which has changed absolutely nothing fundamental as to the propositions put forward, or even their proofs; but here and there it departs so much from the previous edition in the method of exposition, that the task could not be carried out merely by adding a few bits. I hope that this small loss, which can in any case be remedied by comparing it with the first edition if anyone wishes, will be more than compensated for by its greater comprehensibility.

<p68> In various publications (partly in occasional reviews of a number of books, and partly in my own writings), I have observed with grateful satisfaction that the spirit of thoroughness has not died out in Germany, but has only been drowned out for a short while by the fashionable noise of a freedom of thought which thinks it is being clever. [Bxliii] Courageous and clear-headed people have not been deterred from mastering the thorny paths of the Critique, which lead to a science of pure reason; and because this science is intellectually rigorous, it alone will survive, and hence it is of the utmost necessity. I leave it to these worthy people to complete the revision of my work. They are lucky to combine thoroughness of insight with the gift of clear exposition, which I am conscious of lacking myself — and I know that my revision is still defective in a number of places. In the case of the present book, the danger is not that it will be refuted, but that it will not be understood.

<p69> For my own part, I can no longer let myself become involved in controversies. However, I shall take careful note of any suggestions, whether from supporters or from opponents, so that I can use them in the future development of the system which will be based on the present introductory work. During the course of my labour I have become rather advanced in age (I am 64 this month). So I must be careful with my time if I am to fulfil my ambition of producing both a Metaphysics of Nature and a Metaphysics of Morals, confirming the correctness of the critique, both of speculative and of practical reason. I must leave it to those worthy people who have made my teaching their own, to defend it as a whole, and to clarify the obscurities in the present work, which are hardly to be avoided in a new venture.

<p70> [Bxliv] Every philosophical treatise will have a number of vulnerable points, since it cannot come before the public as fully armoured as a mathematical one. Nevertheless, the overall structure of the system, considered as a unity, is not in the least danger. When a system is new, only a few people have the mental agility to grasp it as a whole, and even fewer have the inclination to do so, because any novelty is a nuisance to them. Furthermore, if individual passages are torn out of their context and compared with each other, it is possible to winkle out apparent contradictions, especially in a work which has been written in free continuous prose. In the eyes of those who rely on the judgment of others, these apparent contradictions cast an adverse light on the work; but they can very easily be resolved by those who have mastered the grand conception of the work as a whole. In any case, if a theory is essentially robust, the forces of action and reaction which threaten great danger to it in its initial stages will, in time, only serve to smooth over its rough spots. If people who are impartial, insightful, and sincere communicators devote themselves to the task, then it will not be long before it also acquires the required elegance of expression.

Königsberg, April 1787.

<i1> [B1] Introduction

1. On the difference between pure and empirical knowledge

There is no doubt whatever that all our knowledge begins with experience, since our faculty of knowledge could not be awakened into activity unless objects affected our senses. These objects partly produce representations by themselves, and partly stimulate the activity of our understanding into comparing, combining, or separating these representations, thus converting the raw material of sensory impressions into a knowledge of objects which is called ‘experience’. So, in the order of time, we have no knowledge before experience, and all knowledge begins with experience.

<i2> But although all our knowledge begins with experience, it does not follow that it all originates from experience. For it could well be the case that even our experiential knowledge is a combination of what we get from impressions, and what our own faculty of knowledge supplies from its own resources, merely on the occasion of sensory impressions. However, we cannot distinguish this additional element from the [B2] basic material until lengthy practice has made us sensitive to it, and skilled at separating it out.

<i3> So there is at least a question which needs closer investigation, and which is not to be rejected out of hand. This is the question whether there is such knowledge that is independent of experience, and independent even of all impressions of the senses. Such knowledge is called apriori, as contrasted with empirical knowledge, which has its sources aposteriori, namely in experience.

<i4> However, the expression ‘apriori’ has not yet been defined precisely enough to bring out the full meaning of the question at hand. For we customarily say of much knowledge derived from experiential sources that we have it or are capable of having it apriori, because we do not derive it directly from experience, but from a general rule — even though we have borrowed the rule itself from experience. For example, we might say of someone who was digging under the foundations of their house, that they could know apriori that it would collapse; in other words, they need not wait for the experience of its actually collapsing. However, they could not know this completely apriori, since they would already have to have known through experience that bodies are heavy, and hence that they fall when their support is removed.

<i5> So in what follows, I shall not mean by ‘apriori knowledge’ knowledge which is independent of this or that [B3] experience, but knowledge which is absolutely independent of all experience. Its opposite is empirical knowledge, or knowledge which is possible only aposteriori, i.e. through experience.

<i6> When apriori knowledge contains no empirical element whatever, it is called pure. So, for example, the proposition ‘Every alteration has its cause’ is an apriori proposition, but it is not pure, because the concept of alteration is one which can be derived only from experience.

<i7> 2. We have some apriori knowledge, and even the ordinary understanding is never without it

What we need here is a reliable criterion for distinguishing between pure and empirical knowledge. Experience certainly teaches us that something has such-and-such a nature, but not that it could not be otherwise. So first, if we have a proposition which cannot be thought without being thought as necessary, then it is an apriori judgment; and if, in addition, all the propositions from which it is derived are themselves valid as necessary propositions, then it is absolutely apriori. Secondly, experience never provides its judgments with genuine or strict universality, but only with a hypothetical and relative universality depending on induction. All we can justifiably say is that, as far as we have observed up until now, [B4] there has been no exception to this or that rule. So if a judgment is thought with strict universality (i.e. so that no exception at all is allowed as possible), then it is not derived from experience, but is valid absolutely apriori.

<i8> Empirical universality is merely the unjustified raising of the status of a claim which is valid in most cases, to one which is valid in all cases — for example, in the proposition ‘All bodies are heavy.’ When, on the other hand, a judgment essentially involves strict universality, this indicates a special source of knowledge, namely a faculty for apriori knowledge. Consequently, necessity and strict universality are reliable criteria for apriori knowledge, and are inseparably connected with each other. In practice, however, it is sometimes easier to show that judgments are limited to experience than that they are contingent, and it is often more convincing to show that a judgment has unlimited universality than that it is necessary. So it is advisable to use both the above criteria separately, given that each is infallible by itself.

<i9> Now, it is easy to show that human knowledge does include such judgments, which are both necessary and universal in the strongest sense, and hence are pure apriori judgments. If you want an example from the sciences, you need only consider the propositions of mathematics. If you want an example from the most everyday use of the understanding, [B5] the proposition that every alteration must have a cause will serve the purpose. Indeed, in this last proposition, the concept of a cause so obviously contains the concept of the necessity of its connection with an effect, and the strict universality of the causal law, that the concept would be completely destroyed if you tried to follow Hume’s derivation of it. Hume attempted to derive it from a repeated association of what happens with what precedes it, and a resulting habit of connecting the representations of them — with the consequence that the necessity is merely subjective.

<i10> In fact we do not need examples like these in order to prove that our knowledge actually includes pure apriori propositions, since it can be proved by their indispensability for the very possibility of experience, and hence proved apriori. Where would experience get its certainty from, if all the rules by which it changes from one state to the next were as empirical as experience itself, and hence contingent? Contingent rules could hardly count as primary axioms. However, at this stage it is enough to have established the pure use of our faculty of knowledge as a fact, together with the criteria for it.

<i11> It is not only judgments that reveal themselves as having an apriori origin, but also even some concepts. If you abstract from your empirical concept of a body, one by one, its colour, its hardness or softness, its weight, and even its impenetrability, there still remains the space which it occupied (even though the body itself has now entirely disappeared), and [B6] you could not leave that out of your concept of the body. Similarly, if you leave out of your empirical concept of any object, whether material or immaterial, all the properties which you have learned about through experience, you still cannot deprive it of the property through which it is thought as a substance, or as inhering in a substance — even though this concept is more determinate than that of an object in general. So, convinced by the necessity with which this concept forces itself on you, you must admit that it is located apriori in your faculty of knowledge.

<i12> 3. Philosophy needs a science which will determine apriori the possibility, the principles, and the scope of all apriori knowledge

What is even more important than everything I have said so far is that some knowledge seems even to transcend the domain of all possible experiences, and to broaden the reach of our judgments beyond all limits of possible experience, through concepts for which no corresponding object at all can be given in experience.

<i13> This sort of knowledge, which transcends the world of the senses, and where experience can neither guide us nor correct us, is precisely the area investigated by our reason. We [B7] consider these investigations to be much more important and much more exalted in their aims than anything which the understanding can learn within the domain of appearances. We would rather run every risk of error, than give up such important investigations because of some grounds for caution, or because we might consider them of little value or a matter of indifference.

<i14> These unavoidable tasks for pure reason itself are God, freedom, and immortality. The science which, after all its preliminary work, is essentially directed towards solving just these problems, is called metaphysics. In the earliest stages of its development, the procedure of metaphysics is dogmatic — that is, it undertakes the execution of its task with confidence, and without first assessing the capacity or incapacity of reason for such a major undertaking.

<i15> Now it seems perfectly natural that, as soon as you have left the firm ground of experience, you would not immediately erect a building out of knowledge you possess without knowing where the knowledge came from; nor would you trust in axioms you did not know the source of. Rather, you would first assure yourself of the foundations of the building through careful investigations. In other words, you would start by raising the question of how the understanding can come by all this apriori knowledge, and also the question of what scope, validity, and worth it might have. In fact, nothing is more natural, if you take ‘natural’ in the sense of what ought to happen in the most appropriate and rational way.

<i16> [B8] But if by ‘natural’ you mean what usually happens, then the situation is reversed, and there is nothing more natural or understandable than that this investigation should have been neglected for so long. One branch of this kind of knowledge, namely the mathematical, has long been established as reliable; and this therefore gives rise to a presumption in favour of other branches, even though these might be of a completely different nature. Besides, when you are outside the realm of experience, you can be certain that you will not be refuted by experience. The urge to extend our knowledge is so great, that we can be stopped in our tracks only by running up against a clear contradiction. However, this can be avoided simply by formulating our fictions with care — but they are still fictions none the less.

<i17> Mathematics gives us a shining example of how far we can get in apriori knowledge independently of experience. Now, mathematics deals with objects and knowledge only so far as they are capable of being displayed in intuition. But this circumstance is easily overlooked, because the said intuition can itself be given apriori, and hence is hardly distinguishable from a pure apriori concept. Captivated by such a proof of the power of reason, our drive to extend our knowledge knows no limits.

<i18> The light dove, cleaving the air in free flight and feeling its resistance, could get the idea that it would be much better off in empty space. [B9] In the same way, Plato abandoned the world of the senses as imposing excessively narrow restrictions on the understanding, and ventured beyond them on the wings of his Ideas in the empty space of the pure understanding. He did not realise that, despite all his efforts, he had made no progress, since there was no resistance to serve as a sort of launchpad against which he could brace himself, and exert his forces in order to set his understanding in motion.

<i19> However, when indulging in speculation, it is the normal fate of human reason to complete the structure it is building as quickly as possible, and only afterwards to investigate whether its foundations were properly laid. But at that point all sorts of excuses will be sought to reassure us of its strength, or, even better, to persuade us against such a delayed and risky examination. During the building of the structure, what keeps us free from any worry or suspicion, and soothes us with its illusory solidity, is the following. A large part — perhaps the largest part — of the business of our reason consists in the analysis of the concepts which we already have of objects. This provides us with a considerable amount of knowledge. But in fact this knowledge is nothing more than a clarification or explanation of what we have already thought in our concepts, if only in a confused way. Nevertheless, at least as far as its form is concerned, this knowledge is valued as if it consisted in new insights, even though, as far as its matter or content is concerned, it does not extend the concepts we already have, but merely elucidates them.

<i20> [B10] Since this procedure does result in genuine apriori knowledge which constitutes a reliable and useful advance, our reason is unconsciously deluded into smuggling in assertions of a very different sort. In these assertions, our reason adds concepts entirely alien to those it already has (and indeed it does so apriori), but without our knowing how it achieves this, and without our letting any such question even enter our thoughts. So the very next topic I shall deal with is the distinction between these two kinds of knowledge.

<i21> 4. On the distinction between analytic and synthetic judgments

(In what follows, I shall consider only affirmative judgments, since what I say can easily be extended to negative ones.) In all judgments in which what is thought is the relation of a subject to its predicate, this relation can be of two sorts:

• either the predicate B belongs to the subject A as something which is (implicitly) contained in the concept of A;
• or B lies entirely outside the concept of A, even though it is connected to it.

In the first case I call the judgment analytic, and in the second case I call it synthetic. Thus analytic judgments (affirmative ones, that is) are those in which the connection between the predicate and the subject is thought through identity, whereas those in which this connection is thought without identity are to be called ‘synthetic’ judgments.

<i22> [B11] Analytic judgments could also be called ‘clarificatory’, and synthetic judgments ‘expansive’. An analytic judgment does not use the predicate to add anything to the concept of the subject, but merely breaks up the concept of the subject into its component sub-concepts, which were already thought in it, if in a confused way. By contrast, a synthetic judgment adds to the concept of the subject a predicate which was not thought in it at all, and which could not have been extracted from it by any process of breaking it up into its constituent parts.

<i23> For example, if I say ‘All bodies are extended,’ this is an analytic judgment, since I need not go beyond the concept which I attach to the word ‘body’, in order to find that extension is connected to it. To extract the predicate of extension from the concept of body, I merely have to break it up into its constituent parts — in other words, I only need to become conscious of the complex whole which I always think in the concept, in order to encounter this predicate in it. So it is an analytic judgment. By contrast, if I say ‘All bodies are heavy,’ the predicate is something quite different from what I think in the mere concept of a body in general. So the addition of such a predicate to the concept of the subject results in a synthetic judgment.

<i24> Judgments of experience are, as such, all synthetic. It would be absurd to base an analytic judgment on experience, because I have no need at all to go beyond my concept in order to form the judgment, and thus the evidence of experience is unnecessary for it. That a body is extended is a proposition which is apriori certain, and not a judgment of experience. [B12] Rather than appealing to experience, I already have all the prerequisites for my judgment in the concept. I only have to draw the predicate out of it in accordance with the law of contradiction, and in doing so I can at the same time become conscious of the necessity of the judgment — something that experience would never have taught me.

<i25> By contrast, I do not include the predicate ‘heavy’ in the concept of a body in general. However, the concept of a body does denote an object of experience through one of the components of an experience; and I can add to it another component of the same experience as belonging to the first component, by virtue of which it is a body. I can know the concept of body analytically, in advance of experience, through the characteristics of extension, impenetrability, shape, etc., all of which are thought in this concept. Now I expand my knowledge by reviewing the experience from which I abstracted this concept of body, and, finding that heaviness is always connected with the above characteristics, I add the predicate ‘heavy’ to the concept of body synthetically. So it is experience which grounds the possibility of the synthesis of the predicate ‘heavy’ with the concept of body. Although neither of the two concepts is contained in the other, they are nevertheless parts of a whole, namely experience, which is itself a synthetic combination of intuitions. So they belong to each other through experience, even if only contingently.

<i26> However, the resource of experience is entirely lacking in the case of synthetic apriori judgments. If I am to go beyond a concept A, [B13] so as to know that a concept B is connected with it, what is there that will justify me in making this connection? And what is there that will make the synthesis possible, given that in this case I do not have the opportunity to look for it in the world of experience? Take the proposition ‘Everything which happens has its cause.’ In the concept of something which happens, I think an existence before which there is a time, etc., and analytic judgments can be derived from this. But the concept of a cause lies entirely outside that concept. It denotes something different from that which happens, and therefore is certainly not contained in the latter representation.

<i27> So how do I get to say about that which happens in general, something which is completely different from it? How can I know that the concept of cause belongs to it, and even belongs to it necessarily, despite the fact that the concept of cause is not contained in the concept of that which happens? What, here, is the unknown=x which the understanding relies on, when it believes it can discover, outside the concept of A, a predicate B which is alien to A, but which the understanding considers to be connected with it? It cannot be experience, because the axiom appealed to connects the two representations together, not only with greater generality than experience can provide, but also with the stamp of necessity, and hence completely apriori and on the basis of concepts alone.

<i28> The whole aim of our apriori speculative knowledge depends on synthetic axioms like this, which extend our knowledge. Analytic judgments are indeed very important and necessary, but only [B14] in order to attain the clarity of concepts which is required for a reliable synthesis which extends our knowledge as a genuinely new acquisition.

<i29> 5. All theoretical sciences of reason contain apriori synthetic judgments as principles

1. Mathematical judgments are all synthetic. Up to now, this proposition seems to have escaped the notice of analysts of human understanding, and even seems to directly contradict everything they have assumed. Nevertheless, it is incontrovertibly certain, and very important in its consequences. These analysts found that all mathematical reasoning proceeds in accordance with the principle of contradiction, as is required by the nature of demonstrative certainty. They therefore persuaded themselves that the axioms of mathematics could also be derived from the principle of contradiction. But they were wrong in this. It is true that a synthetic proposition can always be assessed in accordance with the principle of contradiction, but only as presupposing another synthetic proposition from which it can be deduced. Synthetic propositions can never be self-evident.

<i30> First it must be observed that all mathematical judgments are essentially apriori and not empirical, because they involve necessity, which can never be derived from experience. [B15] But if this is not accepted, then I am willing to limit my proposition to pure mathematics, since its very concept implies that it does not include any empirical knowledge, but only pure apriori knowledge.

<i31> At first sight, it might be thought that the proposition 7+5=12 is merely an analytic proposition, which follows from the concept of a sum of seven and five in accordance with the law of contradiction. But if you consider it more closely, you will find that the concept of the sum of seven and five contains no more than the union of the two numbers in a single number. Through this concept, there is no thought at all of what the single number is which embraces both the others. In no way do I already think the concept of twelve simply by virtue of my thinking the union of seven and five, and however long I analyse my concept of such a possible sum, I shall not find twelve in it.

<i32> In order to find the number twelve, I have to go beyond the above concepts, and obtain the help of an intuition which corresponds to one of the two concepts. This might be the five fingers of my hand, or five points (following Segner in his Arithmetic). I then add, one by one, the units of the five which is given in the intuition, to the concept of seven. For I first take the number seven, and then take the fingers of my hand as an intuition which helps me represent the concept of five. One by one, I add to the number seven the units which I previously took as a single whole [B16] making up the number five. So it is with the aid of the image of my hand that I see the number twelve emerge. In the concept of the sum = 7+5, I did indeed think that 5 must be added to 7, but not that this sum is equal to the number twelve.

<i33> Therefore arithmetical propositions are always synthetic. This is even clearer in the case of somewhat larger numbers, since it is obvious that, however we twist and turn our concepts, we could never find the sum of the numbers by the mere analysis of our concepts, and without getting the help of intuition.

<i34> Just as little is any axiom of pure geometry analytic. That the straight line between two points is the shortest is a synthetic proposition, since my concept of straight contains nothing about quantity, but only a quality. Therefore the concept of the shortest is entirely additional to it, and cannot be derived by any analysis from the concept of a straight line. So here the help of intuition must be obtained, since it is only through the mediation of intuition that the synthesis of the concepts is possible.

<i35> A few axioms presupposed by geometry are indeed genuinely analytic and depend on the principle of contradiction. However, like identical propositions, their only function is as links in the deductive chain, and [B17] not as axioms — for example, a=a, i.e. the whole is similar to itself, or (a+b)>a, i.e. the whole is greater than its part. And yet, although these are valid by virtue of concepts alone, they too are allowed in mathematics only because they can be displayed in intuition.

<i36> Here, what makes us usually believe that the predicate of such demonstratively certain judgments already lies in our concept of the subject, and therefore that the judgment is analytic, is merely an ambiguity of expression. It is said that we ought to join in thought a particular predicate to a given concept, and that this necessity is already inherent in the concepts. But the question is not what we ought to add in thought to the given concept, but what we actually think in it, however obscurely. Then it is obvious that the predicate does indeed necessarily belong to the given concept, but not as being thought in the concept itself, but through the mediation of an intuition which must be added to the concept.

<i37> 2. Natural science (physics) contains within itself synthetic apriori judgments as axioms. I shall mention just a couple of axioms as examples:

• the axiom that in alterations of the material world the quantity of matter remains unaltered;
• the axiom that in all communication of motion, mutual action and reaction must always be the same.

It is clear that both axioms are not only necessary (and hence have an apriori origin), but are also synthetic [B18] propositions. For I do not think permanence in the concept of matter, but merely its presence in the space it fills. In fact I have to go beyond the concept of matter, in order to add to it apriori in thought something I did not think in it. And the same goes for the remaining propositions of the pure part of natural science.

<i38> 3. As for metaphysics, you may consider it to be a science which has not yet been established, but which the nature of human reason makes unavoidable. Even if this is your view, metaphysics must consist of synthetic apriori knowledge. It is not its business merely to analyse concepts of things which we form for ourselves apriori, and thus to clarify them analytically. Rather, our ambition is to extend our apriori knowledge. To do this we must use axioms which add to the given concept something which was not already contained in it, and to take synthetic apriori judgments so far that experience itself cannot follow us — for example, in the proposition: ‘The world must have a first beginning,’ and the such like. Thus metaphysics, at least as far as its objective is concerned, consists of nothing but synthetic apriori propositions.

<i39> [B19] 6. The general problem of pure reason

We have already made great progress if we can bring a number of investigations under the formula of a single problem. In this way we not only lighten our own task by defining it precisely, but we also make it easier for others to assess whether or not we have successfully met our objectives. The essential problem of pure reason is contained in the question:

• How are synthetic apriori judgments possible?

<i40> The reason why metaphysics has till now remained in such a precarious state of uncertainty and controversy is entirely because no-one has previously let this problem enter their minds — or perhaps even the distinction between analytic and synthetic judgments. Metaphysics now stands or falls on the solution of this problem, or on a satisfactory proof that in fact there is no such possibility, and hence nothing which requires an explanation.

<i41> Among all philosophers, David Hume came nearest to dealing with this problem; but he fell far short of defining it closely enough, or of conceiving it in its full universality. Instead, he confined himself to the synthetic proposition about the connection between an effect and its cause (the principle of causality), and he believed [B20] he had shown that such an apriori proposition is completely impossible. Following his arguments, everything we call metaphysics would amount to no more than a mere delusion, in which we suppose ourselves to have rational insight into what is in fact merely borrowed from experience, and has taken on the appearance of necessity as the result of habitual repetition. This claim is destructive of all pure philosophy, and Hume would never have stooped to it if he had kept our problem fixed before his eyes in its full universality. He would have recognised that, according to his argument, there could be no such thing as pure mathematics either, since it certainly consists of synthetic apriori propositions. But his good sense would surely have kept him from making any such claim.

<i42> In solving the above problem, we are at the same time dealing with the possibility of the pure use of reason for grounding and developing all sciences which contain theoretical apriori knowledge of objects — that is, we are answering the questions:

• How is pure mathematics possible?
• How is pure natural science possible?

Since these sciences are actually given, it is perfectly proper to ask how they are possible, since their actuality proves that they must be possible.*

<i44> As for metaphysics, however, [B21] everyone must be left with grounds for doubting its possibility, both because of its poor progress so far, and because no single metaphysical system put forward up till now can be described as actually established, at least as far as the essential goal of metaphysics is concerned.

<i45> However, there is another sense in which this kind of knowledge can also be considered as given. Even if metaphysics has not been actualised as a science, it is actual as a natural disposition (natural metaphysics). For, quite apart from being motivated by simple pride in wealth of knowledge, human reason advances unstoppably, driven by its own special urge, to questions which cannot be answered through any use of reason within the world of experience, or through principles borrowed from experience. So a kind of metaphysics always has been, and always will be actualised in every human being, as soon as their reason extends to speculation. So this now raises another question, namely: [B22]

• How is metaphysics possible as a natural disposition?

That is, how does the nature of universal human reason give rise to questions which pure reason poses for itself, and which it is driven, by its own special urge, to answer as well as it can?

<i46> All previous attempts to answer these natural questions (such as whether the world has a beginning, or has existed since eternity) have always led to unavoidable contradictions. So the task cannot be left simply to the natural disposition towards metaphysics — that is, to the pure faculty of reason itself, which permanently gives rise to some sort of metaphysics, whatever it may be. It must be possible for reason to attain certainty as to whether the objects of metaphysics are knowable or not — that is, to come to a decision, either about the objects of its questions, or about the capacity or incapacity of reason to make judgments about them. If so, we can either extend the scope of our pure reason with confidence, or set definite and firm limits to it. The final question, which arises out of the general problem above, would justifiably be the following:

• How is metaphysics possible as a science?

Thus the critique of reason necessarily leads in the end to scientific knowledge. By contrast, the dogmatic use of reason without a critique leads to unfounded assertions, [B23] which can be counterbalanced by equally plausible opposite ones — and hence leads to scepticism.

<i47> We should not be deterred from embarking on this science on the grounds that it will be an enormous undertaking, since it does not deal with the objects of reason, which are indeed infinitely various. Rather, it merely deals with itself — with problems which arise entirely from within itself, and are posed for it by its own nature, and not by the nature of things distinct from it. Once reason has become completely familiar with its own powers in relation to the objects it might encounter in experience, it must become easy for it to determine, with completeness and certainty, the extent and limits of its attempted use beyond all bounds of experience.

<i48> So we can and must consider as abortive all the attempts which have been made till now to establish a metaphysics dogmatically. Whatever analytic content the various systems have consists merely in the dissection of the concepts which reside apriori in our reason. This is not the goal of metaphysics at all, but only a preparation for metaphysics proper, the goal of which is to extend our synthetic apriori knowledge. Analysis is useless for achieving this goal, because it merely shows what is contained in these concepts. It does not show how we attain such concepts apriori, so that we can then also determine their valid use in relation to the objects [B24] of all knowledge in general.

<i49> It takes little self-denial to give up all these dogmatic claims, since the authority of every metaphysical system so far has long since been destroyed by the internal contradictions of reason with itself. These cannot be covered up, and they are also unavoidable if reason proceeds dogmatically. More perseverance will be required not to be held back by the intrinsic difficulty of the task at hand, or by resistance from others. This task is to apply a method which is diametrically opposed to any that has been used before, in order finally to bring about a thriving and fruitful growth in a science which human reason cannot avoid. You can cut off every stem it has sprouted till now, but you cannot dig out its roots.

<i50> 7. The idea and structure of a distinct science called ‘the critique of pure reason’

All I have said so far results in the idea of a distinct science which can be called the critique of pure reason. Reason is the faculty which makes the principles of apriori knowledge ready for use. Hence it is pure reason that contains the principles by which we can know something strictly apriori. An instrument of pure reason would be the totality of principles by which all [B25] pure apriori knowledge can be acquired and actualised. The complete application of such an instrument would result in a system of pure reason. However, it would be overambitious to expect such a system at this stage, when it is still uncertain whether an extension of our knowledge in this area is even possible at all, and if it is, in which cases. So we can regard a science which merely assesses pure reason, its sources, and its limits, as an introduction to the system of pure reason. Such an introduction would not amount to a body of knowledge to be taught. Rather, it must be no more than a critique of pure reason. Its usefulness would in fact be purely negative as far as speculation is concerned, since it would serve, not to widen the scope of our reason, but only to purge it, and keep it free of errors — but this is already a considerable achievement.

<i51> I call ‘transcendental’ all knowledge which deals universally, not so much with objects, but with our way of knowing objects, in so far as this is to be possible apriori. A system of such concepts would be called ‘transcendental philosophy’. But again, even this is too much for the initial stage. Such a science would have to cover the whole of analytic knowledge as well as of synthetic apriori knowledge. So its scope is too wide for our purposes, since we must carry analysis no further than is absolutely necessary for us to understand, in their whole extent, the principles of apriori synthesis, which are our only concern here.

<i52> [B26] It is this investigation with which we are now concerned. We cannot call it a body of knowledge to be taught, but only a transcendental critique, since its purpose is not to extend knowledge as such, but only to correct it, and to provide the touchstone for whether any apriori knowledge is valid or not. So such a critique is a preparation, as far as is possible, for an instrument of pure reason; and if this should turn out not to be possible, then at least for a rule-book of pure reason. This rule book would show how it might be possible, at some time in the future, to lay out the complete system of the philosophy of pure reason, using both the analytic and the synthetic methods — irrespective of whether it extends or merely limits the knowledge pure reason can attain.

<i53> Even in advance it can be calculated that such a system is possible, and indeed that it could not be too great in scope for us to hope to complete it entirely. This is because our subject-matter is not the nature of things, which is inexhaustible, but the understanding, which makes judgments about the nature of things — and then only in relation to its apriori knowledge. Since we do not need to look for its stock of apriori knowledge in sources external to us, it cannot remain hidden from us, and it is likely to be small enough for it to be catalogued in its entirety, assessed as to its validity or otherwise, and given its correct valuation.

<i54> [B27] Still less should you expect here a critique of books or systems of pure reason, but rather a critique of the pure faculty of reason itself. It is only on the basis of the critique of pure reason that we have a reliable touchstone for evaluating the philosophical content of old and new works in this discipline. Without a critique, unqualified historians and critics judge the groundless assertions of others in the light of their own equally groundless assertions.

<i55> Transcendental philosophy is the idea of a science, for which the critique of pure reason has to lay out the whole plan architectonically — that is, on the basis of principles, with an absolute guarantee of the completeness and robustness of all the parts which make up this construction. Transcendental philosophy is the system of all the principles of pure reason. However, this critique does not yet amount to a transcendental philosophy in the full sense of the term, simply because it is not a complete system unless it includes an exhaustive analysis of all human apriori knowledge.

<i56> Our critique must certainly provide us with a complete list of all the foundational concepts on which pure human knowledge is based. However, it stops short of a detailed analysis of these concepts themselves, let alone a complete review of all the concepts which can be derived from them. This is reasonable on two counts:

• such an analysis would be irrelevant [B28] to the essential purpose of the entire critique, which is to resolve problems about synthetic a priori knowledge — problems which do not arise in the case of analytic a priori knowledge;
• it would be inconsistent with the coherence of our plan if we became involved in responsibility for the completeness of such an analysis and what can be derived from it, when it is not part of our objective to do so.

It will be easy to complete the analysis of the foundational concepts and the subsequent derivation of the apriori concepts they give rise to, once they are established as a complete list of the principles of synthesis, and nothing belonging to their essential purpose is left out.

<i57> So the critique of pure reason covers everything which belongs to transcendental philosophy. But although it constitutes the complete idea of transcendental philosophy, it is not this science itself, since it does not pursue analysis beyond what is necessary for the complete assessment of synthetic apriori knowledge.

<i58> In specifying the sub-divisions of such a science, the most important thing to pay attention to is that it must under no circumstances admit any concepts which have any empirical content whatever. In other words, the knowledge must be utterly pure apriori. It follows that, although the most fundamental axioms and concepts of morality are instances of apriori knowledge, they do not belong to transcendental philosophy. It is true that the concepts [B29] of pleasure and pain, appetite, inclination, and so on, which are all of empirical origin, themselves play no role in the basic prescriptions of morality. Nevertheless, they must necessarily be included in the drawing up of a system of pure morality through the concept of a duty, whether as an obstacle to be overcome, or as an impulse which should not be turned into a reason for acting. So transcendental philosophy is confined to pure speculative reason. Since everything practical involves motives, it relates to feelings, which belong to empirical sources of knowledge.

<i59> If we want to set up the division of the science I am now proposing on the general lines of any system whatever, then it must include first a Doctrine of Elements, and second a Doctrine of Method. Each of these main divisions will have its sub-divisions; but I am not yet in a position to explain the grounds for these. All I need to say by way of introduction or preliminary reminder, is that there are two branches of human knowledge, which perhaps grow from a common root, even if it is unknown to us. These are sensibility and understanding. Through the former objects are given to us, and through the latter they are thought. Sensibility will belong to transcendental philosophy in so far as it contains apriori representations which constitute the preconditions for [B30] objects to be given to us. The transcendental doctrine of sensibility must belong to the first part of the science of elements, because the preconditions for objects to be given to human knowledge precede the preconditions for these objects to be thought.

<a1> [B33] The Transcendental Doctrine of Elements

First Part

The Transcendental Aesthetic

§1

Knowledge can relate to objects in various ways and through various intermediaries. Intuition is that through which it is immediately related to objects, and to which all thought is directed as the intermediary of knowledge. But intuition takes place only in so far as the object is given to us. Again, in the case of us humans at least, an object can be given to us only if it affects the mind in a certain way. Receptivity, or the capacity to acquire representations through the way in which we are affected by objects, is called sensibility. So it is by means of sensibility that objects are given to us, and it is sensibility alone that provides us with intuitions. But intuitions are thought through the understanding, and it is from the understanding that concepts arise. However, all thought must ultimately relate to intuitions, whether directly or indirectly, by virtue of certain properties. So in the case of us human beings, thought relates to sensibility, because no object can be given to us in any other way.

<a2> [B34] The effect of an object on the faculty of representation, in so far as we are affected by it, is sensation. An intuition which is related to the object through sensation is called empirical. The undetermined object of an empirical intuition is called an appearance.

<a3> That in an appearance which corresponds to sensation, I call its matter, and that which enables the multiplicity of the appearance to be organised in particular relationships, I call the form of the appearance. That which is essential for sensations to be organised and put into a particular form, cannot itself be a sensation. Therefore, while the matter of all appearance is indeed given to us only aposteriori, the whole of its form must lie ready for it in the mind apriori, and hence its form can be considered separately from all sensation.

<a4> I call any representation pure (in the transcendental sense) if it contains nothing that belongs to experience. So the pure form of sensory intuition in general will be found apriori in the mind, and through it all the multiplicity of appearances will be intuited in particular relationships. This pure form of sensibility is also itself called pure [B35] intuition. Thus if I abstract from the representation of a body everything that the understanding thinks about it (substance, force, divisibility, etc.), and also everything in it that belongs to sensation (impenetrability, hardness, colour, etc.), I am still left with something from this empirical intuition, namely extension and shape. These belong to pure intuition, which exists apriori in the mind as a pure form of sensibility, even when there is no actual object of the senses, or any actual sensation.

<a5> I call a science of all the principles of apriori sensibility the transcendental aesthetic.*

• either let the term revert to its original meaning, and reserve it for a doctrine which is a genuine science — in which case we would come closer to the terminology and meaning of the ancients, who were renowned for their division of knowledge into what is known by the senses (aestheta) and what is known by the intellect (noeta);
• or share the term between speculative philosophy and the critique of taste, so that the term ‘aesthetic’ can be taken both in a transcendental sense, and as having a psychological meaning.]

<a6> There must be such a science as the Transcendental Aesthetic, and it [B36] constitutes the first part of the Transcendental Doctrine of Elements. It is complemented by the second part, which contains the principles of pure thought, and is called the Transcendental Logic.

<a7> So in the Transcendental Aesthetic, we shall:

1. isolate sensibility, by abstracting everything which the understanding thinks in it through its concepts, so that nothing remains except empirical intuition; then
2. separate off from empirical intuition everything which belongs to sensation, so that nothing remains except pure intuition and the mere form of appearances — which is all that sensibility can supply apriori.

In the course of this investigation, it will emerge that there are two pure forms of sensory intuition which serve as apriori principles, namely space and time. I shall now proceed to a consideration of these.

<a8> [B37] The Transcendental Aesthetic

First Section

On Space

§2

The Metaphysical Exposition of this Concept

Outer sense is a property of our mind, and it is the means by which we represent to ourselves objects as outside us, and as occupying a single space. It is in space that their shape, size, and relations with each other are, or can be determined. Inner sense is the means by which the mind intuits itself or its inner state. It does not supply any intuition of the soul itself as an object, but it is a determinate form, namely time, which is essential for the soul to be able to intuit its inner state. Everything which belongs to inner determinations is represented in relations of time.

<a9> Time cannot be intuited externally, any more than space can be intuited as something internal to us. So what are space and time? Are they actual beings? Are they merely determinations or even relations of things, although ones which would still intrinsically belong to things even if they were not intuited? Or do they belong only to the form of intuition, and hence to the [B38] subjective nature of our minds, so that without this nature, spatio-temporal predicates could not be ascribed to things at all?

<a10> In order to answer these questions, I shall begin by expounding the concept of space. By exposition I mean the clear (though not complete) representation of what belongs to a concept. An exposition is metaphysical when it contains what shows the concept as given apriori.

<a11> 1. Space is not an empirical concept abstracted from outer experiences. For the representation of space must already be presupposed in order for me to be able:

• to relate certain sensations to something outside me (in other words, to something in a different part of space from that in which I find myself); and
• to represent them as separated from or next to one another, and hence not merely as different from each other, but also as in different places.

So the representation of space cannot be obtained empirically from the properties of outer appearance. Rather, this outer experience itself becomes possible only through the representation of space.

<a12> 2. Space is a necessary apriori representation, which is presupposed by all outer intuitions. You can never form a representation of space not existing, though you can easily think that it is empty of objects. [B39] So it must be regarded as the precondition for the possibility of appearances, and not as a determination depending on them. It is an apriori representation, which necessarily grounds outer appearances.

<a13> 3. Space is a pure intuition, and not a discursive or (as is said) a universal concept of relations of things in general. For, first, you can represent only one single space, and if you talk of different spaces, you really mean only different parts of one and the same unique space. Secondly, these parts cannot exist before the single, all-embracing space, as, so to speak, building-blocks from which it can be assembled together as a whole. Rather these parts can be thought only as in space.

<a14> Space is essentially unitary. The multiplicity it contains, and hence also the universal concept of spaces in general, depends wholly on limitations of unitary space. From this it follows that, as far as space is concerned, all concepts of it are based on an apriori intuition, which is not empirical. So it also follows that no geometrical axioms (e.g. that in a triangle, the sum of two sides is greater than the third), can ever be deduced from the universal concepts of line and triangle, but only from intuition — and indeed deduced apriori with demonstrative certainty.

<a15> 4. Space is represented as an infinite given quantity. Now it is true that every concept [B40] must be thought as a representation which is contained in an infinite number of different possible representations as their common characteristic. So the concept contains these representations in the sense that they come under it. But no concept, as such, can be thought as containing an infinite number of representations in itself. However, this is just how space is thought, since all parts of space, right down to infinity, exist simultaneously. Thus the originative representation of space is an apriori intuition, and not a concept.

<a16> §3

The Transcendental Exposition of the Concept of Space

By a transcendental exposition, I mean explaining a concept as a principle which enables us to understand the possibility of further synthetic apriori knowledge. In order to fulfil this purpose, it is required:

1. that such knowledge does actually flow from the given concept; and
2. that the possibility of this knowledge presupposes a given way of explaining the concept.

<a17> Geometry is a science which determines the properties of space synthetically, and yet also apriori. So what must the representation of space be, for such knowledge of it to be possible? It must be an originative intuition, and not just a concept. For [B41] no propositions which go beyond a concept can be deduced from it alone — and as I showed in the Introduction (section 5), the propositions of geometry do go beyond geometrical concepts. But this intuition must be found in us apriori, that is, before any perception of an object. Hence it must be a pure, and not an empirical intuition. For all geometrical propositions are demonstratively certain — that is, we cannot be conscious of them without at the same time being conscious of their necessity. For example, propositions like ‘Space has only three dimensions’ cannot be empirical or experiential judgments, nor can they be deduced from such judgments, as I showed in the Introduction (section 2).

<a18> But how can the mind contain an outer intuition, which exists before its objects themselves, and in which the concept of its objects can be determined apriori? Obviously, the only way this is possible is because the intuition is located in the subject of perception, as the capacity of the subject to be affected by objects, but only so far as their form is concerned. It is the means by which the mind obtains a direct representation of its objects, i.e. intuition. Consequently, the intuition of space is merely the form of outer sense in general.

<a19> So my explanation is the only one which makes it comprehensible how it is possible for geometry to consist of synthetic apriori knowledge. Any other kind of explanation which fails to achieve this is clearly distinguishable from mine by virtue of this very failure, even if it seems to bear some similarity to mine in other respects.

<a20> [B42] Conclusions from the above concepts

(a) Space does not represent any property of things in themselves, nor does it represent them in terms of their mutual relationships. In other words, it does not represent any determination of things which inheres in objects themselves, and which remains even when you leave out of account any subjective preconditions for intuition. For no determinations of things, whether absolute or relative, can be intuited before the existence of the things in which they inhere, and hence they cannot be intuited apriori.

<a21> (b) Space is nothing other than the form of all appearances of outer sense. In other words, it is the precondition for sensibility on the side of the subject, and it alone is what makes outer intuition possible for us. The receptivity of the subject, that is, its capacity to be affected by objects, necessarily precedes any intuitions of these objects. Consequently, it is easy to understand how the form of all appearances can be given in the mind before any actual perceptions, and hence apriori. It is also easy to understand how space, as a pure intuition in which all objects must be determined, can contain principles of the relations between objects before any experience.

<a22> So it is only from our standpoint as human beings that we can talk of space, extended beings, and so on. If we go beyond the preconditions which are in ourselves as subjects, and which are necessary for us to have outer intuition, the representation of space [B43] has nothing at all to refer to. The predicate of spatiality is attributable to things only in so far as they appear to us, that is, only in so far as they are objects of sensibility. Space, as the all-present form of this receptivity, which we call sensibility, is a necessary precondition for all relationships in which objects are intuited as outside us. If we leave these objects out of account, there remains a pure intuition called ‘space’. We cannot turn the preconditions which are peculiar to sensibility into preconditions for the possibility of things, but only into preconditions for the possibility of their appearances.

<a23> Therefore we can indeed say that space encompasses all things that can appear to us as external; but not that it encompasses things in themselves, whether they are intuited or not, or even whatever subject they are intuited by. For we can make no judgment at all about the intuitions of other thinking beings, and we cannot tell whether or not they are bound by the same preconditions which limit our intuition, and which are universally valid for us.

<a24> If we add the limited scope of a judgment to the concept of its subject, the judgment then becomes valid unconditionally. For example, the proposition ‘All things are related to each other in space’ is valid with the proviso that these things are taken as objects of our sensory intuition. If I now add the precondition to the concept, and say: ‘All things as outer appearances are related to each other in space,’ this rule is valid universally and without any limitation of scope.

<a25> So my [B44] exposition teaches the reality (that is, the objective validity) of space with regard to everything that can come before us outwardly as an object, but at the same time the ideality of space with regard to things when they are considered in themselves through reason, that is, without reference to the properties of our sensibility. I therefore assert the empirical reality of space with regard to all possible outer experience, but also its transcendental ideality. This means that space is nothing as soon as we forget that it is the precondition of the possibility of all experience, and take it as something which things in themselves depend on.

<a26> Apart from space, there are no other subjective representations related to something outer, which can be called apriori objective. For none of them give rise to synthetic apriori propositions in the way that intuition in space does (see §3, above). To be more precise, they have no ideality at all, even though they have it in common with the representation of space, that they belong merely to the subjective properties of the kind of senses we have. For example, sight, hearing, and touch give us sensations of colours, sounds, and warmth; but since these are merely sensations, and not intuitions, they do not by themselves provide us with knowledge of any object — least of all, apriori knowledge.

<a27> [B45] The purpose of this comment is simply to prevent anyone from making the mistake of using completely inappropriate examples to illustrate the ideality of space which I assert here. For instance, colours, taste, etc. are rightly considered not to be properties of things, but merely alterations in us as subjects; and they can even be different in different people. In this case, something which is itself ultimately only an appearance, e.g. a rose, is taken by the empirical understanding for a thing in itself, despite the fact that, in respect of its colour, it can appear differently to every observer. By contrast, the transcendental concept of an appearance in space is a critical reminder that absolutely nothing intuited in space is a thing in itself, and that space is not a form of things which belongs to them as they are in themselves. Rather, objects as they are in themselves are completely unknown to us, and what we call outer objects are nothing other than mere representations of our sensibility. Their form is space, but space does not and cannot give us any knowledge of their true correlate, namely the thing in itself. But in experience no question is ever asked about the thing in itself.

<a28> [B46] The Transcendental Aesthetic

Second Section

On Time

§4

The Metaphysical Exposition of the Concept of Time

1. Time is not an empirical concept which has been abstracted from any experience. For even the simultaneous or successive existence of things would not be perceived, if the representation of time did not underlie it apriori. Only on the presupposition of time can you represent things as existing at one and the same time (simultaneously) or at different times (successively).

<a29> 2. Time is a necessary representation, which is the foundation of all intuitions. It is universally true of appearances that you cannot remove time itself; but you certainly can take appearances away from time. So time is given apriori. In time alone is any actuality of appearances possible. Appearances could all be entirely annihilated; but time itself (as the universal precondition of their possibility) cannot be removed.

<a30> [B47] 3. This apriori necessity is also why it is possible for there to be self-evident axioms about the properties of time, or axioms about time in general — that it has only one dimension; and that different times are not simultaneous, but successive (just as different spaces are not successive, but co-existent). These axioms could not be abstracted from experience, since experience would provide neither strict universality nor self-evident certainty. We could only say, ‘This is what we all learn from perception,’ but not ‘This is how things must be.’ These axioms serve as rules, under which alone experiences are possible; and they teach us before experiences, and not through perception.

<a31> 4. Time is not a discursive concept (or ‘universal’ concept, as it is called), but a pure form of sensory intuition. Different times are only parts of one and the same time. But a representation which can be given only through a single object is an intuition. Furthermore, the proposition that different times cannot exist simultaneously could not be deduced from a single universal concept. The proposition is synthetic, and cannot be deduced from concepts alone. Therefore it is contained immediately in the intuition and representation of time.

<a32> 5. The endlessness of time means merely that all determinate tracts of time are possible only through [B48] delimitations of a single time, from which they originate. Consequently, the originative representation Time must be given as undelimited. But the representation of a whole cannot be given through concepts, if its parts themselves (and every quantity of an object) can be represented determinately only through delimitation, since concepts contain only partial representations. Rather, the foundation of the parts must be immediate intuition.

<a33> §5

The Transcendental Exposition of the Concept of Time

For a transcendental exposition, I can refer to §4, paragraph 3, where, in order to save time, I included what is essentially transcendental in the section on the metaphysical exposition.

<a34> Here I shall add that the concept of change, and with it the concept of motion (as change of position) is possible only through and in the representation of time. If this representation were not an apriori intuition (of inner sense), no concept whatever could make intelligible the possibility of a change in one and the same object, since it consists in a combination of contradictorily opposed predicates (for example, one and the same thing being in a place, and not being in the same place). Two [B49] contradictorily opposed determinations can be met with in a single thing only in time, namely one after the other. So our concept of time explains the possibility of all the synthetic apriori knowledge included in the general doctrine of motion — which is by no means unfruitful.

<a35> §6

Conclusions from these concepts

(a) Time is not something which exists in itself, or belongs to things as an objective determination. Consequently, it would not remain if you left out of account all the subjective preconditions of the intuition of things. For in the first case, it would be something actual, but without having an actual object. As for the second case, it could not precede objects as their condition, or be known and intuited apriori through synthetic propositions, because it would be a determination or ordering which belonged to things themselves. But it can indeed be known apriori, if time is nothing other than the subjective condition for any intuition to come into existence within us. For thus this form of inner intuition can be represented before objects are represented, and hence apriori.

<a36> (b) Time is nothing other than the form of inner sense, that is, of the intuition of our self, and of our inner state. For time cannot be any determination of outer appearances. It does not belong [B50] to a shape, or a position, etc., but instead it determines the relationship between representations in our inner state. And precisely because this inner intuition provides nothing which has a shape, we try to make up for this lack through analogies. We represent the sequence of time as a line continuing without end, in which the multiplicity consists of a series which has only one dimension. We use the properties of this line to draw conclusions about all the properties of time, except for the one property, that the parts of the line exist simultaneously, whereas the parts of time always exist successively. From this too it is obvious that the representation of time is itself an intuition, because all its properties can be expressed in an outer intuition.

<a37> (c) Time is the universal apriori formal precondition of all appearances. Space, as the pure form of all outer intuition, is limited to being the apriori precondition merely of outer appearances. However, all representations, whether or not they have external things as their objects, belong in themselves to our inner state, as determinations of the mind. But this inner state is subject to the formal conditions of inner intuition, and therefore to time. Consequently, time is a universal apriori precondition of all appearance. More precisely, it is the immediate precondition of inner appearances (of our souls), and through inner appearances it is also the mediate precondition of outer appearances. [B51] If I can say apriori that all outer appearances are in space, and determined apriori in accordance with the properties of space, then the foundation of inner sense allows me to say quite universally that absolutely all appearances (i.e. all objects of the senses) are in time, and necessarily conform to the properties of time.

<a38> Time is nothing, if we take objects as they might be in themselves — that is, if we leave out of account our way of inwardly intuiting ourselves, and also of including outer intuitions within our faculty of representation by means of this inner intuition. Time has objective validity only in relation to appearances, because these are already things which we take as objects of our senses. However, it is no longer objective if we leave out of account the sensory nature of our intuition (and hence the way of representing things which is peculiar to us humans), and start talking about things as universals. So time is only a subjective condition of our (human) intuition, which is always sensory — that is, we have intuitions only in so far as we are affected by objects. In itself, outside the subject, time is nothing. Nevertheless, it is necessarily objective in relation to all appearances, and hence also to all things which can enter into our experience. We cannot say, ‘All things are in time,’ because [B52] every kind of intuition of things is left out of account in the concept of a thing in general. But intuition is the essential precondition for time to belong to the representation of objects. Now if this precondition is added to the concept, we will then be saying, ‘All things, as appearances (objects of sensory intuition) are in time.’ And this formulation of the axiom will be sound, and objectively true and universal apriori.

<a39> So what I have said implies the empirical reality of time — in other words, its objective validity in relation to all objects which might ever be given to our senses. And since our intuition is always sensory, no object can ever be given to us in experience which does not come under the precondition of time. On the other hand, I dispute any claim of time to absolute reality — that is, as belonging to things intrinsically, as a precondition or essential property, without any reference to the form of our sensory intuition. The essential properties of things in themselves can never be given to us through our senses. This is what the transcendental ideality of time consists in. It means that, if you leave out of account the subjective conditions of sensory intuition, time is nothing at all, and it cannot be counted as either underlying or inhering in objects as they are in themselves (without their relationship to our intuition).

<a40> But the ideality of time, [B53] like that of space, is utterly different from the illusory nature of sensation. In the case of sensation, it is assumed that the appearance itself, in which the predicates of space and time inhere, has objective reality. But in the case of space and time, there is no question of objective reality, except in so far as it is merely empirical — that is to say, except in so far as the object itself is regarded as merely an appearance. On this point, see the first Section, above.

<a41> §7

Explanation

My theory allows time empirical reality, but refuses it absolute and transcendental reality. However, intelligent people have raised an objection to this theory so unanimously, that I conclude it must naturally occur to any reader who is unused to these studies. This objection is as follows. There actually are alterations — this is proved by the change in our own representations, even if you deny the genuineness of all outer appearances, together with their alterations. But alterations are possible only in time; therefore time is something actual.

<a42> There is no difficulty in providing an answer. I accept the whole argument. Time is certainly something actual, namely the actual form of inner intuition. Thus it has subjective reality with respect to inner experience — that is, I actually have the representation [B54] of time and of my determinations in it. So time is to be considered actual — not as an object, but as the way in which I represent myself as an object. But if I could intuit myself, or some other being could intuit me, without this precondition of sensibility, these very same determinations, which we now represent as alterations, would provide a kind of knowledge which contained no representation of time at all, and hence none of alteration either. But time still has empirical reality, as the precondition of all our experiences. It is only absolute reality it cannot be allowed to have, for the reasons given above. Time is nothing other than the form of our inner intuition.*

If we take away from time the special precondition of our sensibility, the concept of time disappears with it, since it does not inhere in objects themselves, but merely in the subject which intuits them.

<a43> I shall now give the reason why this objection has been made so unanimously, even though those who make it have nothing [B55] enlightening to say against the thesis of the ideality of space. They could not hope to establish the absolute reality of space with demonstrative certainty, because they are confronted by idealism, according to which the actuality of outer objects is incapable of strict proof. By contrast, the actuality of the object of our inner sense (my self and my state) is directly obvious through consciousness. Outer objects could be nothing but an illusion; whereas the object of inner sense is undeniably something actual (in their opinion, that is).

<a44> However, they overlooked the fact that both are in the same position. In neither case can their actuality as representations be disputed, but they both belong only to appearance. An appearance always has two sides. On the one side, the object is considered as it is in itself — but since no attention is paid to the way in which it is intuited, the nature of the object always remains problematic. On the other side, the form of the intuition of the object is taken into account. However, the form is to be found, not in the object as it is in itself, but in the subject to which the object appears. Nevertheless, the form of the intuition actually and necessarily belongs to the appearance of the object.

<a45> So time and space are two sources of knowledge, which give rise to synthetic apriori knowledge of various sorts. The most striking example is mathematics, as far as concerns knowledge of space and its properties. [B56] Taken together, both time and space constitute the forms of all sensory intuition, and as such they make synthetic apriori propositions possible. But these sources of apriori knowledge determine their own limits, by virtue of the fact that they are no more than preconditions of sensibility. These limits are that they apply to objects only in so far as objects are considered as appearances — they do not represent things in themselves. The scope of their validity is confined to appearances, and if we go beyond appearances, there is no further objective use for these sources of knowledge.

<a46> Further, this way in which space and time are real leaves the certainty of experiential knowledge untouched, since we are just as convinced of it, whether these forms necessarily belong to things in themselves, or only to our intuition of these things. By contrast, those who assert the absolute reality of space and time (whether they take them as self-subsistent entities, or merely as inhering in things in themselves) must themselves come into conflict with the principles of experience.

<a47> Those who opt for the first alternative (which is the line usually taken by mathematical physicists), are committed to two eternal and infinite self-subsistent non-things (space and time), which are there (yet without there being anything actual) only in order to include everything actual within themselves.

<a48> Those who take the other line (as do some metaphysical physicists), hold that space and time are [B57] relations between appearances (simultaneous and successive respectively), which are abstracted from experience, and represented only confusedly in the process of abstraction. Therefore they must deny apriori mathematics any validity, and at least any demonstrative certainty, when it is applied to actual things (things in space, for example), since demonstrative certainty can never be established aposteriori. On this view, the apriori concepts of space and time are merely products of the imagination, and their source must actually be looked for in experience. The imagination has used the relations abstracted from experience to construct something which does indeed contain what is common to them, but which cannot be established without the restrictions which nature has attached to them.

<a49> The first group have the upper hand in as much as they do not prevent mathematical assertions from being applicable to the world of appearances. On the other hand, when they want to take their understanding beyond the world of appearances, they are completely nonplussed by the above restrictions.

<a50> The second group have the upper hand as far as the latter point is concerned, because the representations of space and time do not prevent them from judging objects, not as appearances, but merely in relation to the understanding. On the other hand, they cannot provide any foundation for the possibility of apriori mathematical knowledge (since they lack a true and objectively valid apriori intuition), nor can they find any necessary connection which brings experiential propositions into harmony with the claims of mathematics.

<a51> My theory [B58] avoids the difficulties faced by both the above groups, by giving a true account of the nature of the two originative forms of sensibility.

<a52> Finally, it needs to be shown that the Transcendental Aesthetic cannot contain any more than these two components, namely space and time. This is obvious, because all other concepts which belong to sensibility presuppose something empirical. This is true even of the concept of motion, which is a combination both of the apriori and of the empirical. The concept of motion presupposes the perception of something movable. But the concept of space, considered in itself, does not contain the concept of anything movable. Consequently, the movable must be something which is found in space only through experience, and hence given empirically.

<a53> For the same reason, the Transcendental Aesthetic cannot include the concept of alteration among its apriori data, since time itself does not alter, but only something which is in time. The concept of alteration requires the perception of some being or other, and of the succession of its determinations — and this can be supplied only by experience.

<a54> [B59] §8

General Notes on the Transcendental Aesthetic

Note 1

In order to avoid any misunderstanding, it is first necessary for me to explain, as clearly as possible, my opinion as to the fundamental nature of sensory knowledge in general.

What I have meant to say is that all our intuition is nothing other than the representation of appearance. The things we intuit are not, in themselves, the kind of things we intuit them as being; nor do their properties, in themselves, have the same nature as appears to us. If we took away ourselves as subjects, or even only the subjective nature of the senses in general, then the whole nature and all the properties of objects in space and time, and even space and time themselves, would disappear. Since they are appearances, they cannot exist as things in themselves, but only in us. It remains entirely unknown to us what objects are like in themselves and independently of all this receptivity of our sensibility. All we know is our way of perceiving them, which is peculiar to us; and although it is shared by all humans, it is not necessarily shared by other beings. But here we are concerned only with humans.

<a55> Space and time are the [B60] pure forms of human perception, and sensation in general is its matter. Only the forms can be known apriori, that is, before all actual perception; and that is why this knowledge is called pure intuition. The matter is the component of our knowledge by virtue of which it is called aposteriori knowledge, that is, empirical intuition. The forms inhere in our sensibility with absolute necessity, whatever kind of sensations we have, whereas our sensations can be very different from one another.

<a56> Even if we could raise the distinctness of our intuitions to the highest degree, this would not bring us any closer to the nature of objects in themselves. Whatever happened, we would have a complete knowledge only of our manner of intuition, that is, of our sensibility; and this would still come under the preconditions of space and time, which have their ultimate source in the subject. We could still never know what objects might be in themselves, since even the clearest knowledge is only of their appearance, which is all that is given to us.

<a57> According to the Leibniz-Wolff philosophy, the whole of our sensibility is nothing but the confused representation of things, which includes solely what belongs to things as they are in themselves, but only through an accumulation of characteristics and partial representations which we cannot consciously distinguish. However, this adulterates the concept of sensibility and appearance, and makes the whole of epistemology null and void. The distinction between confused [B61] and distinct representations is purely logical, and has nothing to do with content.

<a58> It is no doubt the case that the concept of right possessed by anyone with a sound understanding contains all that the subtlest speculation can draw out of it, except that in its ordinary and practical use, we are not conscious of the multiplicity of representations contained in this thought. But this does not allow us to say that the ordinary concept is sensory, and contains merely an appearance. The right cannot ‘appear’ at all. Rather, its concept is to be found in the understanding, and it represents a property (the moral property) of actions, and it belongs to them as they are in themselves. By contrast, the representation of a body in intuition contains nothing at all which could belong to an object in itself, but merely the appearance of something, and the way in which we are affected by it. This receptivity of our faculty of knowledge is called ‘sensibility’, and it remains worlds apart from knowledge of the object in itself, even if we could see right through to the innermost depths of the appearance.

<a59> The Leibniz-Wolff philosophy has therefore sent all investigations into the nature and origin of our knowledge in entirely the wrong direction, by treating the difference between sensibility and intellectual knowledge as merely a logical one. But the difference is obviously transcendental, and it depends, not simply on the formal question of whether they are distinct [B62] or confused, but on the difference between the origin and content of each. It is not that sensibility gives us confused knowledge of the nature of things in themselves, but that it gives us no knowledge of them at all. Once we take away the subjective nature of our sensibility, nothing at all is, or can be, left of the object represented, or of the properties our sensory intuition attributes to it, since it is precisely this subjective nature of our sensibility that determines the form of the object as an appearance.

<a60> In appearances, we normally make a perfectly good distinction between what inheres in the intuition of them essentially, and hence is universally valid for the senses of every human being, and what belongs to them only contingently. The contingent element is not valid of the universal properties of sensibility, but only of a particular disposition or structure of this or that sense. So it is normally said that the first kind of knowledge represents the object in itself, and the second only its appearance. However, this distinction is only empirical. People usually stick with it, and fail to see (as they should) that the empirical intuition is in its turn merely an appearance, so that it contains nothing at all that belongs to any thing in itself. When this happens, my transcendental distinction is lost, and we end up believing that we know things in themselves, even though we never (in the world of the senses) have any dealings with anything other than appearances, however deeply we research into [B63] their objects.

<a61> For example, we would certainly call a rainbow in a sunny shower a mere appearance, and the rain a thing in itself. This is acceptable, as long as we understand the concept of a thing in itself merely in the physical sense, as that which is determined in intuition just this one way, in all our experience, and irrespective of its situation relative to our senses. But if we take this empirical object as a universal, that is, ignoring its conformity with all human senses, we can ask whether it represents a thing in itself. (And here I am not talking about the raindrops, since they are surely empirical objects, by virtue of being appearances.) This question is the transcendental one about the relation between a representation and its object. Not only are the raindrops mere appearances, but also their round shape, and even the space within which they fall, are nothing in themselves, but mere modifications or prerequisites of our sensory intuition. But the transcendental object remains unknown to us.

<a62> The second major concern of my Transcendental Aesthetic is that it should not gain a certain amount of favour merely as a plausible hypothesis. Rather, it should be as certain and indubitable as could ever be required of a theory which is to serve as an instrument of the understanding. In order to make the reader completely convinced of its certainty, I shall take a case in which its validity can become obvious, [B64] and which can serve to clarify what I said in §3.

<a63> Let us just suppose that space and time were objective in themselves, and preconditions for the possibility of things in themselves. For a start, it appears that both give rise to a large number of demonstrably certain synthetic apriori propositions. Since this is especially true of space, I shall use space as my main example in this investigation.

<a64> Given that the propositions of geometry are synthetic apriori and known with demonstrative certainty, I ask the following question: Where do you get such propositions from, and what does our understanding depend on, in order to attain such utterly necessary and universally valid truths? The only way is through concepts or through intuitions, and both are given either apriori or aposteriori. Empirical concepts, along with the empirical intuition on which they are based, cannot yield any synthetic proposition other than one which is also merely empirical, that is, an experiential proposition. Consequently it cannot contain any necessity or absolute universality — yet these are precisely the characteristics of all geometrical propositions.

<a65> So the only remaining means is the first, namely to attain such knowledge through pure concepts or through apriori intuitions. However, it is clear that no synthetic knowledge can be obtained from pure concepts, but only analytic knowledge. [B65] Just take the proposition ‘With two straight lines it is impossible to enclose a space and hence to construct a figure,’ and try to derive it from the concepts of straight lines and of the number two. Again, take the proposition ‘It is possible to construct a figure out of three straight lines,’ and try to derive it simply from these concepts. All your efforts are in vain, and you find yourself forced to have recourse to intuition, as geometricians always do.

<a66> So an object has been given to you in intuition. But what sort of intuition is this? Is it a pure apriori intuition, or an empirical one? If it were an empirical one, it could never give rise to a universally valid proposition, let alone one known with demonstrative certainty; for experience can never provide anything of this sort.

<a67> You must therefore give yourself an object apriori in intuition, and base your synthetic proposition on it. Suppose the following were the case:

• you do not have within you a faculty for apriori intuition;
• these subjective preconditions, with respect to their form, are not at the same time the universal apriori preconditions for the possibility of the object itself of this outer intuition;
• the object (the triangle) is something in itself, without any relation to you as subject.

On these suppositions, how could you say that what is included among the subjective preconditions necessary for you to construct a triangle, must also necessarily belong to the triangle in itself? For you could not add to your concepts (of three lines) something new (the figure) which must necessarily be found for that purpose in the object, since [B66] the object is given before your experience, and not through it.

<a68> So space (and time as well) is a mere form of intuition, which contains the apriori preconditions for things to be outer objects for you, and these objects are in themselves nothing without these subjective preconditions. If this were not the case, you would not be able to decide anything at all about outer objects that was both synthetic and apriori. Therefore it is indubitably certain, and not merely possible or probable, that space and time are merely the subjective preconditions of all our intuition, since they are the necessary preconditions of all outer and inner experience. Consequently, in relation to these preconditions, all objects are mere appearances, and since they are given in this way, they are not things existing by themselves. This is why we can say many things about them apriori, at least as far as their form is concerned; whereas we can never say anything at all about the thing in itself that might underlie these appearances.

<a69> Note 2

The following note will serve admirably to confirm my theory of the ideality of both the outer and the inner senses, and hence the ideality of the objects of the senses, as mere appearances. Let us consider everything in our knowledge which belongs to intuition — so this immediately excludes the feelings of desire or aversion, and the will, since they are not kinds of knowledge. Now everything which belongs to intuition contains nothing but mere relations: relations of places in one intuition (extension), [B67] change of places (motion), and laws in accordance with which this change is determined (motive forces). But these relations do not tell us what is present in the place, or what brings about change of place in things themselves. A thing is not known as it is in itself merely through relations. So it is easy to judge that, since only representations of relations are given to us through outer sense, this sense can contain in its representation only the relation of an object to the subject, and not the inner properties of the object in itself.

<a70> Exactly the same is true of inner intuition. This is partly because it is in inner intuition that the representations of the outer senses constitute the essential material with which we occupy our minds. But it is also because inner intuition contains the time in which we place these representations, and which itself precedes consciousness of them in experience. Time underlies these representations as the formal precondition of the way in which we place them in our minds, and it already includes the relations of succession and simultaneity, and of that which is simultaneous with succession, namely the persistent.

<a71> Now that which, as representation, can precede any act of thinking something, is intuition; and if it contains nothing other than relations, it is the form of intuition. Since this form does not represent anything unless something is placed in the mind, it cannot be anything other than the way in which the mind is affected through its own activity (namely this [B68] placing of its representation), and hence it is the way in which the mind is affected by itself. In other words, it is an inner sense as far as its form is concerned.

<a72> Everything that is represented through a sense is to that extent always an appearance. In the case of inner sense, we must either deny the existence of such a sense altogether, or accept that the self as subject (which is the object of inner sense) can be represented through it only as an appearance. This is quite different from how the subject would judge itself to be, if its intuition were pure self-activity, that is to say, intellectual.

<a73> The only remaining difficulty is that of how a subject can intuit itself inwardly — but this difficulty is common to all theories. Consciousness of oneself (apperception) is a simple representation of the ‘I’; and if through this alone all the multiplicity within the subject were given through the activity of the self, then the inner intuition would be intellectual. But in humans, this consciousness requires inner perception of the multiplicity already given in the subject, and the means by which this is given in the mind without spontaneity must be called sensibility, in order to keep it distinct from intellectual intuition.

<a74> If the faculty of self-consciousness is to apprehend what lies in the soul, it must affect the soul. This is the only way it can stimulate an intuition of itself. But the form of the intuition, which already underlies it in the mind, determines the way in which the multiplicity is connected together in the mind, and it does this through the representation [B69] of time. So the mind intuits itself, not as it would represent itself if it were directly self-active, but as it is inwardly affected. Consequently, it intuits itself as it appears to itself, and not as it is.

<a75> Note 3

I have said that the intuition of outer objects and the self-intuition of the mind both represent objects and the mind in space and time as they affect our senses — in other words, as they appear. But I do not mean by this that these objects are a mere illusion. For in appearance, objects, and even the properties we attribute to them, are always regarded as something actually given. All I mean is that, if we take into account the relation between the given object and the subject, then these properties depend only on the way the subject intuits them. Consequently, the object as appearance will be distinct from the same object as it is in itself.

<a76> I have also said that the essential nature of space and time, in which I locate bodies and the soul as a precondition for their existence, is to be found in my way of intuiting them, and not in objects as they are in themselves. But again, I do not mean that bodies merely seem to be outside me, or that my soul merely seems to be given in my self-consciousness. It would be my own fault if I turned what I should count as appearance into mere illusion.*

<a78> This [B70] confusion between appearance and mere illusion is not a consequence of my principle of the ideality of all our sensory intuitions. Rather, it is a consequence of attributing objective reality to these forms of representation, which makes it impossible to avoid turning everything into mere illusion. Just suppose that space and time are properties which must be found in things in themselves if they are to be possible. Then consider the absurdities this would involve us in. There would be two infinite things, which are neither substances nor anything actual inhering in substances — yet they would have to be something existent, [B71] and even be the necessary precondition for the existence of all things. Still worse, they would continue to exist, even if all existing things were annihilated. On this showing, we can hardly blame the good Berkeley for demoting bodies to mere illusion. Indeed, the same would have to be true even of our own existence. If it were similarly made dependent on the self-subsistent reality of a non-thing such as time, it would be reduced to sheer illusion along with time. But no-one has yet allowed themselves to be guilty of such an absurdity.

<a79> Note 4

I now turn to natural theology. Here, we think an object which not only cannot be an object of intuition for us, but which also can in no way be an object of sensory intuition for himself. We are therefore careful to remove the preconditions of space and time from all his intuition — and all his knowledge must consist of intuition rather than thought, since thought always involves limitations. But by what right do we remove these preconditions, if we have already made both of them forms of things in themselves? As such, they would remain apriori preconditions for the existence of things, even if the things themselves did not exist. Therefore, as preconditions for all existence in general, they would also have to be preconditions for the existence of God.

<a80> But if we do not want to make space and time objective forms [B72] which apply to all things, the only alternative is to make them the subjective forms of both our outer and our inner ways of intuiting things. This way of intuiting things is called ‘sensory’, because it is not originative — that is, it is not such that through it alone the existence of the object of intuition is given. As far as we are aware, only God has originative intuition. Our way of intuiting things depends on the existence of the object; so it is possible only if the faculty of representation in the subject is affected by the object.

<a81> It is not necessarily the case that humans are the only beings whose sensibility is restricted to intuitions in space and time. It might be that every finite thinking being must necessarily share this feature with humans — though we are not in a position to judge whether this is so or not. But however universal it might be, it would not cease to be sensibility, precisely because it is a derivative, and not an originative intuition, and hence not an intellectual one. For reasons I have already given, intellectual intuition seems to belong only to God, and it should never be attributed to a dependent being, which is dependent both as to its existence and as to its intuition (which determines its existence in relation to the objects given to it). However, this last remark must be taken merely as a clarification of my theory of the Aesthetic, and not as part of its proof.

<a82> [B73] Conclusion of the Transcendental Aesthetic

Here we now have one of the elements required for the solution of the general problem of transcendental philosophy, namely: how are synthetic apriori propositions possible? This element consists in the pure apriori intuitions of space and time. When we wish to make an apriori judgment which goes beyond the concept given, it is space and time that contain what can be discovered apriori, and connected synthetically with the concept. It is not in the concept, but in the intuition which corresponds to the concept. But for this reason, such a judgment cannot extend beyond objects of the senses, and can be valid only for objects of possible experience.

<log1> [B74] The Transcendental Doctrine of Elements

Our knowledge arises from two fundamental sources in the mind. The first of these is the faculty of receiving representations (the receptivity of impressions); the second is the faculty of knowing an object through these representations (the spontaneity of concepts). Through the first, an object is given to us; through the second, the object is thought in relation to the representation of it (which is a mere determination of the mind). Thus intuition and concepts constitute the elements of all our knowledge. Neither concepts without an intuition corresponding to them in some way or other, nor intuition without concepts, can result in any knowledge.

<log2> Both intuitions and concepts are either pure or empirical. They are empirical if they contain sensation — which presupposes the actual presence of the object. They are pure when no sensation is mixed in with the representation. Sensation can be called the matter of sensory knowledge. So pure [B75] intuition contains only the form under which something is intuited, and a pure concept contains only the form of the thought of an object in general. Only pure intuitions or concepts are possible apriori; empirical intuitions or concepts are possible only aposteriori.

<log3> In my terminology, sensibility is the receptivity of our mind to receiving representations, in so far as it is affected in some way or other. By contrast, understanding is the faculty of producing representations by ourselves, or the spontaneity of knowledge. Our nature is such that our intuition can never be other than sensory, that is, it contains only the way in which we are affected by objects. By contrast, our understanding is the faculty for thinking the object of sensory intuition.

<log4> Neither of these faculties is to be preferred over the other. Without sensibility, no object would be given to us; and without understanding no object would be thought. Thoughts without content are empty, and intuitions without concepts are blind. Therefore it is just as necessary for us to make our concepts sensory (that is, to add to them their object in intuition), as it is for us to make our intuitions intellectual (that is, to bring them under concepts). Neither faculty (or power of the mind) can take over the function of the other. The understanding cannot intuit anything, and the senses cannot think anything. They cannot give rise to knowledge unless they are united. [B76] But this should not lead us to blend their roles together — rather, we have every reason to keep them carefully separate and distinct from each other. This is why I distinguish between the science of the rules of sensibility in general (i.e. Aesthetic), from the science of the rules of the understanding in general (i.e. Logic).

<log5> Logic in turn can be undertaken with two different aims: either as the logic of the general use of the understanding, or as the logic of its special use. General logic contains the absolutely necessary rules of thought, without which no use at all can be made of the understanding. It therefore deals with these laws without reference to differences between the objects which the understanding is directed towards. The logic of the special use of the understanding contains the rules for thinking correctly about a particular class of objects. General logic can be called the logic of elements, and special logic can be called the instrument of this or that science. Special logic will usually be taught in universities as an introductory training for the sciences. This is despite the fact that it comes last in the order in which human reason proceeds, and is arrived at only after the science has long been ready, and needs nothing but the final touch for it to become perfectly adjusted and complete. For we already have to know the objects of a science pretty well, before [B77] we can specify the rules for establishing the science of these objects.

<log6> General logic is either pure or applied. In pure logic, we leave out of account any empirical circumstances surrounding the exercise of our understanding — for example, the influences of the senses, the play of the imagination, the laws of memory, the force of habit, our inclinations, etc. Thus we leave out of account the sources of prejudice, and indeed all the causes which might, rightly or wrongly, be supposed to give rise to particular items of knowledge. These are relevant merely to the particular circumstances in which the understanding is exercised, and experience is required for us to know them. So a pure general logic deals with absolutely apriori principles. It is a rule-book of the understanding and of reason, but only in respect of what is formal in their use, whatever the content — i.e. whether it is empirical or transcendental.

<log7> A general logic is called applied when it is directed towards the rules for the use of the understanding under the subjective empirical circumstances which are the province of psychology. So applied logic includes empirical principles, even though they are still universal in so far as it is concerned with the use of the understanding without regard to differences between objects. Therefore it is neither a rule-book for the understanding in general, nor an instrument of particular sciences, [B78] but only a means for eliminating fallacies from the understanding of ordinary people.

<log8> In general logic, the part which is to constitute the pure doctrine of reason must be kept entirely separate from the part which constitutes applied logic (even though this is still general). Only the first part is essentially a science, even though it is a brief and boring one, as is required for the academically appropriate exposition of a doctrine of the elements of the understanding.

<log9> In expounding pure general logic, the logician must always bear in mind two rules:

1. As a general logic, it leaves out of account any content of the knowledge had by the understanding, or any differences among its objects. It deals with nothing other than the pure form of thought.
2. As a pure logic, it has no empirical principles. So it does not (as some people have persuaded themselves) derive anything from psychology, which is therefore entirely irrelevant to the rule-book of the understanding. Pure logic is a discipline in which everything is demonstrated, and everything in it must be certain completely apriori.

<log10> The expression ‘applied logic’ usually means a discipline which contains particular exercises in applying rules supplied by pure logic. But what I mean by it is a representation of the understanding, and of the rules of its necessary use in practice — in other words, its use under the contingent circumstances of the subject [B79] which can hinder or help this use, and which are all given only empirically. It deals with attentiveness (and its hindrances and consequences), the causes of error, the state of doubt, scruples, conviction, etc.

<log11> The relation between pure general logic and applied logic is the same as the relation between pure and applied ethics. Pure ethics contains only the necessary moral laws of a free will in general. By contrast, moral instruction as such considers these laws in the context of obstacles such as feelings, inclinations, and passions, which human beings are subject to in varying degrees. Moral instruction can never yield a true and demonstrative science of ethics, because it depends on empirical and psychological principles, just like applied logic.

<log12> II

As I have shown, general logic leaves out of account any content of knowledge — that is, any relation between knowledge and its object. It considers only the logical form of the relations between one item of knowledge and another — that is, the form of thought in general. But, given that there are pure as well as empirical intuitions (as I have proved in the Transcendental Aesthetic), there may well be a similar distinction between pure and empirical [B80] thoughts of objects. Including pure thoughts would generate a logic in which not all the content of knowledge was left out of account. Such a logic, which contained merely the rules for the pure thought of an object, would still exclude knowledge which had any empirical content. However, it would extend to the source of our knowledge of objects, in so far as that source cannot be ascribed to objects themselves.

<log13> By contrast, general logic has nothing to do with this source of knowledge. General logic deals with all representations, whether they are originally given apriori in ourselves or are given only empirically. It considers representations merely with reference to the laws which govern how the understanding relates them to one another when it thinks. So it deals only with the form of understanding which can be imposed on representations whatever their source.

<log14> Here I make an observation which covers everything that follows, and which must be carefully borne in mind. The term ‘transcendental’ refers to the possibility of apriori knowledge or of its apriori use. So it must not be applied to just any apriori knowledge, but only to knowledge through which we know that and how certain representations (whether intuitions or concepts) are used or are possible entirely apriori. Hence neither space, [B81] nor any apriori geometrical determination of it, can be called a transcendental representation. The term ‘transcendental’ applies only to the knowledge that geometrical representations are not of empirical origin at all, and to the possibility that they can nevertheless relate apriori to objects of experience. Similarly, the application of space to objects in general would also be transcendental; but if it is restricted solely to objects of the senses, then it is called empirical. So the distinction between the transcendental and the empirical belongs only to the critique of knowledge, and it is irrelevant to the relation between knowledge and its object.

<log15> It is reasonable to expect that perhaps there could be concepts which relate to objects apriori, not as pure or sensory intuitions, but simply as actions of pure thought — and hence as concepts which are of neither empirical nor aesthetic origin. So in anticipation of this possibility, I form for myself the idea of a science of pure understanding and rational knowledge, by means of which we think objects completely apriori. Such a science determines the origin, the scope, and the objective validity of such knowledge. It must therefore be called Transcendental Logic, since it deals only with the laws of the understanding and of reason. However, it is concerned with reason only in so far as it relates to objects apriori, [B82] unlike general logic, which ignores any distinction between empirical and pure rational knowledge.

<log16> III

There is an old and famous question, which was asked of logicians in order to drive them into a corner, and put them into a position where they must either fall into a wretched circular argument, or admit their ignorance, and hence the futility of their whole discipline. The question was: ‘What is truth?’ Here the definition of the word ‘truth’ is taken for granted — namely that it is the correspondence of knowledge with its object. The question at issue is that of the universal and reliable criterion for the truth of any item of knowledge.

<log17> It is already a major and necessary indication of intelligence and insight, if someone knows what questions can rationally be asked. Some questions are intrinsically absurd, and do not need to be answered. If such questions are asked, they bring shame on the person who asks them, and sometimes also have the damaging effect of misleading the unwary listener into giving absurd answers. We then have the laughable picture [B83] (as the ancients used to say) of one person milking a he-goat, and the other holding a sieve underneath.

<log18> If truth consists in the correspondence of knowledge with its object, then this object must thereby be distinguished from other objects. For knowledge is false if it does not correspond to the objects it relates to, even if it contains something which could well be true of other objects. Now a universal criterion of truth would be one which was valid of all knowledge without distinction of object. But such a criterion leaves out of account all content of knowledge (which is its relation to its object). So, since truth involves precisely this content, it is clearly quite impossible and absurd to ask for a criterion for the truth of this content of knowledge. Therefore a sufficient and at the same time universal criterion of truth cannot possibly be produced. Since above I have already called the content of knowledge its matter, this must be rephrased as: There can be no requirement for a universal criterion of the truth of the matter of knowledge, since it is self-contradictory.

<log19> It is quite different if we consider knowledge merely in respect of its form — that is to say, setting aside anything to do with its content. In this case, it is just as clear that a logic must specify a criterion of truth through the universal and [B84] necessary rules of the understanding which it provides. For anything that contradicts these rules is false, since in such a case the understanding contradicts its own general rules of thought, and hence contradicts itself. But these criteria apply only to the form of truth (that is, of thought in general), and to this extent they are perfectly correct, but not sufficient. Knowledge might be completely consistent with the requirements of logical form (i.e. that it must not contradict itself), yet still fail to correspond to its object. The purely logical criterion of truth is the correspondence of knowledge with the universal and formal laws of the understanding and of reason. This is certainly the necessary condition for all truth; but it is a negative one, and logic can take us no further. Logic can provide no touchstone for revealing any error which concerns content rather than form.

<log20> General logic analyses the whole formal business of the understanding and of reason into its elements, and presents them as the principles of any logical critique of our knowledge. So this part of logic can be called the analytic part. It is at least the negative touchstone of truth, in that all knowledge must first be tried and tested against these rules with respect to its form, before the knowledge itself can be investigated with respect to its content, in order to find out [B85] whether it contains any positive truth in relation to its object.

<log21> But however consistent the mere form of knowledge may be with the laws of logic, it falls far short of settling the truth of knowledge as far as its matter is concerned — that is, its objective truth. So no-one can be so rash as to make judgements or assertions about objects on the basis of logic alone. It is first necessary to draw on information about the objects which has been established from outside logic. Only then can we use the laws of logic to investigate the use of this information, and its interconnection within a coherent whole — or to put it a better way, only then can we use these laws to test it.

<log22> We seem to possess an art, by which we can provide all our knowledge with the form of the understanding, however empty and impoverished that knowledge may be with regard to its content. But this deceptive art has misled people into using general logic, which is merely a rule-book for judging, as if it were an instrument for actually producing at least the illusion of objective assertions. Consequently, it has in fact been misused. When general logic is treated as if it were an instrument, it is called dialectic.

<log23> The ancients employed the term ‘dialectic’ for a science or art in many different senses. Yet we can infer from their actual use of the term that for them [B86] it was never anything other than the logic of illusion. It was the sophistical art of giving the appearance of truth to ignorance, or even to deliberate deception. It did this by imitating the method of thoroughness which logic prescribes universally, and by using its classification system to adorn every empty pretension. So it can be taken as a reliable and useful warning that, whenever general logic is considered to be an instrument of the understanding, it is always a logic of illusion — in other words, it is dialectical. For logic tells us nothing about the content of knowledge, but only about the merely formal preconditions for its correspondence with the understanding; and these preconditions are in any case completely indifferent as to the objects of knowledge. It is unreasonable to expect, or even to pretend that logic can serve as an instrument for broadening and extending knowledge. Any such pretension will end up in mere verbal disputes, in which anyone asserts or denies what they like with equal plausibility.

<log24> If philosophy is taught in this way, it is quite unworthy of the dignity of the discipline. This is why I have preferred to include dialectic within logic, as the critique of the dialectical illusion; and it is how the term is to be understood in the present work.

<log25> [B87] IV

Just as I isolated sensibility in the Transcendental Aesthetic, so in the Transcendental Logic I isolate the understanding. From our knowledge, I abstract just that component of our thinking which has its origin solely in the understanding. However, the use of this pure knowledge depends on the precondition that objects must be given to us in intuition for this knowledge to apply to. Without intuition, all our knowledge lacks objects, and remains completely empty. So the Transcendental Analytic is the part of the Transcendental Logic which deals with the elements of the pure knowledge of understanding, and the principles without which no object can be thought at all. It is at the same time a logic of truth, since no knowledge can contradict it without at once losing all its content — that is, all relation to some object or other, and hence all truth.

<log26> However, there is a great temptation to use this pure knowledge of understanding and its axioms independently of experience, and even beyond its limits. This is despite the fact that only experience can provide us with the material (objects) [B88] for these pure concepts of the understanding to apply to. Therefore the understanding is in danger of making a material use of the merely formal principles of pure understanding, through empty sophistries. It is also in danger of making indiscriminate judgments about objects which are not given to us, and perhaps which could in no way ever be given to us.

<log27> Essentially, transcendental logic can only be a rule-book for judging the empirical use of the understanding. So it is misused if we take it as the instrument for a universal and unlimited use of the understanding, and if we are so bold as to use the pure understanding by itself to judge, assert, and decide synthetically about objects in general. As soon as we do this, the use of the pure understanding becomes dialectical.

<log28> So the second part of the Transcendental Logic must be a critique of this dialectical illusion, and it is called the Transcendental Dialectic. It is not the art of producing such illusions dogmatically — an art which is unfortunately all too prevalent among the many and varied forms of metaphysical conjuring. Rather, it is a critique of the understanding and of reason in so far as they are applied beyond the natural world. Its purpose is to expose the false illusion of groundless pretensions, and unfounded claims to have made new discoveries, and to have extended our knowledge through transcendental axioms alone. Instead, the Transcendental Dialectic will be confined to judging the pure understanding, and protecting it against sophistical illusion.

<m1> [B89] Transcendental Logic

This Analytic consists in the resolution of all our apriori knowledge into the elements of the pure knowledge of the understanding. Essentially it comes down to the following points:

1. the concepts must be pure, and not empirical concepts;
2. they must not belong to intuition or sensibility, but to thought and understanding;
3. they must be elementary concepts, and be kept entirely distinct from concepts derived or compounded from them;
4. the table of these concepts must be complete, and utterly exhaust the whole scope of the pure understanding.

<m2> This completeness required of a science cannot be guaranteed by a rough calculation based on a disconnected heap of experiments. Rather, its completeness can be established only by means of an idea of the apriori knowledge of the understanding as a whole, and through the classification of its component concepts as determined by that idea — in other words, only through the interconnection of these concepts within a system. The pure understanding is entirely separate, not merely from everything empirical, but even from all sensibility. It is therefore a self-subsistent and self-sufficient unity, [B90] which cannot be enlarged by anything additional coming into it from outside. So the sum total of its knowledge constitutes a system which comes under, and is determined by, one single idea. At the same time, the completeness and articulation of the system can provide a touchstone for the correctness and legitimacy of all the components of knowledge contained within it.

<m3> This part of the Transcendental Logic consists of two books, the first of which covers the concepts of the pure understanding, and the second its axioms.

<m4> The Transcendental Analytic

By ‘analytic of concepts’ I do not mean the analysis of concepts, or in other words the usual procedure in philosophical investigations of resolving the content of any concepts that arise into their parts, in order to make these parts explicit. Instead, I mean the analysis of the faculty of understanding itself — something that has rarely been attempted before. The purpose of the analysis is to investigate the possibility of apriori concepts, by looking for them in the understanding alone as their birthplace, and by analysing the pure use of the understanding in general. This is the special business of a [B91] transcendental philosophy — anything else belongs to philosophy in general, as the logical treatment of concepts. I shall therefore trace the pure concepts back to their original seeds with which the human understanding is equipped. These seeds lie ready in the understanding, until they finally germinate on the occasion of experience, and the same understanding frees them from the empirical circumstances by which they are surrounded, and reveals them in their purity.

<m5> The Analytic of Concepts

A faculty of knowledge can be activated by a whole range of stimuli, and each kind of stimulus will bring a different concept to the fore. These concepts make the faculty knowable, and the concepts themselves can be collected together into a more or less complete treatise, depending on how long and how intelligently they have been observed. However, this, so to speak, mechanical procedure will never allow us to determine with certainty when the investigation has actually been completed. Furthermore, since these concepts have been discovered randomly, they will show no order or systematic unity. [B92] Rather, they will ultimately be paired up merely on the basis of similarities, or put into sequences on the basis of the amount they contain, from the simple to the more composite. But although such sequences have been constructed in a way which is to a certain extent methodical, it is anything but systematic.

<m6> Transcendental philosophy has the advantage of being able to seek out its concepts in accordance with a principle (indeed, it has the duty to do so). This is because its concepts spring pure and unmixed from the understanding as an absolute unity, and must therefore be connected together under one single concept or idea. And interconnectedness of this sort supplies us with a rule for determining apriori the place of each pure concept of the understanding, and the completeness of them all taken together. Otherwise this would depend on our arbitrary decisions, or on chance.

<m7> The Transcendental Guide to the Discovery of All Pure Concepts of the Understanding

So far I have explained what the understanding is only negatively, namely as a non-sensory faculty of knowledge. Since we depend on sensibility for all our intuitions, the understanding cannot be a faculty of intuition. Apart from intuition, there is [B93] only one other way of attaining knowledge, namely through concepts. Therefore the knowledge possessed by every understanding (or at least every human understanding) is knowledge through concepts; and it is not intuitive, but discursive. Since all intuitions are sensory, they depend on affections of the senses, whereas concepts depend on functions. By ‘function’, I mean the unity of the act of subsuming different representations under a single representation common to them all. So concepts are grounded in the spontaneity of thought, whereas sensory intuitions are grounded in the receptivity of impressions.

<m8> The only use the understanding can make of concepts is to form judgments with them. Since intuitions are the only representations which relate to their object directly, a concept never relates to an object directly, but only to some other representation of it, whether this is an intuition, or itself already a concept. So judgment is the knowledge of an object through an intermediary, and hence a representation of a representation of the object. In every judgment, there is a concept which applies to many representations; and of these possible representations just one is actually given, and it relates directly to the object. For example, in the judgment ‘All bodies are divisible,’ the concept of the divisible could relate to various other concepts. But in this judgment it is related specifically to the concept of body, and the concept of body is related to certain appearances which are available to us. So [B94] these objects are represented indirectly, through the concept of divisibility.

<m9> Consequently, all judgments are functions of unity among our representations. That is to say, instead of using an individual, direct representation for knowing an object, the understanding uses a higher-order representation, which includes the direct representation as only one among many. In this way, a single act of knowing embraces a whole range of possible instances of knowledge. But we can trace all acts of the understanding back to judgments, with the consequence that the understanding in general can be represented as a faculty for making judgments. For, as I have already said, the understanding is a faculty for thinking, and thinking is knowledge through concepts. But since concepts are predicates of possible judgments, they relate to some representation or other of an object which has not yet been determined.

<m10> For example, the concept of body refers to something — metal, let us say — which can be known through that concept. So it is a concept simply by virtue of the fact that other representations are subsumed under it, and it can relate to objects only by means of these other representations. This is how it comes to be the predicate of a possible judgment — for example, that every metal is a body. So we can discover the sum total of all the functions of the understanding, if we can provide a complete list of the functions of unity in judgments. The following section will show that this can be achieved very easily.

<m11> [B95] The Guide to the Discovery of All Pure Concepts of the Understanding

If we leave out of account all the content of a judgment in general, and attend only to the pure form of understanding it contains, we find that the function of thought in a judgment can be subsumed under four headings, with three elements in each. It is simplest to lay them out in the form of a table:

[B96] Since this division appears to diverge on some points (though not essential ones) from the technical distinctions traditionally observed by logicians, the following observations may be useful for fending off misunderstandings which could be a cause for concern.

<m12> Note 1

Logicians rightly say that, when judgments are used in syllogisms, singular judgments can be treated in the same way as universal ones. For precisely because they have no extension at all, the predicate cannot relate to just one of many things covered by the concept of the subject, and fail to relate to some of the rest. So it is valid of that concept without exception, just as if it were a universal concept which had an extension to which the whole denotation of the predicate applied. On the other hand, if we compare a singular judgment with a universal one simply in terms of the quantity of knowledge they contain, then the ratio between them is one to infinity — so in this respect they are in themselves essentially different from each other. So when I evaluate singular judgments, not merely as to their inner validity, but also as to the quantity of knowledge in general they contain in comparison with other knowledge, then they are utterly different from universal judgments. They therefore deserve their own special place in a complete table of the elements of thought in general, though certainly not in a logic which is limited merely to the use [B97] of judgments in relation to each other.

<m13> Note 2

Similarly, in a transcendental logic, infinite judgments must be kept distinct from affirmative ones, even though in general logic they are rightly included under them, and do not constitute a distinct member of its classification system. General logic leaves out of account all content of the predicate (even if it is negative), and considers only whether the predicate or its opposite is attributed to the subject. But transcendental logic also considers the value or content of the logical affirmation that is made in a judgment by means of a merely negative predicate, and what sort of addition it makes to our knowledge as a whole.

<m14> If I said ‘The soul is not mortal,’ I would at least have prevented an error through a negative judgment. But if I utter the sentence ‘The soul is immortal,’ I actually affirm something as far as the logical form of the sentence is concerned, since I place the soul in the unlimited scope of the immortal. Now the scope of all possible beings contains two parts: that of mortal beings, and that of immortal beings. So all my sentence says is that the soul is one of the infinite number of things which remain if I take away all the mortal ones. But my sentence restricts the infinite scope of all possible beings only to the extent that mortal beings are separated from it, [B98] and the soul is placed in the remaining part of the scope of all possible beings. But even after this separation, the remaining part is still infinite; and yet more parts can be removed without the concept of the soul being enlarged at all, or determined positively.

<m15> So these judgments are infinite with respect to their logical scope, but in fact they are merely limiting with respect to the content of knowledge in general. They must not be omitted from the transcendental table of all the elements of thought in judgments, since the function of the understanding exercised by infinite judgments can perhaps be of importance in the area of the pure apriori knowledge of the understanding.

<m16> Note 3

The only relations between thoughts in judgments are:

1. that of the predicate to the subject;
2. that of the ground to the consequent;
3. that between disjunctive knowledge and all the parts of the disjunction.

In the first kind of judgment we consider the relationship only between two concepts, in the second between two judgments, and in the third between a number of judgments.

<m17> The hypothetical proposition: ‘If there is perfect justice, then obstinately evil people will be punished,’ essentially contains the relationship between two propositions: ‘There is perfect justice,’ and ‘Obstinately evil people will be punished.’ Here it remains undecided whether either of these propositions is actually true. All that is thought in this judgment is the inference from the one to the other.

<m18> Ultimately, a disjunctive judgment contains [B99] a relation between two or more propositions. However, the relation is not that of logical consequence, but that of logical opposition, since the scope of the one excludes the scope of the other. On the other hand, the relation is also one of community, in that, taken together, the disjuncts completely fill the scope of the knowledge in question. It is therefore a relation between the parts of the scope of such knowledge, since the scope of each part is complementary to the scope of the other parts, so as to make up the sum total of the disjunctive knowledge.

<m19> Take, for example, the proposition: ‘The world exists either through blind chance, or through an inner necessity, or through an external cause.’ Each of these propositions takes up a part of the scope of all possible knowledge about the existence of the world, and all of them together occupy its scope completely. Taking knowledge out of one of these areas means putting it into one of the others; on the other hand, putting it into one area means taking it out of the others.

<m20> So in a disjunctive judgment there is a certain community between the items of knowledge it consists in, since, although they exclude each other, this very mutual exclusion means that they determine genuine knowledge when taken together as a whole. For, taken together, they constitute the whole content of a single given item of knowledge. In view of what follows, this is all I find necessary to say here.

<m21> Note 4

The modality of judgments is a quite special function, in that it contributes nothing to the content of a judgment. This makes it essentially [B100] distinct from the other functions, since quantity, quality, and relation are the only functions that constitute the content of a judgment. Instead, modality concerns only the value of the copula in relation to thought in general. Judgments are problematic when we take their affirmation or denial as merely possible (voluntary); they are assertoric when we consider their affirmation or denial as actual (true); and apodeictic when we consider their affirmation or denial as necessary.*

<m22> When a judgment relates two subordinate judgments, then both the subordinate judgments are problematic: that is, in the case of hypothetical judgments (antecedent and consequent) and disjunctive judgments, where there is a reciprocal relation between the subordinate judgments (they are members of a divided whole). In the example I gave above, the proposition: ‘There is perfect justice,’ is not stated assertorically, but is thought only as a voluntary judgment which anyone can assume. Only the logical relation between the two judgments is assertoric. Consequently, it is possible for both antecedent and consequent to be evidently false, but taken problematically, to be preconditions for knowledge of the truth. Again, in the other example of a disjunctive judgment, the judgment: ‘The world exists through blind chance’ is meant only problematically, in the sense that anyone might entertain the proposition [B101] for a brief moment. Yet it helps us find the true proposition, like indicating a wrong route at a crossroads where there are a number of possible routes.

<m23> So:

• A problematic proposition is one which expresses only a logical rather than an objective possibility — a free choice to take such a proposition as valid, and complete discretion to entertain it in the understanding.
• An assertoric proposition refers to logical actuality, or truth. For example, in a hypothetical syllogism, the antecedent occurs problematically in the major premise, and assertorically in the minor premise. What an assertoric proposition indicates is that the proposition has already been taken into the understanding in accordance with the laws of the understanding.
• In an apodeictic proposition, an assertoric proposition is thought as determined through these laws of the understanding themselves, and hence as making an apriori affirmation. In this way, it expresses logical necessity.

<m24> Thus everything is incorporated into the understanding by stages. First something is judged problematically, then it is taken as true assertorically, and finally it is affirmed as inseparably bound up with the understanding — that is, as necessary and apodeictic. Consequently, we can call these three functions of modality so many elements of thought in general.

<m25> [B102] The Guide to the Discovery of All the Pure Concepts of the Understanding

As I have already said many times, general logic leaves out of account all content of knowledge. It waits to be given representations from some other source, whatever it may be, before it can turn them into concepts by a process of analysis. By contrast, transcendental logic has in front of it a multiplicity of apriori sensibility, which is supplied by the Transcendental Aesthetic. This serves as the material for the pure concepts of the understanding, without which they would be without any content, and therefore completely empty.

<m26> Space and time contain a multiplicity of pure apriori intuition. Nevertheless, they are among the preconditions for the receptivity of our mind. These preconditions must be met if the mind is to receive representations of objects, and therefore they must also always affect the concept of such objects. However if the spontaneity of our thought is to make any knowledge out of the multiplicity of pure intuition, it must first go through it, take it up, and connect it together in a particular way. I call this act ‘synthesis’.

<m27> [B103] By synthesis in its widest sense, I mean the act of putting different representations together and embracing their multiplicity in one act of knowledge. Such a synthesis is pure, when the multiplicity is not empirical, but is given a priori, as in the case of space and time. Our representations must be given before they can be analysed, and no concepts can come into being analytically, as far as their content is concerned. The synthesis of a multiplicy (whether this multiplicity is given empirically or apriori) is what first produces knowledge, although this knowledge may initially still be raw and confused, and therefore in need of analysis. However, synthesis is still essentially what collects together the elements necessary for knowledge, and unites them into a specific content. So synthesis is the first thing we must attend to, if we are to judge about the first source of our knowledge.

<m28> As we shall see later, synthesis in general is merely the operation of the imagination, which is a blind, though indispensable function of the soul. Although we are hardly ever conscious of it, we would have no knowledge at all without it. However, bringing this synthesis to bear on concepts is a function which belongs to the understanding, and through which the understanding first provides us with knowledge properly so called.

<m29> [B104] Now pure synthesis, conceived universally, gives us pure concepts of the understanding. By this synthesis, I mean one that depends on an apriori basis of synthetic unity. For example, our counting is a synthesis in accordance with concepts — and this is especially obvious in the case of large numbers. It is such a synthesis because counting is carried out in accordance with a common basis of unity — the number ten, for example. Through this concept, the unity in the synthesis of the multiplicity becomes a necessary one.

<m30> Different representations are brought under a single concept analytically; but this is a process which is dealt with by general logic. What transcendental logic teaches us is, not how to bring representations to concepts, but how to bring the pure synthesis of representations to concepts. In order for us to have apriori knowledge of all objects, the first thing that must be given is the multiplicity of pure intuition. The second requirement is the synthesis of this multiplicity through the imagination — but this is still not enough to give us knowledge. The third requirement for knowledge of an object that comes before us is the concepts which give unity to this pure synthesis, and which consist only in the representation of this necessary synthetic unity. And these concepts depend on the understanding.

<m31> The function that gives unity to the different representations in a judgment is the same function as also [B105] gives unity to the pure synthesis of different representations in an intuition. In general terms, this function is called a pure concept of the understanding. Therefore one and the same understanding performs one and the same action in order to achieve two outcomes:

• to bring about the logical form of a judgment in concepts by means of analytic unity;
• to bring a transcendental content into its representations by means of the synthetic unity of the multiplicity in intuition in general.

This is why they are called pure concepts of the understanding. Moreover, they apply to objects apriori — which is something that general logic cannot achieve.

<m32> The earlier table specified the number of logical functions in all possible judgments. But the argument I have just given shows that there must arise exactly the same number of pure concepts of the understanding applying apriori to objects of intuition in general. For the understanding has absolutely no functions other than the above, and they constitute an exhaustive list of all its powers. I shall follow Aristotle in calling these concepts categories, since our fundamental objective is the same, even though we have carried it out very differently.

<m33> [B106] Table of Categories

<m34> This is a complete catalogue of all the originative pure concepts of synthesis which the understanding contains within itself apriori. It is only because of them that it is a pure understanding, since through them alone can it understand anything in the multiplicity of intuition — that is, can think an object of intuition. The classification has been generated systematically from a single common principle, namely the capacity to form a judgment — which amounts to exactly the same as the capacity to think. It has not come into being randomly, as the result of a serendipitous search for pure concepts. If it had, we could never be certain of its completeness, [B107] since it would have been inferred merely by induction. We should also bear in mind that induction could never tell us why just these concepts and no others should reside in the pure understanding.

<m35> Aristotle’s project of searching out these fundamental concepts was worthy of such a clever man. However, since he had no principle to guide him, he grabbed at whatever he stumbled upon, and originally rounded up ten of them, which he called categories or ‘predicaments’. Later, he believed he had discovered five more, which he added to the list, calling them ‘postpredicaments’. But his table of categories still had some omissions. On the other hand, it also includes various items which do not belong to such a list of the originative contents of the understanding. For example, ‘when’, ‘where’, ‘position’, ‘before’ and ‘at the same time as’ are modes of pure sensibility; and ‘motion’ is an empirical concept. There are also some derivative concepts which Aristotle treats as primary ones (‘action’, ‘passion’), and some primary concepts are missing altogether.

<m36> As for these primary concepts, it should be noted that, since the categories are the genuine originative concepts of the pure understanding, as such, they also have their pure derivative concepts. These derivative concepts could in no way be omitted from a complete system of transcendental philosophy. But in an essay which is confined to a critique, it is enough for me simply to mention them.

<m37> [B108] Let me call these pure but derivative concepts of the understanding the predicables of the pure understanding, to distinguish them from the ‘predicaments’. Once we have the originative and primitive concepts, it is easy to add the derivative and subsidiary ones, and to fill out the details of the family tree of the concepts of the understanding. I leave this completion for a later work, since here I am concerned only with the principles for a complete system, and not with the system itself. However, this objective can be largely fulfilled with the help of ontological textbooks — for example, by classifying the predicables of force, action, and passion under the category of causality; those of presence and resistance under the category of community; those of coming to be, ceasing to be, and alteration under the predicaments of modality, and so on. A large number of derivative apriori concepts are generated by combining the categories with the modes of pure sensibility, or even with each other. It would be a useful and not unpleasant task to identify, and, where possible, to make a complete catalogue of such derivative concepts. However, it is unnecessary for me to do this here.

<m38> In this treatise, I deliberately refrain from providing definitions of the categories, even though I might be in possession of them. In what follows, I shall analyse these concepts only to the extent that is required [B109] for the doctrine of method I am developing. Definitions would rightly be expected in a system of pure reason. But in this treatise, they would merely divert attention from the main point of the investigation, by giving rise to doubts and objections. So I can easily defer them to a later task, without detracting from my essential purpose. Nevertheless, it is obvious from the little I have said about this, that a complete dictionary with all the necessary explanations is not only possible, but even easy to create. The divisions of a classification system are already in place, and all that is needed is to fill them in. With a systematic classification such as the present one, it is difficult to make mistakes about the proper place in it for every concept, and it is at the same time easy to detect which divisions are still empty.

<m39> §11

Interesting points can be made about this table of the categories — points which could perhaps have considerable consequences for the scientific form of all rational knowledge. For a start, in theoretical philosophy, this table is exceptionally useful — indeed, indispensable — for outlining the complete plan for a whole science derived from apriori concepts, and for classifying it systematically in accordance with determinate principles. This is already self-evident from the fact that the above table contains all the elementary concepts of the understanding in their entirety, and even the form of a system [B110] of these concepts in the human understanding. Consequently it specifies all the elements of a projected speculative science, and even their order — as I have proved elsewhere.*

<m40> The following are some of the points that can be made:

Although the table contains four classes of concepts of the understanding, there is a more basic distinction between two higher-level classes:

1. those that are concerned with objects of intuition, pure as well as empirical; and
2. those that are concerned with the existence of these objects, whether in relation to each other, or in relation to the understating.

I would call the categories in the first class mathematical, and those in the second class dynamical. As you can see, the categories in the first class have no existing object corresponding to them, whereas those in the second class do. Yet this distinction must be grounded in the nature of the understanding.

<m41> Point 2

Since every apriori classification of concepts must consist in binary divisions, the fact that the number of categories in each class is three must give pause for thought. But in each case, the third category arises from the combination of the second category in each class with the first.

<m42> [B111] Thus totality is nothing other than plurality considered as a unity; limitation is nothing other than reality combined with negation; community consists in substances mutually causing each other’s determinations; and, finally, necessity is nothing other than existence given through possibility alone.

<m43> But it should not be thought that this makes the third category in each class merely derivative, and not an originative concept of the pure understanding. For the connecting of the first and second concepts in order to generate the third, requires a special act of the understanding, which is not the same as that performed in the case of the first or second concepts. Thus the concept of a number (which belongs to the category of totality) is not always itself possible in cases where the concepts of plurality and unity are possible — for example, in the representation of the infinite. Nor do I get the concept of influence simply by combining the concepts of a cause and of a substance, since this does not give me to understand how one substance can be the cause of something in another substance. From this it is obvious that a special act of the understanding is required — and the same goes for the other categories.

<m44> Point 3

In the case of one category, it is not as obvious as it is with the others, how it accords with the corresponding form in the table of logical functions. This is the category of community, which comes under the third heading; [B112] and the corresponding form is that of a disjunctive judgment.

<m45> In order to be assured that it does indeed accord with it, we must note that in every disjunctive judgment, its scope (the totality of everything that is contained under it) is represented as a whole divided into parts (the subordinate concepts). Since one subordinate concept cannot be contained under the other, they are thought as co-ordinated with each other, and not as subordinated one to another. Moreover, they determine each other, not in one direction only (as in a series), but in all directions (as in an interactive whole, where assuming one member of the classification excludes all the others, and vice versa).

<m46> A similar connection is thought in a whole consisting of things. Here, one thing is not subordinated to another as an effect, where the other is the cause of its existence. Rather, each is simultaneously and reciprocally co-ordinated with the other, with each being the cause of the determination of the other (as, for example, the parts of a body reciprocally attract, but also repel each other). This is a completely different kind of connection than is to be found in the simple relation between cause and effect (or ground and consequence). Here, the consequence does not reciprocally determine the ground, and hence the two together do not constitute a single whole — just as the world and its creator do not constitute a single whole.

<m47> So the understanding follows the same procedure when it [B113] represents to itself the scope of a disjunctive concept, as when it thinks a thing as divisible. In the case of concepts, the members of the disjunction exclude each other, and yet are combined in a single scope. Similarly, in the case of things, the understanding represents to itself the parts of a thing as substances, each of which exists exclusively of the rest, and yet as combined in a single whole.

<m48> §12

In the history of transcendental philosophy, there is another chapter which contains pure concepts of the understanding. Although they are not numbered among the categories, the ancients took them to be apriori concepts of objects. But if so, these concepts would enlarge the number of categories — which cannot be. They are listed in the famous scholastic tag: Every being is one, true, and good. In fact, this principle has turned out to be of very little use, since only tautologies follow from it — so useless that, in modern times, it is usually allowed a place in metaphysics only out of little more than courtesy. Nevertheless, despite its apparent vacuity, a thought which has survived for such a long time always deserves to have its origins investigated. It is also reasonable to suppose that it is based on some rule or other of the understanding, which has merely been misinterpreted — as often happens.

<m49> These supposedly transcendental [B114] predicates of things are nothing other than logical requirements and criteria for any knowledge of things in general, and they ground this knowledge in the categories of quantity, namely those of unity, plurality, and totality. However, the ancients must have taken these predicates, which are essentially material, as belonging to the possibility of things themselves. In fact they needed them only in a formal sense, as belonging to the logical requirements for any knowledge; but they carelessly turned these criteria for thought into properties of things in themselves.

<m50> To explain:

1. In all knowledge of an object, there is the unity of the concept. This can be called qualitative unity, in that only the unity of the synthesis of the multiplicity of knowledge is thought through it — this is rather like the thematic unity of a play, a speech, or a story.
2. Then there is the truth of a concept with respect to its consequences. The more true consequences that flow from a given concept, the more indications there are of its objective reality. This could be called the qualitative plurality of the common, defining characteristics which belong to the core of a concept, and which are not thought in it quantitatively.
3. Finally there is perfection, which consists in the fact that the above plurality goes inwards as well as outwards. It leads back to the unity of the concept, and it is in complete harmony with this concept, and with no other. This can be called its qualitative perfection, or totality.

<m51> From this it is obvious [B115] that confusing these logical criteria for the possibility of knowledge in general with the three categories of quantity corrupts the categories. In the categories, the unity of the process of creating a particular quantity must be taken as thoroughly homogeneous. But here the categories are transformed, simply in order to connect additional heterogeneous elements of knowledge in a single consciousness, using the quality of the knowledge as a principle.

<m52> So the criterion for the possibility of a concept is its definition; but the definition is not the criterion for the possibility of the object of the concept. The definition includes everything required for constructing the whole concept:

• the unity of the concept;
• the truth of everything that can be immediately deduced from it;
• and finally the completeness of what has been deduced from it.

<m53> Similarly, the criteria for the validity of a hypothesis are:

• the reasonableness of the assumed basis for explanation, or its unity without auxiliary hypotheses;
• the truth of the consequences which can be drawn from it — that is, their internal consistency and their correspondence with experience;
• and finally the completeness of the basis for explanation of these consequences.

These consequences lead us back to nothing more or less than what was already assumed in the hypothesis. What was thought synthetically apriori comes back to us analytically aposteriori, and the two are in accordance with each other.

<m54> So the transcendental table of the categories would not be completed by adding the concepts of unity, truth, and perfection, as if it were somehow defective without them. [B116] Rather, we use them as coming under the universal logical laws of the consistency of knowledge with itself, since the relation of these concepts to objects is completely irrelevant.

<t1> The Analytic of Concepts

When teachers of law discuss entitlements and claims, they distinguish between two kinds of question which arise in a lawsuit: questions of law (‘By what right?’), and questions of fact (‘What are the facts?’). Given that both need to be proved, they call the proof of the first the deduction, and its function is to demonstrate the entitlement or legal claim.

<t2> We use many empirical concepts without anyone objecting, and we consider ourselves justified in giving them a sense and a supposed meaning, even without any deduction of them. This is because we always have experience to hand [B117] to prove their objective reality. However, there are also other, illegitimate concepts, such as those of good luck and fate, which circulate with almost universal indulgence, but which are sometimes called to account by the question: ‘By what right?’ Then people find themselves in no little difficulty over the deduction of the concepts, since they can derive no clear basis for their justification, either from experience or from reason, which would give clear authority for their use.

<t3> Among the many sorts of concepts which make up the very mixed texture of human knowledge, there are a few which are destined even for pure apriori use, in complete independence of all experience, and their authority for this use always requires a deduction. Since proofs drawn from experience are insufficient to establish the legitimacy of such a use, we need to know how these concepts can relate to objects which they do not get from any experience. So I call the explanation of the way in which concepts can relate to objects apriori their transcendental deduction. This is different from an empirical deduction, which shows the way in which a concept is obtained through experience and reflection on it. It is therefore a question, not of the legitimacy of the concept, but of the facts as to how it came to be possessed.

<t4> [B118] We already have two entirely different kinds of concept which have it in common that they both relate to objects completely apriori. These are the concepts of space and time as forms of sensibility, and the categories as concepts of the understanding. It would be a total waste of time to attempt an empirical deduction of them, because what is distinctive about their nature is precisely that they relate to their objects without having borrowed anything from experience for representing them. So if a deduction of them is necessary, it must in any event be a transcendental deduction.

<t5> Nevertheless, as with all knowledge, we can look for the occasional causes of their formation in experience, even if we cannot look for the principle of their possibility in experience. It is here that the impressions of the senses provide the first stimulus, which opens out the whole faculty of knowledge to considering these concepts, and brings experience into being. Experience consists of two very different elements, namely the matter for knowledge, which comes from the senses; and a certain form for organising this matter. The form comes from the inner source of pure intuition and thought, which are first aroused to activity and produce concepts on the occasion of sense impressions.

<t6> Without doubt, it is very useful to trace these first strivings of our faculty of knowledge to advance from particular perceptions to [B119] universal concepts, and we have the famous Locke to thank for first opening up the way to this area of investigation. However, this would never bring about a deduction of the pure apriori concepts, which is most emphatically not to be found down this route. In view of their later use, which is to be entirely independent of experience, they must be able to present a birth certificate which is quite other than descent from experiences.

<t7> This attempted naturalistic derivation of the categories cannot be called a deduction at all, since it is concerned with a question of fact. Instead, I shall call it an explanation of our possession of pure knowledge. It is therefore clear that only a transcendental deduction can be given of our pure knowledge, and in no way an empirical one. As far as pure apriori concepts are concerned, empirical deductions are a complete waste of effort, and they can be undertaken only by people who have totally failed to grasp the essential nature of this kind of knowledge.

<t8> Even if it is accepted that the only possible kind of deduction of pure apriori knowledge is along the transcendental route, this does not yet make it obvious that a deduction is unavoidably necessary. I have already traced the concepts of space and time back to their source by means of a transcendental deduction, and I have explained and determined [B120] their apriori objective validity. However, geometry follows its sure path by means of strictly apriori knowledge, without having to ask philosophy for any certification of the pure and legitimate pedigree of its foundational concept of space. But the application of the concept of space in geometry is limited to the outer world of the senses, and space is the pure form of sensory intuition. So in this world, all geometrical knowledge is directly evident, because it is based on apriori intuition, and its objects are given apriori in intuition through that very knowledge of them (at least as far as their form is concerned).

<t9> The situation is quite different in the case of the pure concepts of the understanding, where the unavoidable need to find a transcendental deduction first arises — a deduction not only of the concepts themselves, but also of space. For since they refer to objects, not through predicates of intuition and sensibility, but through predicates of pure apriori thought, they relate universally to objects, without any restriction to sensibility. Again, since they are not based on experience, they cannot use apriori intuition to display any object which could form the basis of their synthesis prior to all experience. Consequently, they arouse suspicion, not only as to the objective validity and scope of their applicability, but also because they make the concept of space ambiguous, since they tend to use it beyond the [B121] restrictions of sensory intuition. And this is why I have already found it necessary to provide a transcendental deduction of the concept of space.

<t10> The reader must therefore be convinced that such a transcendental deduction is unavoidably necessary before taking a single step into the realm of pure reason. Without it, you will stumble around blindly, and after many wrong turns you will inevitably end up back in the state of ignorance from which you set out. But right from the start, you must also be clearly aware of the inescapable difficulty of the task, so that you do not complain of obscurity where the matter itself is deeply shrouded, or become discouraged too quickly over the removal of obstacles. The long and the short of it is that, either we see this critical investigation through to the end, or we must completely give up any claim that pure reason can have insight into its most cherished realm, namely that which extends beyond the limits of all possible experience.

<t11> Earlier, it was easy for me to explain how the concepts of space and time must necessarily relate to objects, despite being instances of apriori knowledge. I also explained how they made it possible for us to have synthetic knowledge of space and time independently of all experience. For it is only through the mediation of these pure forms of sensibility that an object can appear to us — in other words, that it can be an object of empirical intuition. It follows that space and time are pure intuitions which contain apriori the precondition [B122] of the possibility of objects as appearances, and also that acts of synthesis which are carried out in them have objective validity.

<t12> By contrast, the categories of the understanding in no way represent to us the preconditions for objects to be given in intuition. Therefore objects can certainly appear to us, but without necessarily having to relate to functions of the understanding, and without the understanding having to contain their preconditions apriori. This gives rise to a difficulty which we did not come up against in the realm of sensibility — namely, how can subjective preconditions of thought have objective validity? In other words, how can they provide preconditions for the possibility of all knowledge of objects? For appearances can certainly be given in intuition without functions of the understanding.

<t13> Take the concept of cause, for example. This concept denotes a particular kind of synthesis, in which, given A, a quite different B is affirmed in accordance with a rule. But it is not clear apriori why appearances should contain anything like the concept of cause — and experience cannot show why they should, since it cannot establish the objective validity of an apriori concept such as this. So, from an apriori point of view, it is conceivable that a concept like that of cause might perhaps be completely empty, and have no object anywhere among appearances.

<t14> It is clear that objects of sensory intuition must be in accordance with [B123] the formal preconditions of sensibility which lie apriori in the mind, because otherwise they would not be objects for us. It is less easy to see why they must also be in accordance with the preconditions which the understanding requires for the synthetic unity of thought. For it would be perfectly possible for our appearances to be such that our understanding found that they were not at all in accordance with the preconditions of its unity. Everything could be in such a state of confusion, that, for example, there was nothing to be found in the succession of appearances which would provide a rule for synthesising the appearances, and thus correspond to the concept of cause and effect. If so, the concept of cause and effect would be completely empty, invalid, and meaningless. Nevertheless, appearances would still provide our intuition with objects, since intuition in no way requires the functions of thought.

<t15> Someone might think of avoiding the laboriousness of these investigations, by the following line of reasoning: experience unceasingly supplies us with examples of a regularity of appearances which gives us sufficient grounds for abstracting the concept of cause from them, and at the same time for confirming the validity of the concept. If so, they will have failed to notice that it is quite impossible for the concept of cause to come into being this way. It must either be grounded in the understanding completely apriori, or it must be given up altogether as a mere figment of the brain. [B124] For the concept of cause absolutely requires that something A is of such a kind that something else B follows from it necessarily and in accordance with a strictly universal rule.

<t16> Appearances do indeed provide us with particular cases, from which we can construct a rule that something usually happens, but never that the succession is necessary. So the synthesis of cause and effect has a special status, which cannot be described at all in empirical terms, namely that the effect is not merely added to the cause, but that it comes into existence through the cause and follows from it. Besides, strict universality is never a property of empirical rules, since induction can give them nothing other than relative universality — that is, widespread applicability. The use of the pure concepts of the understanding would be completely changed, if they were treated merely as the products of experience.

<t17> §14

There are only two possible cases in which synthetic representation and its objects can come together, have a necessary connection to each other, and, as it were, meet each other:

• either if the object alone makes the representation possible;
• or if the representation [B125] alone makes the object possible.

In the first case, the relationship is merely empirical, and the representation can never be possible apriori. This is the case with an appearance, to the extent that what it contains belongs to sensation.

<t18> Now take the second case. Given that we are not here talking about the causality of the will, representation does not by itself bring its object into existence. On the other hand, it does determine its object apriori, since it is only through representation that it is possible to know something as an object.

<t19> There are two preconditions under which alone knowledge of an object is possible. The first is an intuition, through which an object is given, if only as an appearance. The second is a concept, through which an object corresponding to this intuition is thought.

<t20>From what I have already said, it is clear that the first precondition (namely the necessary precondition for objects to be intuited) lies apriori in the mind as the ground of objects as far as their form is concerned. So all intuitions are necessarily in accordance with this formal precondition of sensibility, because it is only through this precondition that they can appear — in other words, that they can be empirically intuited and given.

<t21> The question now arises whether concepts might not also precede objects apriori. If so, they would not be preconditions for anything to be intuited, but they would be necessary preconditions for anything to be thought as an object in general. If so, all empirical [B126] knowledge of objects would necessarily be in accordance with such concepts, since nothing would be possible as an object of experience without presupposing them.

<t22> Now all experience contains both a sensory intuition through which something is given, and a concept of an object which is given in intuition, or appears. Therefore experiential knowledge presupposes concepts of objects in general as apriori preconditions. Consequently, the objective validity of the categories, as apriori concepts, depends on the fact that it is only through them that experience is possible, as far as the form of thought is concerned. So then they relate to objects of experience necessarily and apriori, since no object of experience at all can be thought except by means of the categories.

<t23> Thus the transcendental deduction of all apriori concepts has a principle, which must govern the whole investigation. This principle is that these apriori concepts must be known as apriori preconditions of the possibility of experience — whether of the intuition which it contains, or of the thought. Concepts which provide the necessary foundation for the possibility of experience are necessary by virtue of that very fact. To trace the development of these concepts in the experience in which they are found is not a deduction of them, but an explanation, since this would make them merely contingent. [B127] All objects of knowledge are met with in experience. So it would be impossible to understand how apriori concepts could relate to any sort of object, without this originative relation to possible experience.

<t24> The famous Locke failed to take account of this consideration. Because he found pure concepts of the understanding in experience, he also derived them from experience. But he proceeded so illogically, that he tried to use experience to discover knowledge which lies far outside the limits of experience.

<t25> David Hume recognised that, in order to go beyond experience, it is necessary for these concepts to have an apriori origin. However, he was quite unable to explain how it could be possible that the understanding must think concepts as necessarily connected in the object, when they are not essentially connected in the understanding. It never occurred to him that, through these concepts, the understanding could itself perhaps be the creator of the experience in which the objects of the understanding are met with. So he was forced to derive the concepts from experience.

<t26> More precisely, he derived them from a subjective necessity arising from repeated association in experience, which necessity is eventually, though wrongly, taken to be an objective one — in other words, he derived them from custom. He then continued very consistently, and declared that it was impossible to use these concepts and the axioms they generate to go beyond the limits of experience. However, the empirical derivation [B128] to which both Locke and Hume were attracted, is inconsistent with the scientific apriori knowledge we actually have, namely that of pure mathematics and of general natural science. So the empirical derivation is refuted by the facts of the case.

<t27> The first of these two famous men opened the floodgates to enthusiasm, since once reason has authority on its side, it no longer allows itself to be kept within limits by vague recommendations of moderation. The second gave himself entirely over to scepticism, once he believed he had discovered that what is generally held to be reason is no more than a delusion of our faculty of knowledge. We are now about to begin an experiment, to see whether we can steer human reason safely between these two rocks, by setting definite limits to it, while at the same time leaving open to it the whole realm of its legitimate activity.

<t28> But first I shall provide an explanation of what the categories are. Categories are concepts of an object in general, through which an intuition of an object is considered as determined in respect of one of the logical functions for judging. Thus the function of categorical judgments is that of the relation of subject to predicate — for example, ‘All bodies are divisible.’ As long as we confine ourselves to the purely logical use of the understanding, it remains undetermined [B129] which of the two concepts is to be given the function of subject, and which the function of predicate. For it could equally well be said that ‘Something divisible is a body.’ But if I bring the concept of a body under the category of substance, it becomes determinate that the empirical intuition of a body in experience must always be considered only as a subject, and never as a mere predicate. And the same goes for the other categories.

<t29> The Deduction of the Pure Concepts of the Understanding

The multiplicity of representations can be given in an intuition which is purely sensory — that is, which is nothing other than receptivity. The form of this intuition can lie apriori in our faculty of representation, without being anything other than the way in which the subject is affected. But the unification of a multiplicity in general can never come to us through the senses; nor, therefore, can it already be contained in the pure form of sensory intuition along with the rest. [B130] For unification is a self-generated act of the faculty of representation; and this faculty must be called the understanding, in order to distinguish it from sensibility. So all unification is an act of the understanding:

• whether we are conscious of it or not;
• whether it is a unification of the multiplicity of intuition or of a number of concepts;
• and in the case of intuition, whether it is a unification of sensory or of non-sensory intuition.

I shall apply the general term synthesis to this act of the understanding, in order to make it explicit that we cannot conceive anything as unified in the object, which we have not ourselves already unified.

<t30> Of all representations, unification is the only one which is not given through objects. Since it is an act of the self-activity of the subject, it can be carried out only by the subject itself. Here it is easy to see that this act must have a single origin which is equally valid for all unification. Separation, or analysis, might seem to be its opposite, but it always presupposes unification. For the understanding cannot separate what it has not already unified, since it is only through the understanding that anything can be given to the faculty of representation as unified.

<t31> As well as the concept of multiplicity and its synthesis, the concept of unification also implies the concept of its unity. Unification is the representation of the synthetic unity of the multiple.*

[B131] The representation of this unity cannot arise from the unification. Rather, it is the representation of this unity which first makes possible the concept of unification, through being added to the representation of the multiple.

<t32> Since this unity precedes all concepts of unification apriori, it is not the category of unity specified above in §10. For all the categories are based on the logical functions in judgments; and unification — and hence the unity of the given concepts — is already thought in them. Therefore the category of unity already presupposes unification. So we must look for this unity (as a qualitative unity — see §12) at an even higher level, in that which itself contains the foundation of the unity of different concepts in judgments, and hence of the possibility of the understanding, even in its logical use.

<t33> §16.

It must be possible for the I think to accompany all my representations. If not, something would be represented in me [B132] which could not be thought at all. This is as much as to say that the representation would either be impossible, or at least that it would be nothing for me.

<t34> That representation which can be given before any thought is called intuition. So every multiplicity of intuition has a necessary relation to the I think in the same subject as the multiplicity is found in. But the representation of the I think is an act of self-activity — in other words, it cannot be taken as belonging to sensibility. I call it pure apperception, in order to distinguish it from empirical apperception. I also call it originative apperception, because it is the self-consciousness which cannot be accompanied by any higher-level consciousness. It is itself the source of the representation I think, which must be able to accompany all other representations, and which is one and the same in all consciousness.

<t35> I also call the unity of apperception the transcendental unity of self-consciousness, in order to indicate the possibility of deriving apriori knowledge from it. For the multiple representations which are given in any particular intuition would not as a whole be my representations, unless they belonged as a whole to a single self-consciousness. To put it another way, as my representations (even if I am not conscious of them as such), they must necessarily satisfy the precondition for them to be able to come together under a single over-arching self-consciousness — otherwise they would not belong to me as a systematic whole. [B133] Much follows from this originative unification.

<t36> In particular, this holistic identity of the apperception of a multiplicity given in intuition contains a synthesis of the representations, and it is possible only through the consciousness of this synthesis. For the empirical consciousness which accompanies different representations is essentially scattered among them, and it has no relation to the identity of the subject. So this relation is not brought into being through my accompanying every representation with consciousness. Rather, the relation to the identity of the subject is brought into being through my joining one representation to another, and through my being conscious of their synthesis. Therefore it is only because I can unify a multiplicity of given representations into a single consciousness, that it is possible for me to conceive the very identity of the consciousness in these representations. In other words, the analytic unity of apperception is possible only on the presupposition of some sort of synthetic unity.*

<t38> [B134] So the thought that: ‘These representations given in intuition belong to me as a whole,’ amounts to saying that I unite them in a single consciousness, or at least that I can unite them in a single consciousness. And although it is not yet itself the consciousness of the synthesis of the representations, it still presupposes the possibility of such a synthesis. In other words, I can call these representations as a whole my representations, only because I can embrace their multiplicity in a single consciousness. If I could not do this, I would have a self which was as variegated and fragmentary as the representations I am conscious of.

<t39> So the synthetic unity of the multiplicity of intuitions, as given apriori, is the foundation of the identity of apperception itself, and it precedes all my particular thoughts apriori. Unification does not lie in objects, and it cannot first be taken up into the understanding by being derived from objects through some sort of perception. Rather, unification is [B135] the business of the understanding alone. And the understanding itself is no more than the faculty of unifying priori, and of bringing the multiplicity of given representations under the unity of apperception. This is the supreme axiom of the whole of human knowledge.

<t40> Admittedly, this axiom of the necessary unity of apperception is itself an identical, and hence an analytic proposition. Nevertheless, it does make it explicit that a synthesis of the multiplicity given in an intuition is necessary. Without such a synthesis, it would be impossible to think the holistic identity of self-consciousness. No multiplicity is given in the ‘I’, since it is a simple representation. It is only through intuition, which is distinct from the ‘I’, that multiplicity can be given, and thought through unification in a single consciousness.

<t41> If there were an understanding such that the whole multiplicity was given to it at one and the same time through self-consciousness, it would be an intuitive understanding. But our understanding can only think, and it must look for intuition in the senses. So I am conscious of the identity of my self by reference to the multiplicity of representations which are given to me in an intuition, because I call them as a whole my representations, constituting a single intuition. This amounts to saying that I am conscious of a necessary apriori synthesis of my representations, which is called the originative synthetic unity of apperception. All representations which are given to me must be subject to this unity, but they can be brought under it only through a synthesis.

<t42> [B136] §17

As I said in the Transcendental Aesthetic, the supreme axiom of the possibility of all intuition as far as sensibility is concerned, is that every multiplicity of intuition comes under the formal preconditions of space and time. The supreme axiom of the possibility of all intuition as far as the understanding is concerned, is that every multiplicity of intuition comes under the preconditions of the originative-synthetic unity of apperception.*

<t44> All multiple representations of intuition come under the first axiom in so far as they are given to us, and under the second axiom in so far as it must be possible for them to be unified in a single consciousness. [B137] Without such unification, nothing could be thought or known, because the representations given would not have the act of apperception ‘I think’ in common. Consequently they could not be blended together in a single consciousness.

<t45> Generally speaking, the understanding is the faculty of knowledge. Knowledge consists in the particular relation of given representations to an object. The concept of an object is that in which the multiplicity of a given intuition is united. But all uniting of representations requires unity of consciousness in their synthesis. Consequently, the unity of consciousness is that which alone brings about the relation of representations to an object, and hence their objective validity, and therefore makes them instances of knowledge. Consequently, the very possibility of the understanding depends on the unity of consciousness.

<t46> The primary pure knowledge of the understanding is the axiom of the originative synthetic unity of apperception. All other use of the understanding is based on it, and it is also completely independent of any preconditions of sensory intuition. Thus space, which is merely the form of outer sensory intuition, is not yet knowledge at all. All it provides is the multiplicity of apriori intuition for possible knowledge. In order to know something in space, for example a line, I must pull it out, and thus [B138] synthetically bring into being a particular unification of the given multiplicity. The unity of this action is at the same time the unity of consciousness (in the concept of a line), and through this unity of consciousness an object is first known (as a particular space). So the synthetic unity of consciousness is an objective precondition of all knowledge. It is not merely that I myself need it in order to know an object, but that every intuition must be subject to it in order to become an object for me. If it happened in any other way, and without this synthesis, the multiplicity would not be united in a single consciousness.

<t47> As I have already said, this proposition is itself analytic, even though it makes synthetic unity the precondition of all thought. It says no more than that all my representations in any given intuition must be subject to the necessary precondition for me to be able to ascribe them to one and the same self as my representations, and so to embrace them as synthetically connected together in a single apperception through the universal expression: ‘I think’.

<t48> However, this axiom is not a principle which applies to absolutely every possible understanding, but only to an understanding such that no multiplicity at all is given through its pure apperception in the representation ‘I am’. Let us suppose that there is an understanding such that the multiplicity of intuition is given to it simultaneously with its self-consciousness [B139] — in other words, an understanding such that the objects of its representation exist simultaneously with its representation. Such an understanding would not require an additional act of synthesis of the multiplicity for the unity of its consciousness. By contrast, human understanding does require this act of synthesis, since it merely thinks, and does not intuit. It is so inescapably the primary axiom for human understanding, that human understanding cannot even form the least conception of a different kind of possible understanding — whether of one which itself intuits, or of one which has sensory intuition, but of a very different kind from intuition based on space and time.

<t49> §18

The transcendental unity of apperception is that through which every multiplicity given in an intuition is united in a concept of the object. This is why it is called objective, and must be distinguished from the subjective unity of consciousness. The subjective unity of consciousness is a determination of the inner sense, through which that multiplicity of intuition is empirically given for such a unification.

<t50> Whether I can be empirically conscious of the multiplicity as co-existent or as successive depends on circumstances or empirical conditions. Therefore the empirical [B140] unity of consciousness, which arises from the association of representations, concerns only an appearance, and is completely contingent. By contrast, the pure form of intuition in time is subject to the originative unity of consciousness. This is because time is nothing other than the universal intuition which contains any given multiplicity. And it is subject to the unity of consciousness through the necessary relation of the multiplicity of intuition to the single ‘I think’, and hence through the pure synthesis of the understanding, which is the apriori basis of empirical synthesis.

<t51> Only the transcendental unity of apperception is objectively valid. The empirical unity of apperception (which I am not dealing with here) has only subjective validity, since it is derived from the pure synthesis merely under particular given conditions. One person connects the representation corresponding to a particular word with one thing, and another person with a different thing. Similarly, in an empirical context, the unity of consciousness is not necessarily and universally valid of what is given.

<t52> §19

I have never been satisfied with the definition logicians give of a judgment in general. They say it is the representation of a relation between two concepts. [B141] Here I am not going to quibble with them over the defects of this definition:

• that it applies only to categorical, and not to hypothetical or disjunctive judgments;
• that hypothetical and disjunctive judgments contain a relation, not between concepts, but between judgments themselves.

This is despite the fact that many harmful consequences have arisen from this oversight on the part of logic.*

<t54> All I want to say here is that the logicians’ definition fails to determine what this relation consists in.

<t55> Looking more closely at the relation between the items of knowledge in every judgment, I distinguish between this relation, which belongs to the understanding, from any relationship arising from the laws of the reproductive imagination, which has only subjective validity. I then find that a judgment is nothing other than the way we make given items of knowledge subject to the objective unity of apperception.

<t56> This is the function of the connective ‘is’ in [B142] a judgment, which distinguishes the objective unity from the subjective unity of the representations that are given. The word ‘is’ indicates the relation of the representations to the originative apperception, and to the necessary unity of apperception.

<t57> The above holds even when the judgment itself is empirical, and hence contingent — for example, the judgment ‘Bodies are heavy.’ Here, I certainly do not mean to say that these representations necessarily belong to each other in empirical intuition. Rather, they belong to each other by virtue of the necessary unity of apperception in the synthesis of intuitions. In other words, they belong to each other in accordance with principles of the objective determination of all representations, in so far as they can yield knowledge. And all these principles are derived from the axiom of the transcendental unity of apperception.

<t58> This is the only way the relation can give rise to a judgment, that is, a relation which is objectively valid, and sufficiently distinguished from a merely subjectively valid relation between exactly the same representations — for example, one that arises from the laws of association. If it arises from the laws of association, all I can say is ‘If I lift a body, I feel a burden of heaviness.’ What I cannot say is ‘It, the body, is heavy,’ since this amounts to saying that both these representations are in the object. In other words, it amounts to saying that, irrespective of the state of the subject, being bodily and being heavy are united together in the object, and not merely in perception, however often the same perception might be repeated.

<t59> [B143] §20

The multiple given in a sensory intuition is necessarily subject to the originative synthetic unity of apperception, because it is only through this that the unity of the intuition is possible (see §17). But the act of the understanding through which the multiplicity of given representations is brought under a single apperception in general, is the logical function of judgment (see §19). This is the case whether the representations are intuitions or concepts. So every multiplicity given in a single empirical intuition is determined in respect of one of the logical functions of judgment; and this is how it is brought into a consciousness in general. But the categories are nothing other than just these functions of judgment, in so far as the multiplicity of a given intuition is determined in respect of them (see §10). So it follows that the multiplicity in any given intuition is also necessarily subject to the categories.

<t60> [B144] §21

A multiplicity contained in an intuition which I call mine, will be represented as belonging to the necessary unity of self-consciousness through the synthesis which the understanding carries out by means of a category.*

So this need for a category shows that the empirical consciousness of the multiplicity given in a single intuition is subject to pure apriori self-consciousness, just as empirical intuition is subject to a pure sensory intuition, which is equally apriori.

<t61> The above proposition marks the beginning of a deduction of the pure concepts of the understanding. The categories arise from the understanding alone, without any dependence on sensibility. So I must leave out of account the way in which the multiplicity for an empirical intuition is given, in order to concentrate on the unity which the understanding gives to the intuition by means of the categories. Later (in §26 below), I shall show from the way empirical intuition is given in sensibility, [B145] that the unity of empirical intuition is nothing other than the unity which the categories prescribe to the multiplicity of a given intuition in general (as I said in §20 above). Thus the goal of the deduction will not be fully attained until the apriori validity of the categories with respect to all objects of our senses has been explained.

<t62> However, there is one point in the above proof which I could not leave out of account. This is that the multiplicity for intuition must be given, before the synthesis of the understanding, and independently of it. But how this can be so remains undecided here. I can imagine an understanding which itself has intuitions — for example a divine understanding, which would not conceive objects given to it, but through whose conception the objects themselves would be given or created. However, the categories would have absolutely no meaning with respect to knowledge of this sort.

<t63> The categories are merely rules for an understanding whose powers are limited to thought — that is, to the act of bringing the synthesis of the multiplicity to the unity of apperception; and this multiplicity is given in intuition from some other source. Such an understanding knows nothing at all by itself, but merely unifies and organises the material for knowledge (intuition), which must be given to it through the object. It is impossible to provide any deeper reason for the peculiarity of our understanding, that it can bring about the apriori unity of apperception only by means of the categories, and [B146] only of this particular kind and number. The same goes for why we have precisely these and no other functions of judgment, or why time and space are the only possible forms of our intuition.

<t64> §22

To think an object and to know an object are not the same thing. Knowledge has two components:

1. a concept through which an object is thought in general (the category);
2. an intuition through which the object is given.

If no intuition at all could be given corresponding to the concept, the concept would be a thought as far as its form was concerned; but without any object, it could not possibly provide any knowledge of any kind of thing. This is because, as far as I knew, nothing was given, or even could be given, to which my thought could be directed.

<t65> As I showed in the Aesthetic, the only kind of intuition possible for us is sensory intuition. So, for us, the thought of an object in general, thought through a pure concept of the understanding, can become knowledge only if this concept is related to objects of the senses. Sensory [B147] intuition is either pure intuition (space and time), or empirical intuition of what is directly represented through sensation as actual in space or time.

<t66> Determination of pure intuition enables us to obtain apriori knowledge of objects (in mathematics); but such knowledge consists of appearances only in respect of their form. It still remains undecided whether there could actually be things which must be intuited in this form. It follows that no mathematical concepts constitute knowledge by themselves, unless it is assumed that there actually are things which can be presented to us only in accordance with the pure form of sensory intuition. But things in space and time are given only in so far as they are perceptions (representations accompanied by sensation), and hence through empirical representation. It follows that the pure concepts of the understanding, even when they are applied to pure apriori intuitions (as in mathematics), provide knowledge only in so far as these apriori intuitions can be applied to empirical intuitions. Thus the concepts themselves can also be applied to empirical intuitions through the mediation of the apriori intuitions.

<t67> Consequently, the categories do not supply any knowledge of things by means of pure intuition, but only through their possible application to empirical intuition — in other words, they serve only for the possibility of empirical knowledge, which is called experience. Therefore the categories have a use for the knowledge of things only [B148] in so far as things are taken as objects of possible experience.

<t68> §23

The above proposition is of the utmost importance. It sets limits to the application of the pure concepts of the understanding to objects, just as the Transcendental Aesthetic set limits to the application of the pure form of our sensory intuition. As restrictions on the way in which it is possible for objects to be given to us, space and time have no validity beyond objects of the senses, and hence they are valid only of experience. Beyond these limits, they represent nothing, since they exist only in the senses, and have no actuality outside them.

<t69> The pure concepts of the understanding are free from this restriction, and they extend to objects of any kind of intuition, whether it is like ours or not, provided only that it is sensory and not intellectual. However, this wider scope of concepts beyond our particular kind of sensory intuition is of no use to us. For then they are empty concepts, since they do not provide us with any means at all for judging whether their objects are even possible or not — they are merely forms of thought, without any objective reality. The synthetic unity of apperception presupposes an intuition. But in this case we do not have available an intuition to which the synthetic unity of apperception can be applied, and so we cannot determine any object. [B149] Only our sensory and empirical intuition can provide the pure concepts of the understanding with sense and meaning.

<t70> If I suppose an object of a non-sensory intuition as given, I can certainly represent it through all the predicates involved in the assumption that it contains nothing belonging to sensory intuition:

• it is not extended, or in space;
• its persistence is not over a period of time;
• it does not undergo any alteration (succession of determinations in time) — and so on.

But this is not knowledge as such, if I merely indicate what the intuition of the object is not, without being able to say what the intuition contains. I have in no way represented the possibility of an object for my pure concept of the understanding, because I have not been able to supply an intuition which corresponds to it. All I have been able to say is that our intuition is not valid for it.

<t71> Here, the most important point is that no category at all could ever be applied to such a ‘something’. For example, the concept of a substance is the concept of that which can exist as a subject, but never as a mere predicate. However, I could not know whether anything could be given which corresponded to this particular form of thought, unless empirical intuition provided me with the occasion for applying it. More of this later.

<t72> [B150] §24

The pure concepts of the understanding relate to objects of intuition in general through the understanding alone. This is the case whether the understanding is ours, or some other kind of understanding, provided it is a sensory one. But for this reason, the pure concepts are mere forms of thought, through which no determinate object is yet known. The synthesis or unification of the multiplicity in these concepts relates merely to the unity of apperception. This makes it the basis for the possibility of apriori knowledge in so far as it depends on the understanding. Consequently, the synthesis is not merely transcendental, but it is also nothing but purely intellectual.

<t73> However, we have deep within ourselves a particular kind of apriori form of sensory intuition, and this form depends on the receptivity of our faculty of representation (our sensibility). So, since the understanding is self-active, it can determine inner sense through the multiplicity of given representations in accordance with the synthetic unity of apperception. Thus it can think the synthetic unity of the apperception of the multiplicity of sensory intuition apriori. It thinks it as the precondition which all objects of our (human) intuition must necessarily be subject to. For this is how the categories, despite being mere forms of thought, attain objective reality — that is, application to objects [B151] which can be given to us in intuition. However, these objects are merely appearances, since it is only of appearances that we can have apriori intuition.

<t74> Since this synthesis of the multiplicity of sensory intuition is apriori possible and necessary, it can be called figurative synthesis, to distinguish it from the intellectual synthesis, which is thought with respect to the multiplicity of an intuition in general through the categories alone. Both are transcendental, not simply because they take place apriori, but also because they are the basis for the possibility of further apriori knowledge.

<t75> However, figurative synthesis can concern merely the originative-synthetic unity of apperception, that is, the transcendental unity which is thought in the categories. So in order to distinguish it from purely intellectual unification, it must be called the transcendental synthesis of the imagination.

<t76> Imagination is the faculty of representing an object in intuition, even without its actual presence. But since all our intuition is sensory, the imagination belongs to sensibility. This is because of the subjective precondition under which alone the imagination can supply the concepts of the understanding with a corresponding intuition. But the synthesis of the imagination can also be an exercise of self-activity. If so, unlike sense, [B152] which is merely passively determinable, it is actively determining, and hence it can determine the form of sense apriori, in accordance with the unity of apperception. To this extent, the imagination is a faculty for determining sensibility apriori, and its synthesis of intuitions in accordance with the categories must be the transcendental synthesis of the imagination. This transcendental synthesis is an operation of the understanding on sensibility, and it is the first application of the understanding to objects of the kind of intuition that is possible for us. At the same time, it is the basis for all other applications of the understanding to objects.

<t77> As figurative, this synthesis is distinct from intellectual synthesis, which is performed without any contribution from the imagination, and by the understanding alone. In so far as the imagination is self-active, I sometimes call it the productive imagination. By this means I distinguish it from the reproductive imagination, whose synthesis is subject to purely empirical laws, namely the laws of association. The reproductive imagination makes no contribution to explaining the possibility of apriori knowledge, and it therefore belongs to psychology rather than to transcendental philosophy.

<t78> This is the right place to explain a paradox, which must have occurred to everyone in my exposition of the form of inner sense (§6). The paradox is that inner sense presents even our selves to our consciousness, not as we are in ourselves, but only as we appear to ourselves, [B153] because we intuit ourselves only as we are inwardly affected. It seems to be a contradiction, because we must relate actively to our selves as passive. This is why psychology textbooks usually treat inner sense and the faculty of apperception as one and the same thing, whereas I carefully keep them distinct.

<t79> What determines inner sense is the understanding, and its originative faculty for unifying the multiplicity of intuition — that is, its faculty for bringing the multiplicity under a single apperception. Indeed, the very possibility of the understanding itself depends on this faculty. But in us humans, the understanding is a faculty which essentially has nothing to do with intuitions. So even when intuitions are given through sensibility, the understanding cannot take them up into itself, in order, as it were, to unify the multiplicity of its own intuition. Therefore the synthesis of the understanding, considered in isolation, is nothing other than the unity of the action through which it is able to determine sensibility. Since this is its own action, the understanding is conscious of it as such, even without any sensibility. But through this action, the understanding can itself determine the form in which the multiplicity of intuition can be given to inner sense. So the expression transcendental synthesis of the imagination enables us to say that the understanding carries out this action on a passive subject, even though the understanding is a faculty of that subject; and we can correctly say that inner sense [B154] is affected by the action.

<t80> Apperception and its synthetic unity are utterly different from inner sense. As the source of all unification, apperception applies to the multiplicity of intuitions in general. Through the authority of the categories, it applies to objects in general, before any sensory intuition. By contrast, inner sense contains merely the form of intuition, without any unification of the multiplicity within intuition. Consequently, it does not yet contain any determinate intuition. This is possible only through consciousness of the determination of the multiplicity through the transcendental action of the imagination (the synthetic influence of the understanding on inner sense), which I have called figurative synthesis.

<t81> We also always perceive this in ourselves. We cannot think a line without drawing it out in thought; we cannot think a circle without drawing it round its centre; we cannot represent the three dimensions of space without placing three lines at right-angles to each other from the same point. We cannot even represent time without drawing a straight line, which is the only possible external way of representing time figuratively. In drawing the line, we focus our attention on the act of synthesising the multiplicity. It is through this act that we determine inner sense successively, and focus on the successiveness of this determination in inner sense.

<t82> Suppose we consider motion as an action of the subject, and not as a determination [B155] of an object.*

If we leave out of account the multiplicity in space, and focus simply on the act of synthesising it, through which we determine the form of inner sense, then motion is the first thing that generates the concept of succession. So the understanding does not find such a unification of the multiplicity ready-made in inner sense, but it produces it by affecting inner sense.

<t83> So the I which I think is distinct from the I which intuits itself — even though I can at least conceive the possibility of a different kind of intuition. But, given that they are distinct, how can the two be one and the same subject? So how can I say the following? — ‘I, as intelligence and thinking subject, know myself as the object which is thought, in that I am given to myself as something over and above what is contained in intuition; and yet, like other phenomena, I am given to myself, not as something given to the understanding, but as I appear to myself.’ But these questions are no more or less difficult than the question of how I can be an object to myself at all, and in particular an object of intuition [B156] and inner perceptions.

<t84> However, it can be clearly shown that this must actually be the case, by the following considerations. It has to be accepted that space is nothing other than the form of appearances of outer sense. Now since time is not an object of outer intuition, the only way we can make it conceivable to ourselves is by means of the image of a line, in so far as we draw it out. If we did not represent it in this way, we would be quite unable to know that it had only one dimension. Similarly, in the case of all our inner perceptions, we must always derive the determination of periods of time, and also points in time, from changes presented to us by outer things. So, given that the determinations of inner sense are appearances in time, they must be ordered in exactly the same way as we order the appearances of outer sense in space. Therefore, if we accept that outer appearances give us knowledge of objects only in so far as we are outwardly affected, then we must also admit that inner sense gives us intuitions of our selves only as we are inwardly affected by our selves. In other words, as far as inner intuition is concerned, we know our own subject only as an appearance, and not as it is in itself.*

<t86> [B157] §25

On the other hand, in the transcendental synthesis of the multiplicity of representations in general, and hence in the synthetic originative unity of apperception, I am conscious of my self, not as I appear to myself, still less as I am in myself, but only that I exist. This representation is a thought, not an intuition. In order to know ourselves, it is not enough for there to be the activity of thought which brings the multiplicity of any possible intuition under the unity of apperception — we also require a particular kind of intuition, through which this multiplicity is given. So my own existence is not an appearance, and still less is it a mere illusion. However, the determination of my existence* [B158] can take place only in accordance with the form of inner sense, in the particular way in which the multiplicity which I unify is given in inner intuition. Hence I have no knowledge of myself as I am, but merely as I appear to myself.

<t88> So consciousness of the self is far from being knowledge of the self, since it leaves out all the categories, which make up the thought of an object in general by unifying the multiplicity in a single apperception. In the case of my knowledge of an object distinct from myself, I require not only the thought of an object in general (which is thought through the categories), but also an intuition to make this general concept determinate. Similarly, in order to have knowledge of my self, I require not only consciousness (or my thinking my self), but also an intuition of the multiplicity in me, to make this thought determinate. I exist as an intelligence which is conscious only of its power of unification. But [B159] with respect to the multiplicity which it is to unify, it is subject to a limiting condition, which is called inner sense. That is, this unification can be intuited only in accordance with time-relations, which lie completely outside the concepts of the understanding as such. Consequently, this intelligence can know itself only as it seems to itself by reference to an intuition; and the intuition cannot be an intellectual one provided by the understanding itself. The intelligence cannot know itself as it would if its intuition were intellectual.

<t89> §26

In the Metaphysical Deduction, I proved the apriori origin of the categories in general, through their complete correspondence with the universal logical functions of thought. In the Transcendental Deduction, I have established their possibility as apriori knowledge of objects of intuition in general (§§20–21). Now I must explain how we can know apriori, through the categories, any objects whatever that could come before our senses. Indeed, I shall explain how we can know, not just the form of their intuition, but the laws of their interconnection, so that we can, as it were, lay down the law to nature, and even make nature possible. [B160] If the categories could not fulfil this function, it would be impossible to explain how everything that could ever come before our senses must be subject to laws which have their origin apriori in the understanding alone.

<t90> First of all, I should note that by the synthesis of apprehension, I mean putting together the multiplicity in a single empirical intuition. Without this, there could be no perception, or empirical consciousness of the intuition as an appearance.

<t91> We have apriori forms of both outer and inner sensory intuition in the representations of space and time. The synthesis of the apprehension of the multiplicity of appearance must always conform to these, because synthesis itself can take place only in accordance with this form. But space and time are represented apriori, not merely as forms of sensory intuition, but as intuitions themselves, also containing a multiplicity. So they are represented together with the determination of the unity of this multiplicity which they contain (see the Transcendental Aesthetic).*

<t93> Thus [B161] the unity of the synthesis of the multiplicity (whether outer or inner) is itself already given apriori as the precondition for the synthesis of any apprehension, along with (but not in) these intuitions of space and time. The same is therefore also true of a unification, to which everything that is to be represented as determined in space and time must conform. However, this synthetic unity cannot be anything other than the unity of the unification of the multiplicity of a given intuition in general in an originative consciousness. The unification is carried out in accordance with the categories, and it applies only to our sensory intuition. It follows that all synthesis is subject to the categories. But perception itself is possible only through synthesis, and since experience is knowledge through interconnected perceptions, the categories are preconditions for the possibility of experience, and are therefore also valid apriori of all objects of experience.

<t94> [B162] So, for example, if I turn the empirical intuition of a house into a perception by apprehending its multiplicity, my apprehension is grounded in the necessary unity of space, and of outer sensory intuition in general. I so to speak draw the shape of the house in accordance with this synthetic unity of the multiplicity in space. But if I leave the form of space out of account, exactly the same synthetic unity has its place in the understanding. It is the category of the synthesis of the homogeneous in an intuition in general — in other words, the category of quantity. So the synthesis of apprehension (perception, that is) must be completely in accordance with this category.*

<t96> To give another example: if I perceive the freezing of water, I apprehend two states (fluidity and solidity) as standing in a temporal relation to one another. But this appearance is grounded in time, in so far as the appearance is an inner intuition. [B163] So I necessarily represent the synthetic unity of the multiplicity in time; and without this unity, the temporal relation could not be given in an intuition as determined in respect of succession in time. But this synthetic unity is the apriori precondition for me to be able to unify the multiplicity of an intuition in general. So if I leave out of account the permanent form of my inner intuition, namely time, I am left with the category of cause. When I apply the category of cause to my sensibility, I use it to determine everything that happens in time in general in respect of its relation. Therefore the apprehension of such an event, and hence the event itself considered as a possible perception, is subject to the concept of the relation of effects and causes. The same goes for all other cases.

<t97> Categories are concepts which prescribe apriori laws to appearances, and hence to nature as the sum total of all appearances (or nature considered in its material aspect). But this means that these laws are not derived from nature, nor do they accommodate themselves to nature as their pattern, otherwise they would be merely empirical. So the question then arises: How are we to make sense of the fact that nature must accommodate itself to apriori laws? In other words, how can these laws determine the interconnection of the multiplicity of nature apriori, and not be derived from nature? Here is the solution to this puzzle.

<t98> [B164] It may seem strange that the laws of appearances in nature must agree with the understanding and its apriori form, namely its power to unify the multiple in general. But it is no stranger than the fact that the appearances themselves must agree with the apriori form of sensory intuition. For laws do not exist in appearances, but only relative to the subject in which the appearances inhere, provided that the subject has an understanding — just as appearances do not exist in themselves, but only relative to the same being, provided that it has senses.

<t99> Things in themselves will necessarily obey their own laws, independently of whether or not they are known by an understanding. But appearances are only representations of things, and it is unknown what these things might be in themselves. As mere representations, the only law of interconnection they are subject to is that which is prescribed by the faculty which connects them. The faculty which connects the multiplicity of sensory intuition is the imagination; and the imagination depends on the understanding for the unity of its intellectual synthesis, and on sensibility for the multiplicity of its apprehension. Now all possible perception depends on the synthesis of apprehension, and the synthesis of apprehension, which is an empirical synthesis, depends in turn on the transcendental synthesis, and hence on the categories. So it follows that all possible perceptions are subject to the categories for their unification, and hence the same is true of absolutely anything that can ever attain empirical consciousness — in other words, [B165] all appearances of nature.

<t100> Nature, considered merely as nature in general, depends on the categories as the originative basis for its necessary conformity to laws (nature considered in its formal aspect). However, the pure faculty of understanding cannot, through the categories alone, prescribe to appearances apriori laws which go beyond what is essential for a nature in general to be a system of law-governed appearances in space and time. Since particular laws concern appearances which are empirically determined, they cannot be derived in all their detail from the categories, even though they are all subject to them. Experience must be added for us actually to come to know them. But only the apriori laws tell us about experience in general, and about what can be known as an object of experience.

<t101> §27

We cannot think any object, except through categories; and we cannot know any object we have thought, except through intuitions corresponding to those concepts. Since all our intuition is sensory, this knowledge is empirical, in so far as the object of knowledge is given. But empirical knowledge [B166] is experience. So it follows that the only apriori knowledge possible for us is knowledge of objects of possible experience.*

<t103> But although this knowledge is confined to objects of experience, it is not on that account all derived from experience. The pure intuitions and the pure concepts together make up the elements of knowledge, and they are found apriori within us.

<t104> There are only two ways in which it is possible to think a necessary agreement of experience with the concepts of its objects:

• either experience makes these concepts possible;
• or these concepts make experience possible.

[B167] The first alterative is ruled out in the case of the categories (as also in the case of pure sensory intuition), since they are apriori concepts, and hence independent of experience. To claim that they had an empirical origin would be a sort of spontaneous generation.

<t105> So only the second alternative remains. It is, as it were, a system of the epigenesis of pure reason — in other words, the understanding supplies the categories, which contain the foundation of the possibility of all experience in general. In the next chapter (on the transcendental use of the faculty of judgment), I shall say more about how the categories make experience possible, and what axioms of the possibility of experience they supply in their application to appearances.

<t106> Someone might wish to propose a compromise between the two ways I have mentioned above as the only possible ones. It might be claimed that the categories are neither self-thought apriori first principles of our knowledge, nor derived from experience, but that they are subjective. In other words, they are natural dispositions to thought which are planted in us at the very moment of our coming into existence. Our creator has set them up in such a way that their application corresponds exactly to the laws of nature which experience obeys. This would be a kind of preformation system of pure reason.

<t107> An immediate objection is that, on this hypothesis, there is no limit to the number of predetermined dispositions which must be presupposed in order to cater for future judgments. But the decisive objection against this proposed [B168] middle way is that, if it were true, then the categories would lack the necessity which belongs essentially to the concept of them.

<t108> For example, the concept of cause expresses the necessity of a consequence on the assumption of a certain precondition. But it would be false if it depended merely on a subjective necessity, arbitrarily planted in us, of connecting particular empirical representations in accordance with such a rule of causal relation. I would not be able to say: ‘The effect is connected with the cause in the object,’ (that is, necessarily connected), but only: ‘I am so constituted that I cannot think this representation as connected in any other way.’

<t109> This is precisely what the sceptic wants most. It turns all our insight depending on the supposed objective validity of our judgements into nothing other than sheer illusion. Furthermore, there would be no lack of people who would refuse to admit even this subjective necessity as applying to themselves, since it has to be felt. At the very least, there is no scope for arguing with anyone about something which depends merely on the way they are constituted as a subject.

<t110> Brief Summary of this Deduction

This deduction is the exposition of:

• the pure concepts of the understanding (together with all theoretical apriori knowledge) as principles of the possibility of experience;
• experience as the determination of appearances in space and time in general;
• this determination (which has its source in the principle of the originative synthetic unity of apperception) as the form of the understanding in relation to space and time (which are the originative forms of sensibility).

<t111> I have considered division into numbered sections necessary up to this point, because I was dealing with the fundamental concepts. Now that I am going to explain their application, I can dispense with numbered sections, and continue my exposition without such breaks.

<s1>[B169] The Transcendental Analytic

The structure of general logic corresponds exactly to the division between the higher cognitive faculties. These are understanding, judgment, and reason. So, in its analytic part, the discipline of logic deals with concepts, judgments, and inferences, exactly in accordance with the functions and order of these cognitive faculties — though we usually use the term ‘understanding’ in a wider sense, to cover all three.

<s2> [B170] This purely formal logic ignores the content of knowledge (whether pure or empirical), and is concerned only with the form of thought (i.e. inferential knowledge) in general. Consequently, in its analytic part, it can also cover the basic set of rules which reason must obey. This is because the form of reason has its own fixed prescription, which we can have insight into apriori, simply by analysing rational functions into their elements, and without considering the particular nature of the knowledge involved.

<s3> Transcendental logic cannot imitate general logic in such an analysis, since it is restricted to a specific content, namely pure apriori knowledge. For it emerges that the transcendental use of reason is not objectively valid at all, and hence does not belong to a logic of truth, i.e. to the Analytic. Instead, as a logic of illusion, it requires a separate part of the curriculum, called the Transcendental Dialectic.

<s4> So understanding and judgment do belong to the analytic part of transcendental logic, because it contains the set of rules for their objectively valid, and hence true use. Only reason is utterly dialectical, in its ambition to discover something about objects apriori, and to extend knowledge beyond the limits of possible experience. [B171] Its illusory assertions are utterly incompatible with the sort of rules the Analytic must contain.

<s5> So the Analytic of Axioms will be a set of rules only for the faculty of judgment. They tell it how the concepts of understanding, which contain the precondition for rules apriori, are to be applied to appearances. Consequently, while I am discussing what are properly the axioms of understanding, I shall indicate my purpose more accurately by calling it the doctrine of judgment.

If the understanding in general is defined as the faculty of rules, then judgment is the faculty of subsuming under rules — that is, of deciding whether or not something falls under a given rule (or is an instance to which a given law applies). General logic does not and cannot include any prescriptions for judgment. For since it takes no account of any content of knowledge, the only thing left for it to do is to dissect analytically [B172] the mere form of knowledge in concepts, judgments, and inferences, and thus to establish formal rules for all use of the understanding.

<s7> Now if logic aimed to show, quite universally, how one is to subsume things under these rules (i.e. to decide whether something comes under them or not), then this could be done only by means of yet another rule. But precisely because it is a rule, the faculty of judgment would need a completely new instruction as to how to apply it. So it emerges that, while the understanding is capable of being taught and educated through rules, judgment is a special innate gift, which cannot be taught at all, but only exercised.

<s8> Hence judgment is also the essential ingredient of so-called ‘mother wit’, which no teaching can replace the lack of. Teaching can provide people who have limited understandings with abundant rules drawn from the insights of others, and, as it were, graft these rules into their understandings. However, the ability to take advantage of these rules must lie within the learners themselves. If they lack the natural gift of judgment, they will always be liable to misapply any rule they may be prescribed for how to take advantage of rules.*

<s10> So a doctor, a [B173] lawyer, or a political scientist can have many fine medical, judicial, or political rules in their heads, to the extent that they themselves can teach their disciplines from first principles; yet they can easily go wrong in the application of these rules. One way they can go wrong is because they lack innate judgment (though not understanding); and although they have insight into the general in abstract, they cannot decide whether a particular case comes under the general. The other way they can go wrong is because they are not sufficiently trained to make such judgments through examples and case studies.

<s11> The one great benefit of examples is that they sharpen the faculty of judgment. But as far as the correctness and precision of the insights of the understanding are concerned, examples are usually harmful, since it is rare that they completely fulfil the conditions specified in a rule (as particular cases falling within the terms of the rule). In addition, examples often make the understanding less inclined to strive for insight into its rules in general, despite the fact that its rules are self-sufficient, and do not depend on the particular circumstances of experience. The consequence is that we tend to use the rules of understanding as a check-list rather than as a set of fundamental axioms. So examples are the [B174] baby-walker of judgment; but no-one can do without them if they lack judgment as an innate gift.

<s12> Now although general logic cannot give any prescriptions to judgment, the situation is quite different with transcendental logic — so much so, that the essential function of transcendental logic seems to be that of correcting or confirming the faculty of judgment in its use of pure understanding, through specific rules. For if the role of philosophy is to extend the scope of understanding in the realm of pure apriori knowledge, and hence to be a discipline with positive content, then it seems that philosophy is quite unnecessary — or rather that it is wrong to bring it in at all. This is because, despite all the efforts made up till now, little or no territory has been gained by using philosophy. But if philosophy is a critique, then its sharp-wittedness and technique of scrutiny will put it in demand for preventing errors of judgment in the use of the few pure concepts of understanding that we have (even though its usefulness is then only negative).

<s13> However, transcendental philosophy has a unique feature: not only can it point out the rule which is given in the relevant pure concept of understanding (or rather the universal precondition for rules), but it can also point out apriori the instance to which the rules must be applied. [B175] This makes transcendental philosophy superior in this respect to all other disciplines (except maths). The source of its superiority lies precisely in the fact that it deals with concepts which must relate to their objects apriori. Hence its objective validity cannot be established aposteriori, since any attempt to establish its validity in this way would completely fail to do justice to its exalted status. Instead, transcendental philosophy must specify not only the concepts, but also the universal but sufficient defining characteristics of the preconditions under which objects can be given in conformity with these concepts. For otherwise the concepts would lack any content, and hence would be mere logical forms rather than pure concepts of understanding.

<s14> Now this transcendental doctrine of judgment will contain two chapters. The first is the Schematism of the Pure Understanding, which deals with the sensory preconditions under which alone pure concepts of understanding can be used. The second is the Axioms of the Pure Understanding, which deals with the synthetic judgments which flow apriori from pure concepts of understanding under these preconditions, and which are the basis for all other apriori knowledge.

<s15>[B176] The Transcendental Doctrine of Judgment

Whenever an object is brought under a concept, the representation of the object must have something in common with the representation of the concept. In other words, the concept must include whatever is represented as coming under it in the object. For this is precisely what is meant by the maxim that an object is included under a concept. For example, the empirical concept of a plate has something in common with the pure geometrical concept of a circle, in that the circularity which is thought in the plate can be intuited in the circle.

<s16> Now pure concepts of understanding can never be found in any intuition, since they have nothing at all in common with empirical intuitions (or indeed with sensory intuitions in general). So how is it possible for empirical intuitions to come under pure concepts, and hence for a category to be applied to appearances? For no-one will say that a particular category, for example that of causality, could also be discerned by the senses, [B177] and be included in appearance. And this question, which is so natural and yet so profound, is the essential reason which makes a transcendental doctrine of judgment necessary — namely so that it will be shown, quite generally, how it is possible for pure concepts of understanding to be applied to appearances. In no other discipline is it necessary to give a detailed explanation of how general concepts apply to its subject matter, because the concepts through which the subject matter is thought in general are not so heterogeneous and distinct from those which represent it as it is given in concrete detail.

<s17> Now it is obvious that there must be some third thing, which has to have something in common both with the category and with the appearance, and which makes it possible to apply the former to the latter. This mediating representation will have to be pure (free from anything empirical), and yet both intellectual and sensory. Such a thing is the transcendental schema.

<s18> A concept of the understanding contains pure synthetic unity of a multiplicity in general. Time contains an apriori multiplicity in pure intuition, since it is the formal precondition of the multiplicity of inner sense, and hence of the connecting together of all representations. Now a transcendental determination of time has something in common with a category (which brings about its unity), in so far as it is universal and is grounded in an apriori rule. [B178] On the other hand, it has something in common with an appearance, in so far as time is involved in every empirical representation of the multiplicity. Hence a category can be applied to appearances through the mediation of a transcendental determination of time, since, as the schema of the concepts of understanding, it mediates the bringing of appearances under the category.

<s19> After what has been proved in the Deduction of the Categories, I hope that no-one will be in any doubt over the answer to the following question: namely whether these pure concepts of the understanding are merely of empirical use, or whether they are also of transcendental use. To put it another way: whether they relate to appearances apriori only as preconditions of a possible experience, or whether, as preconditions of the possibility of things in general, they can be extended to objects in themselves, without any restriction to what we perceive through our senses.

<s20> For we saw that concepts cannot exist, or have any significance whatever, where no object is given, either for the concepts themselves, or at least for the elements of which they are composed. Hence concepts certainly cannot extend to things in themselves, without reference to whether or how these things might be given to us. We also saw that the only way in which objects are given to us is through modulation of our senses. Finally, we saw that pure apriori concepts must contain apriori, not only the [B179] function of the understanding instantiated in the category, but also formal preconditions of sensibility, namely those of inner sense. These preconditions include the universal and necessary precondition for a category to be applicable to any object.

<s21> I shall use the expression ‘the schema of the concept of understanding’ for this formal and pure precondition of sensibility, to which the application of the concept of the understanding is restricted. And I shall use the expression ‘the schematism of pure understanding’ for what the understanding does with these schemata.

<s22> In itself, a schema is never anything other than a product of the imagination. However, a schema must not be confused with an image, since the only goal of the synthesis performed by the imagination is not a single intuition, but unity in the process of reducing sensibility in general to something specific. So if I place five points in a row, thus: · · · · · — then this is an image of the number five. On the other hand, if I think only of a number in general (which could be five or a hundred), then this thought is the representation of a method for representing a multitude (e.g. a thousand) by means of an image which corresponds to a particular concept, rather than the image itself. If it were the image of a thousand, I would hardly be able to review it, and compare it with the concept. So what I call the ‘schema’ of a concept is this representation of a general process by which the imagination generates an image corresponding to a concept.

<s23> [B180] In fact, our pure sensory concepts are based on schemata, and not on images of objects. No image of a triangle in general could ever correspond adequately to our concept of it. It could never do justice to the generality of the concept, because the concept is valid for all triangles, whether right-angled, acute, etc., whereas an image would always be limited to one of this range of possibilities. The schema of a triangle can exist only in thought, and it amounts to a rule determining how the imagination is to synthesise shapes in space.

<s24> It is even less the case that a particular object of experience (or an image of it) ever fully encapsulates its empirical concept. Rather, the concept always relates immediately to the schema of the imagination, as a rule for generating a particular intuition in accordance with a specific general concept. The concept of a dog indicates a rule, in accordance with which my imagination has the general ability to draw the figure of such a four-footed animal, without being restricted to any one particular figure which experience presents me with, or even to any possible particular image which I can form.

<s25> This schematism of our understanding, in respect of appearances and their form alone, is an art hidden in the depths of the human soul. It is only with difficulty that we can ever divine its actual [B181] manner of working by natural means, and lay it bare before our eyes. All we can say is that an image is a product of the empirical faculty of the productive imagination, whereas a schema of sensory concepts (such as of shapes in space) is a product of pure imagination apriori, and is a sort of outline sketch. It is only through and in accordance with the schema that images first become possible. However, the images can never be connected with the concept other than through the mediation of the schema which they indicate; and in themselves they are not fully congruent to the schema.

<s26> By contrast, the schema of a pure concept of understanding is something which cannot be brought into relation with any image at all. The schema is only the pure synthesis, in conformity with a rule of unity for concepts in general, which the category expresses. It is a transcendental product of the imagination, which deals with the determination of inner sense in general, in accordance with the preconditions imposed by its form (namely time) on all representations. This is because representations must be connected together apriori under a single concept, in order to conform to the unity of apperception.

<s27> I shall not waste time on a tedious and boring analysis of what is required for transcendental schemata of pure concepts of understanding in general. Instead, I shall set them out in the order of the categories, and in connection with them.

<s28> [B182] The pure image of all quanta which are objects of outer sense is space; and that of all objects of the senses whatever is time. The pure schema of quantity, as a concept of the understanding, is number, which is a representation which treats as a whole the successive addition of one unit to another (of the same kind). Thus number is nothing other than the unity of the synthesis of the multiplicity of a uniform intuition in general, because I create time itself in the apprehension of intuition.

<s29> In the pure concept of the understanding, reality is that which corresponds to a sensation in general, and hence is that whose concept in itself indicates a being (in time). Negation is that whose concept represents an absence of being (in time). Thus the opposition between the two arises from the contrast between one and the same time being a filled or an empty time. But time is only the form of intuition, and hence of objects as appearances. Consequently, that in appearances which corresponds to sensation is the transcendental matter of all objects as things in themselves (i.e. thingliness, or reality).

<s30> Now every sensation has a quantity or degree to which it fills one and the same time, i.e. inner sense in respect of one and the same representation of an object. This can be greater or less, until it disappears into nothing (= 0 = negation). Hence there is a relation and connection between reality and negation, or rather [B183] a transition from the one to the other, which makes it possible to represent every reality as a quantum. And the schema of a reality, as the quantity of something in so far is it fills time, is just this continuous and uniform production of the reality in time. One can either start with a sensation which has a certain degree of reality, and then diminishes over time to a point when it disappears; or one can start with negation, and then it gradually increases to its full quantity.

<s31> The schema of substance is the permanence of the real in time. In other words, it is the representation of substance as a substrate of the empirical determination of time in general, and hence as that which remains the same, while everything else changes. (Time does not pass; but the existence of changeable things passes away in time. So, since time is itself unchanging and enduring, what corresponds to it in appearance is that which is unchanging in its existence, namely substance. And it is only by reference to substance that it can be determined whether appearances are successive or co-existent in time.)

<s32> The schema of cause, and of the causality of a thing in general, is the real which, whenever it is supposed, something else always follows. So it consists in the successiveness of the multiplicity, in so far as it is subject to a rule.

<s33> The schema of community (mutual interaction), or the reciprocal causality of substances in respect of their accidents, is the simultaneity of the determinations [B184] of the one with those of the other, in accordance with a general rule.

<s34> The schema of possibility is the correspondence of the synthesis of different representations with the preconditions of time in general. For example, contradictories cannot exist in one and the same thing at the same time, but only one after another. So this schema is the determination of the representation of a thing to some time or other.

<s35> The schema of actuality is existence at a determinate time.

<s36> The schema of necessity is the existence of an object at every time.

<s37> It can be seen from all this, that the schema of each category contains and makes representable the following:

• in the case of the schema of quantity, the production (synthesis) of time itself, through the successive apprehension of an object;
• in the case of the schema of quality, the synthesis of sensation (perception) with the representation of time, or the filling of time;
• in the case of the schema of relation, the relationship of perceptions to each other at every time (that is, in accordance with a rule for the determination of time);
• finally, in the case of the schema of modality and its categories, time itself, as the correlate of determining whether and how an object belongs to time.

Hence the schemata are nothing other than apriori determinations of time in accordance with rules. These rules apply to all possible objects, and (following the order of the categories), they concern the series of time, the content of time, the order of time, [B185] and finally the totality of time.

<s38> Now from this it is clear that the schematism of the understanding through the transcendental synthesis of the imagination amounts to nothing other than the unity of every multiplicity of intuition in inner sense. Hence it amounts indirectly to the unity of apperception, as the function which corresponds to the inner sense (which is merely receptive). Thus the schemata of the pure concepts of understanding are the true and only preconditions for providing these concepts with a relationship to objects, and hence for giving them meaning.

<s39> So, ultimately, the categories have no application outside any possible experience. Their only role is to subject appearances to the universal rules of synthesis, grounded in a synthesis which is apriori necessary, because it is necessary for all consciousness to be unified in an originative apperception. In this way, the categories make appearances amenable to holistic connection in a single experience.

<s40> However, all our knowledge lies within the totality of all possible experience. Transcendental truth consists in this universal relationship to possible experience, and it precedes and makes possible all empirical truth.

<s41> Another observation is that, although it is the schemata of sensibility which first actualise the categories, [B186] yet they themselves also restrict them. That is, they limit them to requirements which lie outside the understanding — namely in sensibility. Hence the schema is essentially only the phenomenon, or the sensory concept of an object, in conformity with the category. (Number is the quantity of phenomena, sensation is the reality of phenomena, the constant and permanent in things is the substance of phenomena, — and eternity is the necessity of phenomena, etc.)

<s42> Now if we leave out a restricting requirement, it might seem that we are extending a previously curtailed concept. So the categories, in their pure meaning and without any requirements arising from sensibility, should be valid of things in general as they are (instead of their schemata representing things only as they appear). They should therefore have a meaning which was independent of any schemata, and had a much wider extension.

<s43> In fact, the pure concepts of understanding do indeed retain some meaning, even after the removal of any sensory requirement. However, it is the purely logical meaning that there is a unity of representations, and nothing else. But no object of the representations is given, and hence no meaning which could result in a concept of the object.

<s44> Take the concept of substance, for example. If the sensory determination of permanence is left out, it would mean nothing more than a something which can be thought as a subject, without being a predicate of something else. But I cannot do anything with this representation, since it tells me [B187] nothing at all about the determinations which a thing must have in order to count as a primary subject of this sort.

<s45> So, without schemata, the categories are only functions of the understanding for concepts, and they do not represent any object. But meaning consists in reference to an object, and the categories acquire this meaning from sensibility, which actualises the understanding, while at the same time restricting it.

<ai1>[B187] The Transcendental Doctrine of Judgment

In the previous chapter, I considered only the general preconditions for the transcendental faculty of judgment to have the right to use the pure concepts of understanding for making synthetic judgments. My task is now to specify the judgments which the understanding actually makes apriori, within the limits set by the critical philosophy. I need to lay them out systematically, in accordance with their interrelations; and my table of categories must undoubtedly provide the natural and infallible guidance in this. For all pure apriori knowledge of the understanding must consist in the application of just these categories to possible experience. So it is the relation of the categories to sensibility in general [B188] which will reveal all the transcendental axioms of the use of the understanding, completely and in a system.

<ai2> Apriori axioms, or ‘foundational propositions’, are called ‘foundational’, not merely because they contain within themselves the foundation for other judgments, but also because they themselves are not founded upon any superior or more general knowledge. However, this special characteristic does not exempt them from all proof. Certainly a proof could not be carried further on the objective side, since an axiom is the foundation for all knowledge of its object. But this does not mean that it is impossible to construct a proof from the subjective sources of the possibility of knowledge of an object in general. Indeed, it is necessary to do so, since otherwise the axiom would attract the strongest suspicion of being merely an ungrounded assertion.

<ai3> Secondly, I shall confine myself to the axioms which relate to the categories. So my restricted area of inquiry excludes the principles of the Transcendental Aesthetic, according to which space and time are the preconditions for the possibility of all things as appearances; and it also excludes their negative side, namely that they cannot apply to things in themselves.

<ai4> Similarly, mathematical axioms are not a part of this system, because they derive only from intuition, and not from the pure concepts of the understanding. [B189] However, the possibility of mathematical axioms necessarily has a place here, because they are synthetic apriori judgments. But it is not to prove their soundness and self-evident certainty (since this needs no proof at all), but only to make comprehensible and to deduce the possibility of evident apriori knowledge of this nature.

<ai5> However, I must also say something about the axiom of analytic judgments, and contrast it with the synthetic axioms which I am essentially concerned with. It is precisely this contrast which frees the theory of synthetic axioms from all misunderstanding, and lays their special nature clearly before the eyes.

<ai6> The System of the Axioms of Pure Understanding

Whatever the content of our knowledge, and however it relates to its object, the universal (though negative) precondition of absolutely all our judgments is that they are not self-contradictory. Any self-contradictory judgment is intrinsically nothing, even without reference to its object. However, [B190] even if a judgment contains no contradiction, yet it can combine concepts in a way which is not found in the object, or without there being any ground, whether apriori or aposteriori, which would justify such a judgment. So a judgment can be either false or groundless, despite being free of any internal contradiction.

<ai7> The proposition that ‘Nothing has a predicate which contradicts it’ is called the Principle of Contradiction, and it is a universal (though merely negative) criterion of all truth. However, it belongs merely to logic, because it is valid of any item of knowledge, simply as knowledge in general, and irrespective of its content. It says that the contradiction entirely annihilates and cancels the knowledge.

<ai8> However, it can also be used positively — that is, not simply to eliminate falsehood and error (in so far as it arises from a contradiction), but also to know truth. For if a judgment is analytic (whether negative or affirmative), it must always be possible for its truth to be sufficiently known on the basis of the principle of contradiction. For it is always correct to deny the opposite of what already exists and is thought in the knowledge of the object as its concept; whereas its concept itself must necessarily be asserted of it, [B191] because its opposite would contradict the object.

<ai9> Consequently, we must accept the principle of contradiction as the universal and completely sufficient principle of all analytic knowledge. However, its authority and usefulness do not extend as far as its being a sufficient criterion of truth. For the fact that no knowledge can go against it without annihilating itself certainly makes it a necessary condition of our knowledge, but not the basis for determining its truth. Since I am now essentially concerned with the synthetic part of our knowledge, I shall of course always be careful not to go against this inviolable axiom, but I can never expect from it any enlightenment as to the truth of synthetic knowledge.

<ai10>However, despite the fact that this famous axiom is devoid of content and merely formal, there is another way of formulating it, involving a synthesis which is introduced out of carelessness, and quite unnecessarily. This formulation goes: ‘It is impossible for something to be and not to be at the same time.’ One objection to it is the redundant addition of its self-evident certainty (through the word ‘impossible’), when this should be self-evident from the proposition. More seriously, the proposition is infected by the restriction to time, so that it says something like: ‘A [B192] thing A which is B cannot at the same time be not-B; but it can easily be both (B or not-B) successively.’ For example, a person who is young cannot be old at the same time; but one and the same person can easily be young at one time, and not-young (i.e. old) at another time. But since the principle of contradiction is a merely logical proposition, it must not limit its claims to time relationships; and hence a formulation such as the above goes completely against its purpose.

<ai11> The source of the misunderstanding is simply this. First, the predicate of a thing is separated from the concept of the thing; and then the opposite of this predicate is connected with the predicate. But this never gives rise to a contradiction with the subject, but only with its predicate which is connected with the subject synthetically. And indeed, a contradiction arises only when the first and second predicates are affirmed at the same time. If I say: ‘An unlearned person is not learned’, the qualification ‘at the same time’ must be added, since someone who is unlearned at one time can perfectly well be learned at another time. But if I say: ‘No unlearned person is learned’, then the proposition is analytic. This is because the property (of unlearnedness) is now one of the components of the concept of the subject, and thus the negative proposition is immediately obvious from the principle of contradiction, without the qualification ‘at the same time’ needing to be added. This is also the reason why I changed the formulation [B193] of the principle above, so that it clearly expresses the nature of an analytic proposition.

<ai12> The System of the Axioms of Pure Understanding

Explaining the possibility of synthetic judgments is a task which general logic has nothing at all to do with — it doesn’t even need to know its name. But in a transcendental logic, it is the most important business of all; and even the only one, if we are considering the possibility of synthetic apriori judgments, and also the preconditions and scope of their validity. For on completing this task, transcendental logic can fully satisfy its goal of determining the scope and limits of pure reason.

<ai13> In an analytic judgment, I stay with the given concept, in order to discern something about it. If it is an affirmative judgment, I attribute to this concept only what was already thought in it; and if it is a negative judgment, I exclude only the opposite of the concept. But in synthetic judgments, I must go beyond the given concept, to consider its relation to something which is quite different from what was thought in the concept. [B194] So this relation is never one of identity or of contradiction, and hence not one such that the truth or falsehood of the judgment can be established by considering the judgment as it is in itself.

<ai14> Granted that one must go beyond a given concept in order to compare it synthetically with another concept, there must be a third thing, in which alone the synthesis of two concepts can take place. But what is this third thing which mediates all synthetic judgments? There is only one totality which includes all our representations, namely inner sense, and its apriori form, which is time. The synthesis of representations depends on the imagination; but their synthetic unity (which is required for judgment) depends on the unity of apperception. Thus the possibility of synthetic judgments must be sought in these three items, and the possibility of pure synthetic judgments in particular, since all of them contain the sources of apriori representations. Indeed, for these very reasons, they are necessary for there to be any knowledge of objects, since it depends entirely on the synthesis of representations.

<ai15> For knowledge to have objective reality is for it to relate to an object, which gives it sense and meaning. So if knowledge is to have such reality, it must be possible for an object to be given in some way or other. Without an object, a concept is empty; and although we have indeed thought something through the concept, [B195] we have not actually known anything through this thought, and we have merely been playing with representations. When I say that an object is ‘given’, I mean that it is presented directly in intuition, and not merely through the mediation of something else. So for an object to be given is nothing other than for its representation to relate to experience, whether actual or merely possible.

<ai16> The concepts of space and time are completely pure of anything empirical, and it is absolutely certain that they are represented completely apriori in the mind. Nevertheless, they would lack any objective validity or sense and meaning, unless it were established how they necessarily apply to objects of experience. Indeed, their representation is merely a schema, which is always related to the reproductive imagination. And it is the reproductive imagination which summons up the objects of experience, without which the concepts of space and time would have no meaning. And the same is true of every kind of concept.

<ai17> So it is the possibility of experience that gives objective reality to all our apriori knowledge. Now experience depends on the synthetic unity of appearances, that is, on a synthesis, in accordance with concepts, of the object of appearances in general. Without this synthesis, there would never be any knowledge, but only a confused jumble of perceptions. These would not fit together into any unitary network in accordance with rules of a thoroughly connected (possible) consciousness, and hence they would not fit into the transcendental and necessary unity of apperception.

<ai18> [B196] So experience has principles of its form underlying it apriori as its foundation, namely universal rules of unity in the synthesis of appearances. The objective reality of these rules, as necessary preconditions of experience, can always be shown in experience, and even in the possibility of experience. But without this relation to actual or possible experience, synthetic apriori propositions are completely impossible, because they have no third thing (namely a pure object) in which the synthetic unity of their concepts could demonstrate objective reality.

<ai19> We have so much a priori knowledge, expressed in synthetic judgments, about space in general, or about the figures which the productive imagination draws in it, that we actually need no experience at all for this knowledge. Nevertheless, it follows from the above that this knowledge would be nothing, and we would be dealing with a mere figment of the brain, if space were not to be considered as a precondition of the appearances which constitute the material for outer experience. Consequently, those synthetic judgments relate, if only indirectly, to possible experience — or rather to the very possibility of possible experience. And this is the sole foundation of the objective validity of their synthesis.

<ai20> Experience, as empirical synthesis, is the one way of knowing which gives reality to apriori synthesis; and it does so by virtue of its very possibility. Consequently, apriori knowledge also attains truth (correspondence [B197] with its object) only in so far as it includes nothing more than is necessary for the synthetic unity of experience in general.

<ai21> So the supreme principle of all synthetic judgments is: ‘Every object comes under the necessary preconditions of the synthetic unity of the multiplicity of intuition in a possible experience.’

<ai22> The way in which synthetic apriori judgments are possible is by relating the following to the possibility of experiential knowledge in general:

• the formal preconditions of apriori intuition;
• the synthesis of the imagination;
• the necessary unity of this synthesis in a transcendental apperception.

We can then say that the preconditions of the possibility of experience in general are at the same time preconditions of the possibility of objects of experience. This is why they have objective validity in a synthetic apriori judgment.

<ai23>The System of the Axioms of Pure Understanding

That there are any axioms at all in any area of knowledge, is due entirely to the pure understanding. It is not only the faculty of rules [B198] as to what happens, but it is also the very source of the axioms in accordance with which everything which can be presented to us only as an object necessarily comes under rules. For without rules, appearances could never supply knowledge of an object corresponding to themselves.

<ai24> Despite the fact that even the laws of nature are considered to be fundamental laws of the empirical use of understanding, nevertheless they bear the stamp of necessity. Hence there is at least the presumption that they are particular instances of foundations which are valid apriori and independently of any experience. But all laws of nature of every kind come under higher axioms of the understanding, in that they merely apply these axioms to particular instances of appearances. So it is only the axioms which supply the concept containing the general precondition and as it were the parameter for a rule. On the other hand, it is only experience which supplies the particular instance that comes under the rule.

<ai25> There is really no danger of confusing merely empirical axioms with axioms of the pure understanding, or the other way round. This confusion can easily be avoided, since it is easy to perceive the difference between the necessity arising from concepts (which is a mark of the pure understanding), and its absence from every empirical proposition, however general its validity. However, there are pure apriori axioms which I may not attribute exclusively to the pure understanding, because they are derived, not from pure concepts, but [B199] from pure intuitions (though by means of the understanding) — whereas the understanding is the faculty of concepts. Mathematics has the same sort of axioms, but their application to experience still always depends on the pure understanding — as also their objective validity, and even the possibility of such synthetic apriori knowledge (its deduction).

<ai26> Therefore I shall not include among my axioms those of mathematics. I shall however include those axioms which are the apriori foundation of the possibility and objective validity of mathematical axioms. Hence they are to be considered as the principle of the mathematical axioms; and they proceed from concepts to intuition, and not from intuition to concepts.

<ai27> In the application of the pure concepts of understanding to possible experience, the way their synthesis is carried out is either mathematical or dynamical, depending on whether the synthesis involves merely intuition, or the existence of an appearance in general. But the apriori preconditions for intuition in relation to a possible experience are absolutely necessary, whereas those for the existence of the object of a possible empirical intuition are in themselves only contingent. Hence the mathematical axioms can be called necessary without qualification (i.e. self-evident), whereas, although the dynamical axioms do indeed bear the stamp of apriori necessity, they do so only under the precondition of empirical thought in an experience, and hence through something else and [B200] indirectly. It follows that, although the certainty of the dynamical axioms (which depends on their universal relation to experience) is unaffected, they do not have the immediate self-evidence which is exclusive to the mathematical axioms. However, it will be easier to come to a judgment about this after reading the System of Axioms.

<ai28> The table of categories gives us natural guidance for drawing up the table of axioms, because the axioms are nothing other than rules for the application of the categories to objects. A complete list of the axioms of pure understanding is as follows:

<ai29> I have chosen these names deliberately, in order to emphasise the extent to which these axioms are more or less self-evident, and the differences in the ways they are applied. As will soon be shown, the first two sets of axioms, derived from the categories of quantity and quality, are significantly different from the other two. This goes both for their degree of self-evidence, [B201] and for the way they determine appearances apriori (as long as only the form of the first two is considered). Although they are both completely certain, the first two are immediately self-evident, whereas the second two require a reasoned proof. So I shall call the first set mathematical axioms, and the second set dynamical axioms.*

<ai32> It should be carefully noted that here I am no more concerned with [B202] the axioms of mathematics in the one case, than with the axioms of general (physical) dynamics in the other, but only with the axioms of pure understanding in relation to inner sense, whatever the representations given in it. For it is only through the axioms of pure understanding that all the others become possible. So I have given the axioms their names more by virtue of how they are applied, than by virtue of their content. I shall now proceed to consider them in the same order as they are laid out in the table.

<ai33> 1.

The principle of the Axioms of Intuition is: All intuitions are extensive quantities.

As far as their form is concerned, all appearances include an intuition in space and time, which is the apriori foundation of all of them. So they cannot be apprehended (i.e. they cannot be brought into empirical consciousness) except through the synthesis of the multiplicity, by means of which the representations of a particular space or time are generated — that is, except through the unification of that which is homogeneous, and the consciousness of [B203] the synthetic unity of this homogeneous multiplicity. Now the consciousness of a multiple homogeneity in intuition in general, in so far as it first makes the representation of an object possible, is the concept of a quantum. Thus even the perception of an object as appearance is possible only through the same synthetic unity of the multiplicity of the given sensory intuition, as that through which the unity of the unification of a multiple homogeneity is thought in the concept of a quantity. In other words, appearances are all quantities, and in particular extensive quantities, because as intuitions in space or time, they must be represented through the same synthesis as that through which space and time in general are determined.

<ai34> By an extensive quantity, I mean one such that the representation of its parts makes possible the representation of the whole, and hence necessarily precedes it. I cannot represent a line, however short, without first pulling it out in thought — that is, starting from a point and generating all its parts one after another, and thus first drawing this intuition. The same is the case with any stretch of time, however small. The only thing I think in it is the successive progression from one moment to the next, in which a determinate quantity of time is ultimately generated through all the instants and their being added together. Since pure intuition in all appearances is either space or time, [B204] every appearance, as intuition, is an extensive quantity, in that it can become known only through successive synthesis (from part to part) in apprehension. Therefore all appearances are already intuited as aggregates (a heap) of previously given parts. This is not true of all kinds of quantities, but only of those which are represented to us and apprehended by us as extensive.

<ai35> The mathematics of extension (geometry), together with its axioms, is founded upon this successive synthesis performed by the productive imagination in generating figures. Its axioms give apriori expression to the preconditions of sensory intuition, which are the necessary prerequisites for the schema of a pure concept of outer appearance — for example, that there can be only one straight line between two points; that two straight lines do not enclose any space; and so on. These are axioms which essentially involve only quanta as such.

<ai36> But as for quantity (i.e. the answer to the question: how many something is), there are strictly speaking no axioms, even though there are all sorts of propositions which are synthetic and immediately certain (they need no proof). The propositions that the result will be the same if the same number is added to the same number, or that the result will be the same if the same number is subtracted from the same number, are analytic. This is because I am immediately conscious that the [B205] act of producing the quantity is identical in each case. But these propositions are not axioms, since an axiom must be synthetic apriori.

<ai37> On the other hand, self-evident propositions about the relations between numbers are certainly synthetic, but they are not universal like those of geometry. So on this account they cannot be called axioms, but only numerical formulae. 7+5=12 is not an analytic proposition, since I do not think the number 12, either in the representation of 7, or in the representation of 5, or in the representation of combining them together. It is irrelevant that I must think 12 in the sum of the two, since a proposition is analytic only if I actually think the predicate in the representation of the subject. But even though it is a synthetic proposition, it is only singular.

<ai38> Here, in so far as it is a question simply of the synthesis of things of the same kind (namely units), this synthesis can take place only in one way, even though the application of these numbers is subsequently universal. Suppose I say, ‘It is possible to draw a triangle by means of three lines, of which two taken together are longer than the third.’ Here I have nothing but the function of the productive imagination, which enables the lines to be drawn longer or shorter, and hence to be put together with any angles whatever. By contrast, the number 7 can be generated only in a single way; and the same is true of the number 12, which is generated by synthesising it with the number 5. Such propositions must not be called axioms, [B206] because there would be infinitely many of them. Instead, they must be called numerical formulae.

<ai39> This transcendental axiom of the mathematics of appearances greatly extends our apriori knowledge. For it is this axiom alone that makes the perfect accuracy of pure mathematics applicable to objects of experience. Without this axiom, the applicability of mathematics to experience would not be self-evident in this way — indeed, the lack of it has been the source of much controversy. Appearances are not things in themselves. Empirical intuition is possible only through pure intuition (of space and time); and so what geometry says of the pure intuition of space is, without dispute, also valid of empirical intuition. Nor can this conclusion be avoided by saying that objects of the senses cannot conform to the rules of construction in space, for example on the grounds that lines or angles are infinitely divisible. For this would be to deny the objective validity of space, and with it the objective validity of the whole of mathematics; and one would no longer know why or how far mathematics is applicable to appearances.

<ai40> The synthesis of spaces and times, as the essential form of all intuition, is what makes possible at the same time:

• the apprehension of appearance; hence
• every outer experience; and consequently also
• all knowledge of the objects of experience.

So, what pure mathematics proves of space or time is also necessarily valid of the objects of experience.

<ai41> Any objections to this are merely sophistries of a wrongly taught [B207] reason, which erroneously tries to free the objects of the senses from the formal precondition of our sensibility. So, despite the fact that they are mere appearances, objects are represented as objects in themselves, which are given to the understanding. But if this were the case, there could certainly be no synthetic apriori knowledge of them at all, and hence there could be no such knowledge of them through pure concepts of space. And the science which determines these concepts, namely geometry, would itself be impossible.

<ap1> 2.

[B207] The principle of the Anticipations of Perception is: In all appearances, the real which is an object of sensation has intensive quantity, that is, a degree.

<ap2> Proof

Perception is empirical consciousness, that is, a consciousness in which there is also sensation. Appearances, as objects of perception, are not pure or merely formal intuitions like space and time, since space and time cannot be perceived in themselves. So in addition to pure intuition, appearances also contain the material for any object in general, through which something existent will be represented in space or time. This material is that which is real in sensation, and it is therefore a merely subjective representation. The only consciousness we can have of it is that the subject is affected by it, and that we relate it [B208] to an object in general.

<ap3> Now it is possible for there to be a gradual transition from empirical consciousness to pure consciousness, such that the real in empirical consciousness completely disappears, and all that remains is a formal apriori consciousness of the multiplicity in space and time. So it is also possible for there to be a synthesis which generates the quantity of a sensation, starting from a pure intuition = 0, up to any quantity of it whatever. Now this certainly cannot be an extensive quantity, since sensation in itself is not a representation of an object, and it does not include the intuition either of space or of time. Yet the sensation does have a quantity. This quantity is generated through the apprehension of the sensation, and the empirical consciousness of it can grow from nothing = 0, to its given size over a certain time. So it is an intensive quantity. And corresponding to the intensive quantity of sensations, all objects of perception must have an intensive quantity, since they include sensation. This intensive quantity is the degree of influence on the senses.

<ap4> Any knowledge through which one can know and determine apriori anything that belongs to empirical knowledge can be called an ‘anticipation’. Without a doubt, this is the sense in which Epicurus used his expression prolepsis. However, appearances include sensation (as the matter of perception), which can never be known apriori, and which therefore constitutes the essential difference between empirical and apriori knowledge. [B209] It follows that sensation is essentially that which cannot be anticipated at all.

<ap5> By contrast, we could give the name ‘anticipations of appearances’ to pure determinations in space and time (whether in respect of shape or of quantity), because they represent apriori everything that can ever be given in experience aposteriori. But suppose there is also something else which lets itself be known apriori in every sensation, as sensation in general, without any particular sensation being given. This ought to be called an ‘anticipation’ in a more eminent sense, since it seems contradictory to anticipate experience in that which belongs specifically to its matter, which one can extract only through experience. And this is what is actually the case here.

<ap6> In so far as apprehension is through sensation alone, it takes place in an instant (here I am not talking about a succession of many sensations). So it is an element of appearance which has no extensive quantity, since its apprehension is not a successive synthesis proceeding from parts to a whole representation. The absence of sensation in the same instant would represent the instant as empty, and hence = 0. Now the element of empirical intuition which corresponds to sensation is (phenomenal) reality; and that which corresponds to the lack of it is negation = 0. But every sensation [B210] is capable of diminution, and can decrease and gradually disappear. So in appearance, there is a continuous chain of many possible intermediate sensations between reality and negation; and the difference between these intermediate sensations is always less than the difference between any given sensation and zero, or utter negation. In other words, that which is real in appearance always has some quantity, even if it is not apprehended. This is because its apprehension takes place by means of sensation alone in an instant, and not through the successive synthesis of many sensations; and hence it does not proceed from parts to a whole. So it does indeed have a quantity; but not an extensive one.

<ap7> Now I call an intensive quantity any quantity which is apprehended only as a unity, and the quantifiability of which can be represented only as its distance from negation = 0. So everything that is real in appearance has an intensive quantity, or a degree. This reality can be considered as a cause — whether of sensation, or of some other reality in appearance, such as an alteration. In such cases, the degree of reality as cause is called a ‘moment’, for example, the ‘moment of gravity’. And the reason for this is precisely because the degree denotes only a quantity which is apprehended instantaneously, and not successively. But I touch on this here only in passing, since I am not yet dealing with causality.

<ap8> [B211] It follows that every sensation, and hence every reality in appearance, has a degree, however small it might be. Its degree is an intensive quantity, which can always become even smaller; and between reality and negation there is a continuous chain of possible realities, and of possible smaller perceptions. Every colour (for example red) has a degree, which, however small, is never the smallest possible; and the same holds universally, with heat, the moment of gravity, etc.

<ap9> The property of quantities which means that they have no smallest possible part (or no simple part) is called their continuity. Space and time are continuous quanta, because no part of them (points or instants) can be given, except as being contained between boundaries, and hence only in such a way that this part itself is again a space or a time. So space consists only of spaces, and time consists only of times. Points and instants are only boundaries, or positions defined by the limitation of space and time. But positions always presuppose the intuitions which must limit or define them. Neither space nor time can be put together out of mere positions, as component parts which could be given even before space or time. Continuous quantities can also be called flowing, because the synthesis (by the productive imagination) involved in their production is a process in time, and its continuity [B212] is usually given special emphasis through the term ‘flowing’ (or ‘elapsing’).

<ap10> Consequently, all appearances without exception are continuous quantities. They are extensive with respect to their intuition, and intensive with respect to their mere perception (or sensation, and hence their reality). If the synthesis of the multiplicity of appearances is interrupted, then the multiplicity is an aggregate of many appearances, and not essentially an appearance as a quantum. This aggregate is produced not through the simple continuation of productive synthesis of a certain sort, but through the repetition of a constantly ceasing synthesis. If I call 13 dollars a quantum of money, I do so correctly as long as I mean the value of a particular weight of fine silver. This is certainly a continuous quantity, since there is no smallest part, and every part could make up a coin containing enough matter for an even smaller one. But if by what I call 13 dollars I mean 13 round 1-dollar coins (whatever their silver content), then I am wrong to call it a quantum of dollars. Instead, I must call it an aggregate — that is, a number of coins. Now since unity must lie at the basis of all number, appearance as unity is a quantum, and as such it is always a continuum.

<ap11> Now if all appearances are continuous quantities, whether considered as extensive or as intensive ones, it might be thought easy to prove here, with mathematical self-evidence, [B213] the proposition that all alteration (the transition of a thing from one state to another) is also continuous. However, the causality of an alteration in general lies quite outside the limits of a transcendental philosophy, and presupposes empirical principles. For the understanding gives us no apriori information at all as to whether it is possible for there to be a cause which changes the state of the thing — that is, which determines it to the opposite of a certain given state. This is not simply because the understanding has no insight into its possibility, since we lack such insight in many cases of apriori knowledge. Rather, it is because alterability concerns only certain determinations of appearances; and only experience can tell us about these determinations; whereas their cause lies in that which is unalterable. Here we have before us nothing we can use except the pure basic concepts of all possible experience, which must exclude everything empirical. Consequently, we cannot prejudge general natural science without damaging the unity of our system, since this science is founded on certain basic experiences.

<ap12> However, we do not lack evidence of the great contribution this axiom of ours makes to anticipating perceptions. It even makes up for lack of perceptions, by ruling out false conclusions which might be drawn from their absence.

<ap13> [B214] Everything which is real in perception has a degree, and between that degree and nothing there is an infinite series of smaller and smaller degrees. Similarly, every one of our senses must have a particular degree of sensitivity to sensations. On these assumptions, there can be no perception, and hence also no experience, which could prove a total lack of any reality in the realm of appearance, whether directly or indirectly (however complicated the reasoning). In other words, experience can never provide any proof of empty space or an empty time. For firstly, a complete lack of reality in sensory intuition can never itself be perceived. And secondly, it cannot be deduced from any single appearance and the differentiation in its degree of reality. Nor is it ever legitimate even to assume it in order to explain the differentiation.

<ap14> Let us suppose that the whole intuition of a particular space or time is real through and through — i.e. no part of it is empty. Now every reality has its degree, which can reduce to nothing (emptiness) through infinitely many steps, while the extensive quantity of the appearance remains constant. Consequently, there must be infinitely many degrees with which space or time is filled. So the intensive quantity can be more or less in different appearances, even though the extensive quantity of the intuition is the same.

<ap15> [B215] I should like to give an example of this. There is a great difference in the quantity of various kinds of matter occupying the same volume. We perceive this difference partly through their moment of gravity, or weight; and partly through their moment of resistance to other matter colliding into them. Nearly all physicists agree in concluding that this volume (the extensive quantity of the appearance) must, in all kinds of matter, be empty to a greater or lesser extent.

<ap16> These scientists are mostly mathematicians and mechanists, who strongly assert that metaphysics should be avoided. But which of them ever realised that they were basing their conclusion merely on a metaphysical assumption? For they assume that the real in space (here I should not call it impenetrability or weight, since these are empirical concepts) is the same everywhere, and that it can be differentiated only by virtue of its extensive quantity, or amount.

<ap17> This assumption is merely metaphysical, because it cannot have any foundation in experience; and I shall counter it with a transcendental proof. Admittedly, my proof cannot explain the different ways in which space is filled. On the other hand, it completely destroys the supposed necessity of the assumption that the differentiation can be explained only by supposing that there are empty spaces. It also has the merit of at least giving the understanding the freedom to think about this differentiation in an alternative way, [B216] in case scientific explanation requires some new hypothesis to explain it.

<ap18> Two spaces having the same volume can be completely filled with matter of different kinds, so that there is no point in either of them where its matter is not present. Nevertheless, we see that what is real in each has its own degree in respect of the above-mentioned qualities of resistance or weight. Without any diminution in extensive magnitude or amount, this degree can become infinitely smaller, before it crosses over into emptiness, and disappears. Consider anything which can spread around and fill a space, for example, warmth — and similarly every other reality in the realm of appearance. Without leaving even the tiniest part of this space empty, it can diminish infinitely in its degree, and yet fill the space with this lesser degree just as much as a different appearance fills it with a larger one.

<ap19> It is certainly not my intention here to claim that this is the actual explanation of why different kinds of matter have different specific gravities. It is merely to establish, on the basis of an axiom of pure understanding, that:

• the nature of our perceptions makes an explanation of this sort possible;
• it is a mistake to assume that what is real in appearances always has the same degree, and that differentiation depends only on aggregation and extensive quantity;
• it is an even worse mistake to claim that this is based on an apriori axiom of the understanding.

<ap20> [B217] Nevertheless, there must always be something shocking about this anticipation of perception for researchers who are used to the transcendental approach, and have therefore become cautious. They will doubt whether the understanding can anticipate a synthetic proposition like the one about the degree of everything which is real in appearances. They will therefore also doubt the possibility of the inner differentiation of sensation itself, when its empirical quality is left out of account. Thus there remains a question which deserves an answer, namely: how can the understanding make synthetic apriori pronouncements about appearances, and how can it anticipate them even in what is essentially only empirical, namely that which belongs to sensation?

<ap21> The quality of sensation (e.g. colours, taste, etc.) is always merely empirical, and can certainly not be represented apriori. However, the real which corresponds to sensations in general (in contrast to negation = 0) does represent something; but its concept is essentially only that of a being, and it signifies nothing other than synthesis in an empirical consciousness in general. That is to say, in inner sense, empirical consciousness can range from zero to any higher degree, so that a single extensive quantity of intuition (e.g. an illuminated surface) can excite the same quantity of sensation as an aggregate of many other less illuminated ones together. Thus we can leave the extensive quantity of the appearance [B218] completely out of account, and still represent, in pure sensation at an instant, a synthesis of the uniform increase from zero up to the degree of empirical consciousness as given. Hence all sensations as such are indeed given only aposteriori; but their property of having a degree can be known apriori.

<ap22> It is remarkable that, in the case of quantities in general, we can know just one quality, namely their continuity. Whereas in the case of all quality (that which is real in appearances), we can know apriori only their intensive quantity, namely that they have a degree. Every thing else is left to experience.

<1a1> 3.

The principle of the Analogies of Experience is: Experience is possible only through the representation of a necessary connection of perceptions.

<1a2> Proof

Experience is empirical knowledge, i.e. knowledge which determines an object through perceptions. Thus it is a synthesis of perceptions, which is not itself contained in perception, but which contains the synthetic unity of the multiplicity of perception in one consciousness. This unity constitutes what is essential to knowledge of objects of the senses, i.e. experience, as contrasted with [B219] mere intuition, or sensation of the outer senses.

<1a3> Now it is certain that, in experience, perceptions come together only in a contingent manner, so that perception itself gives no evidence of any necessity of their connection. Nor can perception give any such evidence, since apprehension is merely a putting together of the multiplicity of empirical intuition. Apprehension contains no representation of the necessity of the connected existence of the appearances which it puts together in space and time. But since experience is knowledge of objects through perceptions, it follows that it must represent the relation between what exists in the multiplicity, not as it happens to be put together in time, but as it is objectively in time. But time itself cannot be perceived, so the existence of objects in time can be determined only through their unification in time in general, and hence only through concepts which connect them apriori. Now since apriori concepts always carry necessity with them, experience is possible only through a representation of the necessary connection of perceptions.

<1a4> The three modes of time are duration, succession, and co-existence. Therefore experience is preceded and made possible by three rules for all time-relations among appearances, in accordance with which the existence of every appearance can be determined with reference to the unity of all time.

<1a5> [B220] The universal axiom of all three Analogies depends on the necessary unity of apperception in relation to any possible empirical consciousness (or perception) at any time. Consequently, since the unity of apperception is the apriori foundation of empirical consciousness, this axiom depends on the synthetic unity of all appearances in respect of their relations in time. For the originative apperception applies to inner sense (i.e. to the totality of all representations); and more specifically, it applies apriori to the form of inner sense, which is the time-order of the multiple empirical consciousness. Now all this multiplicity must be united in the originative apperception in accordance with its time-relations. For this is required apriori by the transcendental unity of apperception, which applies to everything that is to belong to my knowledge (i.e. my unified knowledge), and hence be capable of being an object for me. This synthetic unity in the time-relation of all perceptions, which is determined apriori, is the law that all empirical determinations of time must come under rules for the determination of time in general. The Analogies of Experience, which I am now going to deal with, must be rules of this sort.

<1a6> These axioms have the peculiar characteristic that they do not concern appearances or the synthesis of their empirical intuition, but merely their existence, and their relationship to each other in respect of their existence. Now the way in which something is apprehended in appearance [B221] can be determined apriori in such a manner that the rule for its synthesis can at the same time provide this apriori intuition in every empirical example we come across — i.e. it can produce the appearance from the intuition. It is only the existence of the appearance that cannot be known apriori; and although we could advance far enough along this route to conclude that something or other must be present, we would not know it as something determinate — i.e. we would not be able to anticipate what differentiated its empirical intuition from the intuitions of other things.

<1a7> I called the first two axioms ‘mathematical’, in view of the fact that they justified the application of mathematics to appearances. They were concerned only with the possibility of appearances, and they told us how appearances could be produced in accordance with a mathematical synthesis, both in respect of their intuition, and in respect of that which is real in their perception. Hence both axioms justify the application of numerical quantities to appearances, and along with these quantities, the determination of an appearance as a quantity. So, for example, I can put together the degree of sensations of sunlight out of roughly 200,000 illuminations from the moon, and provide this degree as determined apriori — that is, I can construct it. This is why we can call the first two axioms ‘constitutive’.

<1a8> The situation must be quite different with axioms which are to bring the existence of appearances under rules apriori. For since existence cannot be constructed, [B222] they are concerned only with relations of existence, and they can deliver nothing more than merely regulative principles. Here there is no question of Axioms of Intuition or Anticipations of Perception. Rather, if we are given a perception which has a time-relation to another (even if it is undetermined), we cannot say apriori which other, or what quantity the other perception has, but only how its existence is necessarily connected with that of the first in this particular mode of time.

<1a9> In philosophy, analogies mean something very different from what they represent in mathematics. In mathematics, analogies are formulae which express the identity of two quantitative relationships. They are always constitutive, so that if two members of the proportion are given, the third will also thereby be given — i.e. it can be constructed. But in philosophy, an analogy is not the identity of two quantitative relationships, but of two qualitative ones. Here, if three members are given, I can know, and supply apriori, only the relationship with a fourth member, but not this fourth member itself. Nevertheless, I have a rule for searching for it in experience, and a criterion for identifying it there.

<1a10> So an analogy of experience is only a rule for how unity of experience is to arise from perceptions, and not for how perception itself, as empirical intuition in general, is to come about. As an axiom about objects (appearances), it has merely regulative, and not constitutive validity.

<1a11> [B223] The same is also true of the Postulates of Empirical Thought in General, which are collectively concerned with:

• the synthesis of pure intuition (the form of appearance);
• perception (the matter of appearance); and
• experience (the interrelatedness of these perceptions).

They are only regulative axioms, and they differ from the mathematical ones, which are constitutive. The difference does not lie in their certainty, which is established apriori in both cases; but in the way in which they are evident — i.e. only the mathematical ones are intuitively, and hence demonstrably evident.

<1a12> Here I must stress a point which I have already made about the other synthetic axioms. This is that these Analogies have their sole significance and validity, not as axioms of the transcendental use of the understanding, but only of their empirical use; and hence it is only as such that they can be proved. Consequently, appearances cannot be subsumed under the categories as such, but only under their schemata.

<1a13> For if the objects which these axioms are to apply to were things in themselves, then it would be quite impossible to have any synthetic apriori knowledge of them. But they are nothing other than appearances, and complete knowledge of them (which must always be the ultimate goal of apriori axioms) depends solely on the possibility of experience. Consequently, the axioms can have as their aim nothing other than the preconditions for the unity of empirical [B224] knowledge in the synthesis of appearances. But this unity is thought only in the schema of the pure concept of the understanding. The category contains the function of its unity, as of a synthesis in general, and the function is not restricted by any sensory precondition.

<1a14> So these axioms justify us in unifying appearances only by an analogy with the logical and universal unity of concepts. We do indeed use the category in the axiom itself; but in its implementation (its application to appearances), it is replaced by its schema, as the key to its use — or rather, we set the schema alongside the category as a restricting precondition, and call it a formula of the category.

<1a15> A

<1a16> Proof

All appearances are in time; and in it alone can either coexistence or succession be represented, with time as their substrate (as the permanent form of inner intuition). All [B225] change of appearances must be thought in time; but time itself remains, and does not change. For it is that in which succession or coexistence can be represented merely as determinations of time.

<1a17> Now time in itself cannot be perceived. Consequently, the substrate which represents time in general must be found in the objects of perception, i.e. in appearances. It is in this substrate that all change or coexistence can be perceived, through the relation of appearances to the substrate when they are apprehended. But the substrate of all that is real (i.e. every property of the existence of things) is substance; and everything which belongs to existence can be thought only as a determination of substance. Now, all time-relations between appearances can be determined only by relation to the permanent. Consequently, the permanent is substance in appearance — that is, the real in appearance which, as the substrate of all change, always remains the same. So since it cannot change as to its existence, it is also the case that its quantum in nature can be neither increased nor diminished.

<1a18> Our apprehension of the multiplicity of appearance is always successive, and is therefore always changing. So through apprehension alone, we can never determine whether this multiplicity, as object of experience, is coexistent or successive. In order to determine this, we need some underlying basis which always exists — in other words, something lasting and permanent, of which all [B226] change and coexistence are nothing other than so many ways in which the permanent exists, or so many modes of time. Thus time-relations are possible only in the permanent, since the only time-relations are simultaneity and succession. That is, the permanent is the substrate of the empirical representation of time itself, and no time-determination is possible without it.

<1a19> Permanence universally reveals time as the enduring correlate of all existence of appearances, of all change, and of all co-existence. For time itself is not subject to change, but only appearances in time. Similarly, coexistence is not a mode of time itself, since no parts of time are simultaneous, but all are successive. If we wanted to ascribe succession to time itself, we would have to imagine yet another time in which this succession was possible.

<1a20> It is only through the permanent that existence in different successive parts of the time series acquires a quantity, which is called duration. For in mere succession alone, existence is always passing away and coming into being, and never has the least quantity. So without the permanent, there is no time-relation.

<1a21> Now time in itself cannot be perceived. So the permanent in appearances is the substrate of all time-determination, and hence also the precondition for the possibility of all synthetic unity of perceptions, i.e. of experience. [B227] And in this permanent thing, all existence and all change in time can be considered only as a mode of the existence of that which lasts and is permanent. Thus in all appearances, the permanent is the object itself, i.e. the substance (of the phenomena). But everything which changes, or can change, belongs only to the way in which this substance or substances exist, and hence to their determinations.

<1a22> I find that throughout history, not only philosophers but also ordinary people have presupposed this permanence as a substrate of all change in appearances, and have always taken it as indubitable. The only difference is that philosophers express themselves more precisely on this issue, by saying that in all alterations in the world, the substance remains, and only the accidents change. However, I have never come across so much as an attempt at a proof of this so obviously a synthetic proposition. Indeed, it only rarely occupies the place it deserves at the summit of the laws of nature which are pure and established completely apriori.

<1a23> In fact, the proposition that substance is permanent is tautological, since permanence is the only basis on which we can apply the category of substance to appearance. But one would first have to prove that in all appearances there is something permanent, in which anything changeable is nothing other than a determination of its existence. However, such a proof can never be constructed [B228] dogmatically (i.e. from concepts), because the proposition in question is synthetic apriori. It never occurred to anyone that propositions of this sort are valid only in relation to possible experience, and hence also that they can be proved only through a deduction of the possibility of experience. So it is no wonder that it has never been proved, even though it has been the foundation for all experience, since the need for it is felt in any empirical knowledge.

<1a24> A philosopher was asked: ‘How much does smoke weigh?’ He replied: ‘Subtract the weight of the remaining ash from the weight of the wood that was burned, and then you will have the weight of the smoke.’ He thus assumed as undeniable that, even in fire, the matter (substance) does not disappear, but only its form undergoes a change.

<1a25> Similarly, the old saying that ‘nothing comes from nothing’ was only another corollary of the axiom of permanence — or rather, of the ever-continuing existence of the essential subject in appearances. For if that in appearance which is called ‘substance’ is to be the essential substrate of all time-determination, then every past and future existence must be determinable by reference to it alone, and nothing else. Hence the only reason why we can call an appearance a ‘substance’ is because we presuppose its existence throughout time. The word [B229] ‘permanence’ isn’t quite right, since it refers more to future time. Nevertheless it will do, since the inner necessity to continue to exist is inseparable from the necessity to have always existed in the past.

<1a26> ‘Nothing comes from nothing, and nothing can return to nothing’ were two propositions which the scholastics joined together inseparably. Nowadays they are sometimes separated, due to the mistaken belief that they refer to things in themselves. It was feared that the first was inconsistent with the dependence of the world on a supreme cause, especially as far as its substance is concerned. However, this worry is unnecessary, since here we are dealing only with appearances in the world of experience. The unity of appearances would never be possible if we allowed new things (in the sense of new substances) to come into existence. In that case, we would lose the only thing which can represent the unity of time, namely the identity of the substrate through which alone all change has holistic unity. Yet this permanence is nothing other than the way in which we represent to ourselves the existence of things in appearance.

<1a27> The determinations of a substance, which are nothing other than its particular ways of existing, are called accidents. They are always real, because they involve the existence of a substance. (Negations are merely determinations which express the non-being of something in a substance.) Now that which is real [B230] in a substance is sometimes treated as having a separate existence — for example, motion, as an accident of matter. In such cases, the existence of the accident is called ‘inherence’, in order to distinguish it from the existence of the substance, which is called ‘subsistence’. But this gives rise to many confusions, and it is more precise and correct to adhere to the terminology in which an accident is the way in which the existence of a substance is positively determined.

<1a28> Nevertheless, the preconditions for the logical use of our understanding mean that we cannot avoid separating out that in the existence of a substance which can change while the substance stays the same, and to treat it as standing in relation to that in its existence which is essentially permanent and fundamental. This is why the category of substance comes under the heading of Relation — though more as the precondition of relations than as itself containing a relation.

<2a29> Now this permanence is also the ground for correcting the concept of alteration. Coming into being and going out of being are not alterations of what comes in or out of being. Alteration is when one and the same object exists first in one way, and then in another way. Hence everything which alters continues to exist, and only its state changes. So change applies only to determinations, which can come in or out of being. Consequently we can say (in a way which sounds paradoxical) that only the permanent (i.e. substance) alters; [B231] and that the variable does not undergo alteration, but change, in that some determinations go out of being, and others come into being.

<1a30> Hence alteration can be perceived only in substances. Essentially, it is impossible to perceive coming in or out of being, except in so far as it is merely a determination of the permanent. This is because it is the permanent which makes possible the representation of the transition from one state to another, and from not-being to being. So these transitions can be known empirically only as changing determinations of that which is permanent.

<1a31> Suppose that something begins to exist out of the blue; then you must have a point in time at which it did not exist. But what can you fix this point in time to, unless to something which is already there? For a preceding empty time is not an object of perception. But if you fix what comes into being to things which already exist, and continue to exist until it comes into being, then what comes into being is only a determination of what already exists as that which is permanent. It is the same with ceasing to exist — for it presupposes the empirical representation of a time when there is no longer an appearance.

<1a32> Substances (in appearance) are the substrates of all time-determinations. If some of them came into being and others went out of being, the sole precondition of the empirical unity of time would disappear. [B232] Appearances would then relate to two distinct time streams, in which their existence would flow along parallel paths — which is absurd. For there is only one time, in which no different times can be simultaneous, and all must be successive.

<1a33> So permanence is a necessary precondition, under which alone appearances can be determined as things or objects in any possible experience. As for the question of what the empirical criterion for this necessary permanence is, and the related question of the substantiality of appearances, there will be later opportunities for me to make the necessary points.

<2a1> B

<2a2> Proof

(The previous axiom has shown that absolutely every appearance of temporal succession is only an alteration — that is, a successive being and not-being of determinations of a substance which persists throughout the succession. Consequently, the being of the substance itself cannot follow its not-being, nor can its not-being follow its being. In other words, [B233] a substance cannot begin or cease to exist. The principle could also have been formulated as follows: Every change (succession) of appearances is only an alteration. For if a substance began or ceased to exist, this would not be an alteration to it, because the concept of alteration presupposes one and the same subject as existing with two mutually exclusive determinations, and hence as persisting. After this preliminary note, the proof follows.)

<2a3> I perceive that appearances follow one another — i.e. that the state of things at a given time is contrary to their previous state. So what I am essentially doing is to combine two perceptions in time. Now combining is not the work of sensation by itself, or of intuition, but here it is the product of a synthetic capacity of the imagination, which determines inner sense in respect of relationship in time. However, it can combine these two states in two ways, so that either the one or the other comes first in time. This is because time cannot be perceived in itself, and it is impossible to determine what comes first and what follows in the object by reference to time in a quasi-empirical way.

<2a4> So all I am conscious of is the fact that my imagination puts one first and the other second, and not that the one state precedes the other in the object. In other words, the objective relationship between the appearances which follow one another remains [B234] undetermined through perception by itself. Now in order for it to be known as determined, the relationship between the two states must be thought, in such a way that it is thereby determined as necessary which of them must be put first and which second, rather than the other way round. But the only sort of concept which carries with it a necessary synthetic unity is a pure concept of the understanding, which is not to be found in perception.

<2a5> In the present case, it is the concept of the relation of cause and effect. Of these, the cause determines the effect in time, as that which follows, and not as something which could come first (or even not be perceived at all), as would be the case if only the imagination were involved. So experience (i.e. empirical knowledge of appearances) is possible only through our subjecting the succession of appearances, and hence all alterations, to the law of causality. Hence appearances themselves, as objects of experience, are possible only in accordance with just this law.

<2a6> The apprehension of the multiplicity of appearance is always successive. The representations of its parts follow one after another. It is quite a separate question, not yet raised, whether the representations are also successive in the object.

<2a6> Now we can, of course, call anything an ‘object’, in so far as we are conscious of it — and this even includes any representation whatever. But there is a deeper question as to what this word means when it is applied to [B235] appearances — not in so far as they are objects by virtue of being representations, but only in so far as they represent an object. In so far as they are at the same time objects of consciousness (simply as representations), they are no different from apprehension, i.e. being included in the synthesis of imagination. And so it must be said that the multiplicity of appearances is created successively at every instant in the mind.

<2a7> If appearances were things in themselves, no-one would be able to use the successiveness of the multiplicity of representations to work out how the multiplicity was connected in the object. For we are limited to our representations; and the way in which things in themselves might exist is entirely out of our sphere of knowledge, without reference to the representations through which they affect us. Appearances are not things in themselves; but nothing else can be given to us for knowledge.

<2a8> Nevertheless, I must show what belongs to the multiplicity of appearances itself in order for it to be connected in time, given that the representation of the multiplicity in apprehension is always successive at any given time. For example, the apprehension of the multiplicity in the appearance of a house which stands before me is successive. The question is whether the multiplicity of this house is also in itself successive — which obviously no-one will accept. But as soon as I elevate my concepts [B236] of an object to a transcendental sense, the house is not a thing in itself, but only an appearance, i.e. a representation of which the transcendental object is unknown.

<2a9> So what do I mean when I ask how the multiplicity might be unified in the appearance itself (even though it is nothing in itself)? Here, whatever belongs to the successive apprehension is considered as a representation; whereas the appearance which is given to me (although it is nothing other than a collection of such representations), is considered as their object; and it is to this object that my concept (which I derive from the representations of apprehension) must correspond.

<2a10> Since truth consists in correspondence between knowledge and its object, we can immediately see that here we are concerned only with the formal conditions of empirical truth. An appearance (as contrasted with the representations of apprehension) can be represented through them, as their object distinct from them, only if it stands under a rule which distinguishes it from every other apprehension, and makes necessary a single way of unifying the multiplicity. That in the appearance which contains the condition of this necessary rule of apprehension is the object.

<2a11> Now let us continue with our task. Something happens when there comes into being a thing, or a state of a thing, which did not previously exist. But it cannot be empirically perceived that something happens, [B237] unless there is a preceding appearance which does not include this state. For an actuality which follows an empty time, and hence a coming into existence which is not preceded by any state of things, can no more be apprehended than empty time itself. Thus every apprehension of an event is one perception following another. But since this is what happens in every synthesis of apprehension (as I showed above with the appearance of a house), it does not yet serve to distinguish an event from other cases.

<2a12> But I also note the following. In an appearance which involves an event, let us call the earlier state of the perception A, and the later state B. Then B can only follow A in apprehension, and the perception A cannot follow B, but can only precede it. For example, I see a ship drifting along with the current. My perception of its position downstream in the course of the river follows my perception of its position upstream, and in the apprehension of this appearance, it is impossible for the ship to be perceived first downstream and then upstream. The order in the sequence of perceptions in the apprehension is determined as such, and the apprehension is tied to this order.

<2a13> In the earlier example of a house, my perceptions could begin with the apprehension of the top and end with the bottom, or equally [B238] begin from the bottom and end with the top. Similarly, my perceptions could apprehend the multiplicity of empirical intuition starting from the right, or starting from the left. So in this sequence of perceptions there was no determinate order making it necessary where I had to begin my apprehension in order to combine the multiplicity empirically. Whereas there is always such a rule in perceptions of events; and this rule makes the order of successive perceptions (in the apprehension of such an appearance) a necessary order.

<2a14> So, in the case we are considering, I must derive the subjective succession of apprehension from the objective succession of appearance, because otherwise the subjective succession is completely indeterminate, and does not distinguish any one appearance from any other. By itself, subjective succession proves nothing about the connection of the multiplicity in the object, because it is completely arbitrary. Thus the objective connection will consist in an order of the multiplicity of appearance, such that the apprehension of an event follows the apprehension of what precedes it in accordance with a rule. This is the only way I can be justified in saying that appearance itself contains a succession, and not merely my apprehension — which amounts to saying that I can order the apprehension only with precisely this succession.

<2a15> So in accordance with such a rule, that which precedes an event (taken as a universal) must contain the precondition [B239] for a rule in accordance with which this event always and necessarily follows. On the other hand, I cannot argue backwards from the event, and determine, through apprehension, precisely what precedes it. For no appearance goes back from a later point in time to the preceding one, though it does relate to some or other previous point in time. By contrast, the advance from a given time to the determinate following time is necessary. Hence, because there is still something which follows, I must necessarily relate it to something else in general which precedes it, and from which it follows in accordance with a rule — i.e. necessarily. Consequently, the event, as that which is preconditioned, clearly indicates that there is some precondition or other; but it is this precondition that determines the event.

<2a16> If it is supposed that an event is not preceded by anything which it must follow in accordance with a rule, then every succession of perceptions would be determined only arbitrarily in apprehension — i.e. merely subjectively. And this would certainly not determine objectively which of the perceptions must really be the preceding one, and which the following one. On this supposition, we would have only a play of representations, which would not relate to any object at all. That is, our perception would provide no distinction whatever between one appearance and any other on the basis of their time-relations. This is because the successiveness in apprehending would always be the same, and thus there would be nothing in the appearance which determined the successiveness so as to make a [B240] particular succession necessary by virtue of being objective. So I would not be able to say that, in the realm of appearance, two states of affairs follow each other; but only that one apprehension follows another. This is merely something subjective, and it does not determine any object. Consequently, it cannot count as knowledge of any sort of object — not even in the realm of appearance.

<2a17> So if we experience that something happens, we always presuppose that it follows from something preceding it, in accordance with a rule. For otherwise I would not be attributing the succession to an object, because mere succession in my apprehension is no evidence for any succession in the object, unless it is determined through a rule relating it to something which went before. So it is always the case that I make my subjective synthesis of apprehension objective by reference to a rule, in accordance with which appearances are determined by their previous state as far as their successiveness is concerned — that is, as they actually happen. Only under this assumption alone is it possible for there to be any experience of something happening.

<2a18> It certainly seems that this contradicts everything that has always been said about the way we apply our understanding. The usual account is that we are first led to discover a rule only by perceiving and comparing many sequences of events following in the same way from preceding appearances; [B241] and according to this rule, certain events always follow certain appearances. This is what first stimulates us to construct for ourselves the concept of cause. But on this footing, the concept would be merely empirical, and the rule it supplies (namely that everything that happens has a cause) would be just as contingent as experience itself. The universality and necessity of the rule would then be only spurious, and have no genuine universal validity, since they would not have an apriori foundation, but would depend only on induction.

<2a19> Here the case is the same as with other pure apriori representations, such as those of space and time. We can extract them from experience as clear concepts only because we have put them into experience, and hence used them to bring experience about in the first place. I admit that this representation of a rule determining the sequence of events can attain the logical clarity of a concept of cause only after we have applied it to experience. However, acceptance of the rule, as a precondition of the synthetic unity of appearances in time, was the foundation of experience itself, and therefore preceded it apriori.

<2a20> So in the present case, it is important to show that, even in experience, we never attribute a succession (of an event, in which something happens which previously did not exist) to an object, and distinguish it from the subjective succession of our [B242] apprehension, except on the basis of a rule which necessitates us to observe just this order of perceptions rather than some other order. Indeed, this necessitating is essentially what first makes possible the representation of a succession in the object.

<2a21> We have representations within us, and we can also become conscious of them. But however widely this consciousness might extend, and however exact and precise it might be, there still always remain only representations — that is, inner determinations of our mind in this or that time-relation. So how do we come to provide an object for these representations? Or how do we come to attribute to them some unknown kind of objective reality, over and above their subjective reality as modifications?

<2a22> Objective reference cannot consist in a relationship with another representation, i.e. a representation of what we would want to call an ‘object’. For the same question recurs: how does this second representation in turn get outside itself, and acquire objective reference, over and above the subjective reference which is proper to it as a determination of the state of the mind? So let us consider what sort of new nature is given to our representations by relation to an object, and what status they acquire as a result. We find that all it does is to necessitate us to combine the representations in a particular way, and to subject them to a rule. Conversely, they acquire objective reference only because [B243] a particular order in the time-relations of our representations is necessary.

<2a23> In the synthesis of appearances, the multiplicity of representations is always successive. So far, no object at all is represented, because nothing is distinguished from anything else through this successiveness, since it is common to all apprehensions. But as soon as I perceive or assume that, in this succession, there is a relation to the preceding state, such that the representation follows from that state in accordance with a rule, then something is represented as an event, or as something that happens. In other words, I know an object, which I must locate at a certain determinate position in time; and because of the preceding state, I cannot locate it at any other position.

<2a24> So when I perceive that something happens, the first thing contained in this representation is that something preceded it. For it is precisely in relation to what preceded it that the appearance obtains its time-relation — namely its existing after a preceding time in which it did not exist. But it can obtain its determinate position in this time relation only in so far as the previous state presupposes something by virtue of which it always follows — i.e. in accordance with a rule. From this it turns out, firstly, that I cannot reverse the sequence, and place what happens before what it follows from. Secondly, it turns out that, if the state which precedes [B244] is assumed, then this particular event follows inevitably and necessarily.

<2a25> This is how it comes about that there is an order among our representations. In this order, the present, in so far as it has come into being, indicates some preceding state or other, as a still undetermined correlate of the given event. But the correlate has a determining relationship to the given event as its successor, and it necessarily connects it to itself in the time-series.

<2a26> Let as assume, then, that it is a necessary law of our sensibility, and hence a formal precondition of all perceptions, that the earlier time necessarily determines the later time, since I can arrive at the succeeding time only through the preceding one. Then it will also be an inexorable law of the empirical representation of the time-series, that appearances at an earlier time determine every existence at the following time. Furthermore, these last, as events, can occur only in so far as the earlier appearances determine their existence in time — that is, establish it in accordance with a rule. For it is only through appearances that we can have empirical knowledge of this continuity in the interconnection of times.

<2a27> Understanding is required for all experience, and for the possibility of experience. The first thing it does to it is not to make the representation of objects clear, but to make possible the representation of an object in general. Now it does this [B245] by applying the time-order to appearances and their existence, assigning to each of them, as a succeeding appearance, a position in time determined apriori by reference to preceding appearances. If it did not do this, the appearances would not correspond to time itself, which determines the position of all its parts apriori.

<2a28> Now since time is not an object of perception, this determination of position in time cannot be derived from the relation of appearances to absolute time. Rather, the reverse is the case, and appearances must themselves determine each other’s position in time, and make it a necessary position in the time-order. In other words, that which follows or happens must follow, in accordance with a universal rule, from what was contained in the previous state. This gives rise to a sequence of appearances, which, thanks to the understanding, brings about, and makes necessary, exactly the same order and continuous interconnection in the sequence of possible perceptions, as is met with apriori in the form of intuition (time), in which all perceptions must have their position.

<2a29> That something happens is therefore a perception which belongs to a possible experience. This possible experience becomes actual when I regard the appearance as having a determinate position in time, and hence as an object which can always be found in the interconnection of perceptions in accordance with a rule. [B246] But this rule for determining something in accordance with the time-sequence is as follows: the precondition for an event to follow always (i.e. necessarily) is to be found in what precedes it. So the principle of sufficient reason is the foundation of possible experience, that is, of the objective knowledge of appearances, in respect of their relationship in the sequence of time.

<2a30> The proof of the principle of sufficient reason depends solely on the following stages. All empirical knowledge requires the synthesis of the multiple through the imagination, and it is always successive — i.e. the representations in it always follow one after another. But in the imagination, the order of the sequence (what must come first and what must follow) is quite undetermined, and the series of one representation following another can equally well be taken forwards or backwards.

<2a31> But if this synthesis is a synthesis of the apprehension of the multiplicity of a given appearance, then the order in the object is determined — or to be more precise, this apprehension contains an order of successive synthesis which determines an object. In accordance with this order, something necessarily precedes, and if it is given, the other must necessarily follow. So if my perception is to include knowledge of an event (i.e. knowledge that something actually happens), then it must be an empirical judgment including the thought that the sequence is determined. In other words, it includes the thought that it presupposes another appearance in [B427] time, upon which it follows necessarily, or in accordance with a rule. By contrast, if I supposed the preceding appearance without the event following from it necessarily, then I would have to take it as only a subjective play of my images; and if I still represented it to myself as something objective, I would have to call it a mere dream.

<2a32> The relation between appearances (as possible perceptions) such that the existence of the succeeding appearance (the event) is determined in time, necessarily and in accordance with a rule, by something preceding it, is the relation of cause and effect. This relation is the precondition of the objective validity of our empirical judgments as to the sequence of perceptions, and hence of their empirical truth, and thus of experience. Hence the axiom of the causal relation in the series of appearances is also valid for all objects of experience (since they are all subject to the preconditions of succession), because it is itself the basis of the possibility of such an experience.

<2a33> But here there arises yet another doubt which needs to be removed. As I have formulated it, the axiom of causal connection among appearances is restricted to successive appearances. But it so happens that the axiom also applies to appearances which coexist; and cause and effect can be simultaneous. For example, there is warmth in a room, which is absent from the open air outside. [B248] I look around for the cause, and I find a heated stove. Now the stove, as cause, is simultaneous with its effect, the warmth of the room. So here there is no sequence in time between the cause and the effect. They exist simultaneously, yet the law still holds.

<2a34> The large majority of efficient causes in nature are simultaneous with their effects, and the only reason why the effects are successive in time is because the cause cannot achieve its whole effect in a single instant. But at the instant when the effect first begins, it is always simultaneous with the causality of its cause. This is because, if the cause had ceased to exist an instant earlier, then the effect would not come into existence at all.

<2a35> Here it should be carefully noted that it is a question of order in time, and not of the passage of time: the causal relation remains, even though no time has passed. The time between the causality of the cause and its direct effect can be vanishingly small, so that they are simultaneous. But the time-relation between the one and the other nevertheless always remains determinable. Suppose there is a bullet lying on a stuffed cushion, and pressing a hollow into it. If I consider the bullet as cause, then it is simultaneous with its effect. However, I still distinguish between the one as cause and the other as effect, by virtue of the time-relation of the dynamic connection between the two. For when I place the bullet on the cushion, the hollow follows on from the previously smooth shape of the cushion. But if, for whatever reason, [B249] the cushion has a hollow in it, a lead bullet does not follow on from the hollow.

<2a36> Therefore successiveness in time is certainly the only empirical criterion for distinguishing the effect from the causality of the cause, which precedes it. A glass is the cause which makes water in it rise higher than its horizontal level, although both appearances exist simultaneously. For as soon as I scoop water out of a larger container into the glass, something happens next, namely the alteration of the horizontal surface which the water had in the container, into the concave one which it takes on in the glass.

<2a37> This causality leads to the concept of action; that of action to the concept of power; and that of power to the concept of substance. Since my critical project is concerned only with the sources of synthetic apriori knowledge, I shall not overload it with analyses which involve merely the explanation of concepts, rather than their expansion. So I reserve the detailed exposition of these concepts for a future work to be called the System of Pure Reason — although a large proportion of such an analysis is already to be found in the existing well-known textbooks of this sort. However, there is just one concept which I cannot avoid discussing here. This is the empirical criterion for something to be a substance, in so far as it seems to reveal itself better and more easily through its activity than through the permanence of the appearance.

<2a38> [B250] Wherever there is action (and hence activity and power), there is also substance; and it is in substance alone that the seat of that fruitful source of appearances is to be looked for. So far so good. But if we are to clarify what is meant by ‘substance’ without falling into a vicious circle, it is not so easy to give an answer. How can we conclude directly from an action to the permanence of that which acts? After all, this is such an essential and distinctive criterion for something to be a substance (as phenomenon). However, after what I have already said, the answer to this question is not so difficult, even though it would be completely insoluble using the usual method of proceeding with one’s concepts purely analytically.

<2a39> ‘Action’ already denotes the relation of the subject of causality to its effect. Now every effect is an event, and hence exists in what is changeable, which indicates time through its successiveness. Consequently, the ultimate subject of the changeable is the permanent, as the substrate of everything that changes — in other words, it is substance. For according to the axiom of causality, events are always the ultimate source of all change of appearances. So they cannot belong to a subject which itself changes, because other actions and another subject would then be required to determine the change of appearances.

<2a40> Now by virtue of the above, action is a sufficient empirical criterion for proving substantiality, [B251] without my first having to check its permanence by comparing perceptions. Besides, the method of comparing perceptions would not achieve the completeness required by the greatness and strict universal validity of the concept of substance. For the ultimate subject of the causality of all coming to be and ceasing to be cannot itself come in or out of being (within the realm of appearances). This is a safe conclusion, which leads to empirical necessity and permanence in existence, and hence to the concept of a substance as appearance.

<2a41> When something happens, its mere coming into being, without reference to what it is that comes into being, is already in itself something to investigate. The one thing we must already investigate is the transition from the non-existence of a state to its existence, assuming that the state also contains no quality in the appearance. This coming into being, as I showed in the First Analogy, does not involve substance (since it does not come into being), but its state. So it is merely an alteration, and not a coming into being out of nothing.

<2a42> If this coming into being is considered as the effect of an external cause, then it is called ‘creation’. But such an event cannot be allowed among appearances, since its possibility alone would already destroy the unity of experience. On the other hand, if I consider all things, not as phenomena, but as things in themselves, and as objects [B252] of understanding alone, then, although they are substances, they can be thought of as depending for their existence on an external cause. But then our words would carry very different meanings, and they would not be applicable to appearances as possible objects of experience.

<2a43> Apriori, we do not have the least idea of how, in general, anything can be altered — that is, of how a state at one instant can be followed by a contrary one at another instant. For this we require knowledge of actual powers, which can be given only empirically — for example, motive powers, or (which comes to the same thing) appearances following one another in the particular way which constitutes motion, and which indicates such powers. But let us leave aside the content of any alteration (i.e. the state which is altered, whatever it might be), and consider its form. This form is the precondition for any alteration to take place as the coming into being of another state. Consequently, the successiveness of the states themselves (the event) can still be considered apriori in accordance with the law of causality and the preconditions of time.*

<2a44> [B253] When a substance goes from one state a to another b, the point in time of the second is different from the point in time of the first, and it follows it. Similarly, the second state, as containing what is real in appearance, is different from the first state, as not containing it. So the difference is the difference between b and zero. In other words, even if state b differs from state a only in quantity, the alteration is a coming into being of b–a, which did not exist in the previous state, and in relation to which the previous state is an =0.

<2a45> So there remains the question how a thing passes from one state a, to another state b. Between two instants there is always a time, and between two states at those instants there is always a difference, which has a quantity (since all the parts of appearances are always themselves quantities). So every transition from one state to another takes place during a time which is contained between two instants, of which the first determines the state which the thing leaves, and the second determines the state it arrives at. So both are limits of the time of an alteration, and hence of the intermediate state between two states. As such, both together belong to the whole alteration.

<2a46> Now every alteration has a cause, which exercises its causality throughout the time during which the alteration takes place. So the cause does not produce its alteration suddenly (all at once, or in an instant), but [B254] over a period of time. Consequently, just as the time grows from the initial instant a to its completion at b, similarly the quantity of reality (b–a) is produced through all the smaller degrees which are contained between the first and the last. Thus all alteration is possible only through a continuous action of causality, which, as long as it is uniform, is called a ‘moment’. The alteration does not consist of these moments, but is produced by them as their effect.

<2a47> Now this is the law of the continuity of all alteration, and its basis is as follows. Both time, and also an appearance in time, consist of parts, without there being any smallest parts. Yet the state of a thing undergoing alteration passes through all these parts, as elements, to its second state. No difference in that which is real in appearance is the smallest, just as no difference in the quantity of times is the smallest. The new state of the reality grows from the first state, in which it did not exist, through all its infinitely many degrees; and the sum of the differences between them is less than the difference between 0 and a.

<2a 48> Here I am not concerned with the possible usefulness of this proposition for scientific investigation. What does urgently demand examination is how such a proposition is possible completely apriori, since it seems to extend our knowledge of nature so much. This needs to be explained, even though it seems obvious that the proposition is true and correct, and [B255] it might be thought that this makes the question of how it is possible redundant. But there are so many unfounded claims to the extension of our knowledge through pure reason, that we must take it as a universal axiom that we should be deeply suspicious of any such claim. Even if the clearest dogmatic proof has been provided, we must not believe it, or use it as an assumption, without credentials which can provide a deduction from fundamentals.

<2a49> All increase in empirical knowledge, and every step forward made through perception, is nothing other than an extension of the determination of inner sense — i.e., it is an advance in time, whether its objects are appearances or pure intuitions. This advance in time determines everything, and it is not in itself determined by anything else. In other words, its parts exist only in time and by virtue of the synthesis of time, and they are not given before this synthesis. Consequently, every transition in perception to something which follows in time is a determination of time through the production of this perception. And just as time is always, and in all its parts, a quantity, similarly a perception is produced as a quantity, through all degrees (of which there is no smallest) from zero to its determinate degree.

<2a50> This now makes clear how it is possible to know apriori a law about the form of alterations. All that we anticipate [B256] is our own apprehension, and we must certainly be able to know its formal precondition apriori, since it itself exists in us before any given appearance.

<2a51> Thus there is a parallel between the understanding and time. Time contains the apriori sensory precondition for the possibility of a continuous advance of what exists to what follows. Similarly, the understanding, thanks to the unity of apperception, is the apriori precondition for the possibility of a continuous determination of all positions for appearances in time. It does this through the series of causes and effects. Causes inexorably bring with them the existence of their effects, and thereby make empirical knowledge of time-relations valid for all times — i.e. universally, and hence objectively valid.

<3a1> C

<3a2> Proof

Things are coexistent when, in empirical intuition, the perception of the one can follow the perception [B257] of the other in any order (as I showed in the Second Analogy, this cannot happen in the succession of appearances in time). Thus I can direct my perception first at the moon and then at the earth, or conversely, first at the earth and then at the moon. Since the perceptions of these objects can follow each other in any order, I say that they coexist.

<3a3> Now coexistence is the existence of the multiple at the same time. But we cannot perceive time itself, in order to establish from the fact that things are placed at the same time, that their perceptions can follow each other in any order. The synthesis of the imagination in apprehension would show each of these perceptions as in the subject when the other is not, and vice versa. However, it would not show that the objects coexisted, i.e. that when one exists, the other also exists at the same time, or that this is necessary for the perceptions to be able to follow each other in any order. So what we need is a concept of understanding of the reversible sequence of the determinations of these things which exist externally to each other at the same time. Only then can we say that the reversible sequence of perceptions is grounded in the object, and thus represent the coexistence as objective.

<3a4> Now the relation between substances, such that the ground for determinations of the one [B258] is contained in the other, is the relation of influence. And if, conversely, the ground for determinations of the second is also contained in the first, then the relation is that of community or interaction. So the coexistence of substances in space can be known in experience only on the assumption of an interaction between them. Thus this interaction is also the precondition of the possibility of things themselves as objects of experience.

<3a5> Things coexist in so far as they exist at one and the same time. But how can we know that they exist at one and the same time? When it is arbitrary what order the multiple is synthesised in, when it is apprehended — that is, it can go from A, through B, C, and D, to E, or also the other way round, from E to A. For if it were successive in time (in the order which begins with A and ends with E), it would be impossible for its apprehension in perception to begin with E, and proceed backwards to A, because A belongs to a time which has passed, and so can no longer be an object of apprehension.

<3a6> Now let us suppose that, in a multiplicity of substances as appearances, each of them was completely isolated — that is, none of them influenced the others, or received any reciprocal influences from them. I say that their coexistence would not be the object of a possible [B259] perception, and that the existence of one of them could not lead to the existence of another through any process of empirical synthesis. For if you imagine that they are separated by a completely empty space, then perception, which proceeds from one to the next in time, would certainly determine the existence of the later one by means of a subsequent perception. However, it would not be able to discriminate whether its appearance objectively followed the first, or coexisted with it.

<3a7> So, in addition to mere existence, there must be something through which A determines the position of B in time, and, conversely, B also determines the position of A in time, since only under this precondition can these substances be empirically represented as coexisting. Now the only thing which determines the position of something else in time is its cause, or the cause of its determinations. In the case of substance, only its determinations can be caused. So every substance must contain within itself, both the causality of certain determinations in the other, and the effects of the causality of the other. In other words, if their coexistence is to be known through any possible experience, they must be in dynamic community, whether directly or through intermediaries. Now, as far as objects of experience are concerned, anything which is a precondition of experience of these objects is necessary. [B260] So, in so far as substances in appearance coexist, it is necessary for all of them to be in holistic community through their interaction with each other.

<3a8> The word ‘community’ is ambiguous in our language, since it can mean both ‘coexistence’ and ‘interaction’. Here we are using it in the latter sense, as a dynamic community, without which even a spatial community could never be known empirically.

<3a9>From our experiences, we can easily see that only continuous influences in all positions in space can lead our senses from one object to another. The light pulsating between our eyes and the heavenly bodies creates an indirect community between us and them, which proves that they coexist. We cannot alter our position empirically (i.e. perceive the alteration), unless the matter all around us makes the perception of our position possible. And it is only through its reciprocal influence that matter as a whole can establish its own coexistence, and hence the coexistence of the most remote of objects (if only indirectly). Without community, every perception of appearance in space would be broken off from every other. The chain of empirical representations (i.e. experience) would have to start completely afresh with a new object, [B261] and the earlier representation could not have the least connection or time-relation with the later one.

<3a10> I shall certainly not use this as an argument against empty space. For there could always be a place entirely beyond the reach of perceptions, and therefore where there can be no empirical knowledge of things coexisting. But then it could never be an object of any possible experience for us.

<3a11> The following may be helpful as a further explanation. Since, in our minds, all appearances are contained in a possible experience, they must belong to a community of apperception (in the sense of a coexisting one). In so far as their objects are to be represented as coexisting in connection with each other, they must determine each other’s position at a particular time, and thereby constitute a whole. If this subjective community is to be based on an objective foundation (i.e. apply to appearances as substances), then the perception of the one must make possible the perception of the other as its foundation, and vice versa. This is not so that the successiveness which always characterises perceptions (as apprehensions) will be attributed to the objects, but so that the objects can be represented as coexisting. But this is a reciprocal influence, i.e. a real community of substances (in the sense of an interacting one), without which the empirical relationship of coexistence can have no place in experience. In so far as appearances are separate from each other [B262] yet connected with each other, this interaction turns them into a real compound whole; and compound wholes of this sort are possible in many ways. Hence the three dynamical relations, which are the source of all the rest, are those of inherence, consequence, and composition.

* * *

<3a12> So these are the three Analogies of Experience. They are nothing other than axioms of the determination of the existence of appearances in time in respect of all its three modes, namely:

• relation to time itself as a quantity (the quantity of existence, i.e. duration);
• relation in time as a series (succession); and finally
• relation, also in time, as a totality of all existence (coexistence).

This unity of time-determination is dynamical through and through. In other words, time is not treated as something in which experience directly determines the position of everything that exists. This is impossible, because absolute time is not an object of perception which could hold appearances together. Rather, the position of all appearances in time is determined by the rule of the understanding through which alone their existence can acquire synthetic unity in respect of time-relations. Thus their position is determined apriori, and it is valid for all and every time.

<3a13> [B263] By ‘nature’ (in the empirical sense) I mean the interconnection of appearances, with respect to their existence, through necessary rules, i.e. through laws. Thus there are certain laws, and apriori ones at that, which initially make a nature of any sort possible. On the other hand, empirical laws can exist and be discovered only through experience, and indeed only in compliance with those original laws which initially make experience itself possible. So in essence, what my Analogies do is to plot the unity of nature in the interconnection of all appearances along certain parameters, which represent nothing other than the relation of time (as including all existence) to the unity of apperception, which can be realised only in synthesis according to rules. So taken together, the Analogies say that all appearances belong to, and must belong to a single nature, because without this apriori unity, there could be no unity of experience, and hence no determination of the objects in it.

<3a14> Something needs to be said about the method I have used to prove these transcendental laws of nature, and about their special character. What I have to say is at the same time very important as a necessary guide for any other attempt to prove propositions which not merely belong to the understanding, but are also synthetic apriori.

<3a15> I might have tried to prove the Analogies dogmatically (i.e. from concepts). That is, I might have argued as follows:

• everything that exists is to be found only in [B264] that which is permanent;
• every event presupposes something in the previous state from which it follows in accordance with a rule; and finally
• in every coexistent multiplicity, the states coexist in relation to each other in accordance with a rule (they are in community).

If I had done so, all my efforts would have been in vain. For you cannot get from one object and its existence to the existence or mode of existing of another object, merely by means of concepts of these things, however you care to analyse them.

<3a16> So what is missing? The third item required is the possibility of experience, as a type of knowledge in which it must ultimately be possible for all objects to be given to us, if the representation of them is to have objective reality for us. The essential form of this third item consists in the synthetic unity of apperception of all appearances. In it we discovered apriori preconditions for the holistic and necessary time-determination of everything existent in appearance, without which even the empirical determination of time would be impossible. We also discovered rules for the apriori synthetic unity by means of which we can anticipate experience.

<3a17> Up till now, philosophers have lacked this method, and have suffered from the delusion that it is possible to use a dogmatic method to prove synthetic propositions which the empirical use of the understanding recommends as its principles. This is why it happened that a proof of the principle of sufficient reason was so often attempted, but always in vain. [B265] No-one ever so much as thought of the other two Analogies, even though they were always used without being recognised for what they were.* This was because of the lack of the guiding-thread of the categories, which alone can reveal and make obvious every deficiency of the understanding, whether in concepts or in axioms.

<r1> [B274] Refutation of Idealism

Idealism (by which I mean material idealism) is the theory that the existence of objects in space external to us is either merely doubtful and unprovable, or false and impossible. The first is the problematic idealism of Descartes, who held that there is only one undoubted empirical assertion, namely that ‘I am’. The second is the dogmatic idealism of Berkeley, who held that space, together with all the things it belongs to as an inseparable precondition, is impossible in itself, so that things in space are also mere images. Dogmatic idealism is unavoidable if you consider space to be a property which must belong to things in themselves, since in that case it is a nothing, along with everything which depends on it. However, we have already eliminated the grounds for this idealism in the Transcendental Aesthetic.

<r2> Problematic idealism makes no such claim, but merely holds [B275] that it is impossible to prove the existence of anything other than ourselves through immediate experience. This is reasonable, and in accordance with a fundamentally philosophical way of thinking, since it avoids making any decisive judgment until an adequate proof has been found. So the required proof must show that we have experience and not merely images of external things. This can be done only if we can prove that even our inner experience (which Descartes did not doubt) is possible only on the presupposition of outer experience.

<r3> Theorem

<r4> I am conscious of my existence as determined in time. Every determination in time presupposes something permanent in perception. However, that which is permanent cannot be an intuition in me. For the only grounds for determining my existence which can be met with in me are representations. But as such, they too need something permanent distinct from themselves, by reference to which their changes can be determined, and hence my existence at the time in which they change. So the perception of this permanent element is possible only through a thing external to me, and not through a mere representation of a thing external to me. Consequently, the determination of my existence in time is possible only through the existence of actual things which [B276] I perceive external to myself. But there is a necessary connection between consciousness in time and consciousness of the possibility of this determination in time. So it is also necessarily connected with the existence of things external to myself, as the precondition of determination in time — in other words, consciousness of my own existence is at the same time an immediate consciousness of the existence of other things external to myself.

<r5> Note 1. You will notice that, in the above proof, the game played by idealism has been turned against it — and with some justice. Idealism assumed that the only immediate experience is inner experience, and that outer things can only be inferred from it. But, as is always the case when we infer particular causes from given effects, the inference is unreliable, since the causes of our representations, which we ascribe (perhaps incorrectly) to external things, could also be found within ourselves. However, I have proved here that outer experience is essentially direct.*

<r7> [B277] It is only by means of outer experience that inner experience is possible — not the consciousness of our own existence, but its determination in time. I accept that the representation ‘I am’, which gives expression to the consciousness which can accompany any thought, immediately includes within itself the existence of a subject. However, it does not include any knowledge of a subject, and hence no empirical knowledge, or experience of it. For experience involves intuition as well as the thought of something existing — in this case inner intuition, by reference to which the subject must be determined (i.e. by reference to time). External objects are absolutely necessary for this, so it follows that inner experience itself is only indirect, and possible only through outer experience.

<r8> Note 2. This accords perfectly with all our experience of using our faculty of knowledge to determine time. We can perform a time-determination only by means of the changing relationships of external things (motions) in relation to that which is permanent in space — for example, the motion of the sun by reference [B278] to objects on Earth. Furthermore, we do not even have anything permanent with which we could support the concept of a substance, as intuition, apart from mere matter. And even this permanence of matter is not derived from outer experience, but is presupposed apriori, as the necessary precondition of all determination in time, and hence also as the determination of inner sense in respect of our own existence through the existence of external things. The consciousness of my self in the representation ‘I’ is not an intuition at all, but a purely intellectual representation of the self-activity of a thinking subject. Hence this ‘I’ also has absolutely none of the characteristics of intuition which could, by being permanent, serve as a substitute for time determination in inner sense — somewhat as impenetrability, as an empirical intuition, does in matter.

<r9> Note 3. The existence of external objects is necessary for a determinate consciousness of our selves to be possible. But it does not follow that all representations of external things in intuition simultaneously include their existence, since they may well be merely the product of the imagination (in dreams as well as in mad delusions). However, imagination is possible only through the reproduction of previous outer perceptions, and, as I have shown, our perceptions are possible only [B279] through the actuality of external objects. Here, all I had to prove was that inner experience in general is possible only through outer experience in general. Whether this or that supposed experience is imaginary or not can be settled only by its particular determinations, and through its consistency with the criteria for all actual experience.

<pn1> The Transcendental Doctrine of Judgment

[B294] We have now not only travelled all over the territory of pure understanding and carefully explored every part of it, but we have also measured its maximum limits, and determined the place of every thing in it. But this territory is an island, and confined within unalterable boundaries by nature itself. It is the land of truth (charming name!), [B295] surrounded by a wide and stormy ocean, the natural habitat of illusion, where many a fog bank, and many a sheet of ice about to melt away, look deceptively like new territories. Nevertheless, this ocean never stops deceiving with empty hopes the seafarer full of enthusiasm for new discoveries, and embroiling him in adventures which he can never give up, but which he can also never bring to fulfilment.

<pn2> We are about to venture out into this sea, in order to explore it in all directions, and to achieve certainty as to whether there is anything to hope for in it. But before we do so, it will be useful to throw one more glance at the map of the territory we are about to leave, and ask ourselves two questions. The first question is whether we cannot be satisfied with what it contains anyway, or at least whether we are forced to be satisfied, because otherwise there is no ground at all for us to build on. The second question is by what right we possess even this territory, and can keep it safe from all hostile claims. Although I have already answered these questions in depth during the course of the Analytic, a summary review of the solutions to them can strengthen conviction by bringing its different strands together into a single point.

<pn3> We have seen that the sole function of everything which the understanding derives from itself, without borrowing it from experience, is its application to experience. The [B296] axioms of pure understanding are either constitutive apriori (the mathematical ones) or merely regulative (the dynamical ones). In both cases, they contain nothing other than, as it were, the pure schema for possible experience. For experience gets its unity only from the synthetic unity which the understanding gives, originally and from itself, to the synthesis of the imagination in relation to apperception. Appearances must already have an apriori relation to, and conform to this synthetic unity, as data for possible knowledge. These rules of the understanding are not merely true apriori, but they are actually the source of all truth (i.e. the correspondence of our knowledge to objects), since they contain the basis for the possibility of experience (as the sum of all knowledge), which is required for objects to be given to us.

<pn4> However, we are dissatisfied with an account which is confined to what is true, and we want an account of what we desire to know. It might seem that these critical investigations tell us no more than we could have achieved by ourselves, merely through the empirical use of the understanding, and without such subtle research. If so, the advantage we gain from it would not seem to be worth the investment of effort. To this it can certainly be replied, that nothing is more damaging to the extension of our knowledge, than the spirit of enquiry which always wants to know in advance [B297] what the benefit will be, before getting involved in the research, and before we could even form the least conception of this benefit, even if it were staring us in the eyes.

<pn5> But there is another advantage, which can be made both comprehensible and interesting to even the most difficult and unenthusiastic student of transcendental investigation. This is that the understanding can indeed make very good progress by confining itself to its empirical use, and giving no thought to the sources of its own knowledge. However, the one thing it cannot achieve by itself is to determine the limits of its application, and to know what might lie inside or outside its total sphere. This requires just those deep investigations which I have conducted. But if it cannot decide whether or not certain questions fall within its horizon, it is never sure of its claims and possessions. It can only count on all sorts of humiliating rebuffs, when it inevitably and repeatedly oversteps the limits of its territory, and loses its way in delusion and error.

<pn6> My claim is that the only use the understanding can make of all its apriori axioms, and indeed of all its concepts, is empirical, and that it can never make a transcendental use of them. If this proposition can be known with conviction, it points to important consequences. [B298] The transcendental use of a concept in any axiom is when it is applied to things in general and as they are in themselves; and their empirical use is when they are applied merely to appearances, i.e. to objects of a possible experience. I shall now show that there is no scope for anything other than their empirical use.

<pn7> Every concept requires, first, the logical form of a concept (or of a thought) in general, and secondly, the possibility of being given an object to which it applies. Without the latter, it has no meaning, and it is completely empty of content — even though it might still contain the logical function for making a concept out of any sort of data. Now an object cannot be given to a concept except in intuition. In the case of an apriori intuition, even though it is apriori possible before an object, it too can acquire its object, and hence its objective validity, only through empirical intuition, of which it is merely the form. So all concepts, and with them all axioms, however apriori they may be, relate to empirical intuitions, i.e. to data for possible experience. Without this, they have no objective validity at all, but are a mere play of representations, whether those of the imagination or those of the understanding.

<pn8> Take for example the concepts of mathematics, [B299] more precisely starting with its pure intuitions. Space has three dimensions; between two points there can be only one straight line; and so on. All these axioms, and the representation of the object which the science of mathematics deals with, are produced in the mind completely apriori. However, they would mean nothing at all, if we were not always able to display their meaning through appearances (empirical objects). So we are also required to make an abstract concept sensible, that is, to display in intuition the object corresponding to it; otherwise the concept (as we say) would remain without sense, i.e. without meaning.

<pn9> Mathematics fulfils this requirement by constructing a figure which is an appearance present to the senses, even though it is brought into being apriori. In the same science, the concept of quantity looks for its status and sense in number; and number is presented to the eyes by means of the fingers, the beads of an abacus, or written strokes and dots. The concept is still always produced apriori, together with the synthetic axioms or formulae put together from such concepts. However, their applicability and relation to any objects which might be supposed, can ultimately be looked for only in experience, since the concepts contain apriori the possibility of objects, at least as far as their form is concerned.

<pn10> [B300] That this is also the case with all the categories and the axioms they give rise to, is clear from the following. We cannot give a real definition of any single one of them (i.e. make the possibility of their object comprehensible) without at once digging down to the preconditions of sensibility, and hence to the form of appearances. The categories must be limited to these preconditions, since they are their only objects. For if this restriction is removed, all meaning (i.e. relation to an object) goes by the board, and we cannot use any example to make it intelligible, even to ourselves, essentially what sort of a thing is meant by such a concept.

<pn11> The concept of quantity in general can be explained only as the determination of a thing such that we can think how many times a unit is to be found in it. But this how-many-times is based on successive repetition, and hence on time, and on the synthesis of things of the same kind in it.

<pn12> Reality (by contrast with negation) can be explained only if we think of a time as either filled with being, or empty of it. This is because time is the sum of all being. If I leave out permanence (which is something existing throughout all time), then the only thing I am left with as constituting the concept of substance is the logical representation of a subject. I try to make it real by representing to myself something which can exist merely as a subject, without being the predicate of anything. [B301] However, not only do I not know of any preconditions for this supreme logical property to belong to anything of any kind, but there is nothing more to be done with it, and not the least consequence to be drawn from it. This is because no object is determined for this concept to apply to, and so one cannot know whether it means anything at all.

<pn13> Next, the concept of cause. If I leave out the time in which something follows something else in accordance with a rule, then I am left with the pure category. But all this contains is that there is something from which the existence of something else can be concluded. Not only would it be impossible to use it to distinguish between cause and effect, but, because this license to draw conclusions also requires preconditions of which I know nothing, the concept would not determine how it applied to any object.

<pn14> The supposed axiom that everything contingent has a cause, steps forward rather grandly, as if its dignity were self-justifying. But if I ask: "What do you mean by ‘contingent’"?, and you say: "That of which the non-existence is possible," then I would like to know how you can know that this non-existence is possible. What you need is to represent a successiveness in the series of appearances, and in the successiveness you need to represent an existence which follows from the non-existent (or vice versa), and hence you need to represent a change. To appeal to the fact that the non-existence of a thing is not a self-contradiction, is a lame appeal [B302] to a merely logical precondition. It is certainly necessary for the concept, but it is completely inadequate for its real possibility. I can think any existing substance away without contradicting myself; but I cannot conclude from this that it is objectively contingent in its existence, i.e. that its non-existence is possible in itself.

<pn15> As for the concept of community, it is easy to appreciate that, since the pure categories of substance and causality cannot be defined in such a way as to determine an object, the same must be true of reciprocal causality in the interactive relationship of substances to each other.

<pn16> Possibility, existence, and necessity can only be defined through manifest tautologies, as long as their definition is drawn exclusively from pure understanding. And to misrepresent the logical possibility of the concept (in that it is not self-contradictory) as the possibility of the thing (in that an object corresponds to the concept), is a trick which can deceive and satisfy only the novice.*

<pn17> [B303] Now from this it undeniably follows that the pure concepts of understanding can never have any transcendental application, but always only an empirical application; and that the axioms of pure understanding can apply only to objects of the senses under the universal preconditions of any possible experience, and never to things in general, without reference to the way we might intuit them.

<pn18> The Transcendental Analytic therefore results in the following important conclusion. The most the understanding can achieve apriori is to anticipate the form of any possible experience in general. Since anything which is not an appearance cannot be an object of experience, the understanding can never overstep the limits of sensibility, within which alone objects are given to us. Its axioms are merely principles for displaying appearances; and the boastful name of an ontology, which presumes to provide synthetic apriori knowledge of things in general (e.g. the axiom of causality) as a systematic doctrine, must give way to the humble name of merely an analytic of pure understanding.

<pn19> [B304] Thought is the action of relating a given intuition to an object. If it is in no way given what kind of intuition this is, then the object is merely transcendental, and the concept of understanding has only a transcendental application, namely as the unity of the thought of a multiplicity in general. No object is determined through a pure category, since it takes no account of any of the preconditions of sensory intuition, which is the only kind of intuition possible for us. All it contains is the thought of an object in general, expressed in one of a number of different modes.

<pn20> Now the application of a concept involves a different function of judgment, through which an object is subsumed under the concept, and hence at least the formal precondition for it to be possible for something to be given in intuition. If this precondition for judgment (the schema) is lacking, then nothing can be subsumed under the concept, since nothing is given which could be subsumed under it. Thus the merely transcendental application of the categories is in fact no application at all, and it has no determinate object, nor even an object which is determinable only as to its form. From this it follows that a pure category is insufficient even for any synthetic apriori axiom, and that the axioms of pure understanding have only an empirical application, and never a transcendental one. Beyond [B305] the field of possible experience, there can be no synthetic apriori axioms at all.

<pn21> It might be a good idea to put it the following way. Without formal preconditions of sensibility, the pure categories have transcendental meaning, but no transcendental application. This is because a transcendental application is intrinsically impossible, since it lacks all the preconditions of any application (in judgments), namely the formal preconditions for subsuming under these concepts any object which might be given. Merely as pure categories, they should have no empirical application, and can have no transcendental application. So if they are divorced from all sensibility, they have no application at all — that is, they cannot be brought to bear on any object which might be given. Instead, they are simply the pure form of the application of the understanding with respect to objects in general and to thought, without it being possible for any object to be thought or determined through them alone.

<pn22> Nevertheless, there is here a deep-seated illusion which it is difficult to avoid. In their origin, the categories are not based on sensibility (by contrast with the forms of intuition, namely space and time); so they seem to allow their application to be extended beyond all objects of the senses. But just as space and time are forms of intuition, the categories are nothing other than forms of thought, which contain merely the logical capacity of uniting the multiplicity given [B306] in intuition into a single consciousness apriori. So if we take away sensory intuition (which is the only kind possible for us), they can have even less significance than the pure sensory forms. The sensory forms do at least provide an object, whereas the way of combining the multiplicity which is peculiar to our understanding signifies nothing at all, in the absence of the intuition through which alone the multiplicity can be given.

<pn23> We call certain objects phenomena, because they are appearances, or sensory beings. However, we distinguish between the way we intuit them and their intrinsic nature. So it is already contained in our concept, either that we, as it were, contrast phenomena with their nature, even though we do not intuit their nature in them, or that we contrast phenomena with other possible things, which are not objects of our senses at all. Since these objects are merely thought through our understanding, we call them intellectual beings or noumena. The question now arises as to whether our concepts of pure understanding might not have significance in respect of noumena, and so be a means of knowing them.

<pn24> Right from the start, there emerges an ambiguity which can give rise to a serious misunderstanding. When the understanding calls an object in a certain relationship a mere phenomenon, as well as this relationship, it also forms a representation of an object in itself. So it comes to represent itself as [B307] also being able to make itself concepts of such objects. Since the understanding supplies no concepts other than the categories, it supposes that it must at least be possible for the object to be thought through these pure concepts of understanding. But this misleads it into treating the completely indeterminate concept of an intellectual being, namely a something-in-general beyond our sensibility, as a determinate concept of a being which we can somehow know through the understanding.

<pn25> If by ‘noumenon’ we mean a thing in so far as it is not an object of our sensory intuition, by leaving out of account our way of intuiting it, then this is a noumenon in the negative sense. But if we mean by it an object of a non-sensory intuition, then we presuppose a special kind of intuition, namely intellectual intuition; and this would be a noumenon in the positive sense. However, we do not have this kind of intuition, and we cannot even have any insight into how it might be possible.

<pn26> The thesis that all our knowledge depends on sensibility implies that noumena must be taken in the negative sense. In other words, they are things which the understanding must think independently of our way of intuiting them, and hence as things in themselves, rather than as mere appearances. But at the same time, the understanding is well aware that, because it has separated things in themselves from our way of intuiting them, it cannot apply its categories to things in themselves as if they were objects of intuition. [B308] This is because the categories have meaning only in relation to the unity of intuitions in space and time. And it is only because of the mere ideality of space and time that the categories can determine apriori even this unity, by means of universal concepts which combine things together. Where this unity of time is not to be found, and hence in the noumenon, the categories completely lose all their applicability, and even all their meaning, since we can have no insight into the very possibility of the things which are supposed to correspond to the categories. On this, I would merely refer to what I said near the beginning of the general note to the previous chapter.

<pn27> The possibility of a thing can never be proved simply from the non-contradictory nature of its concept. It can be verified only through an intuition which corresponds to it. So if we wanted to apply the categories to objects which are not considered to be appearances, we would have to base this on a kind of intuition which was non-sensory — but then the object would be a noumenon in the positive sense. Now since an intellectual intuition lies completely outside our faculty of knowledge, it is equally impossible for the categories to have any application beyond the boundaries of the objects of experience. I readily accept that there are intellectual beings corresponding to sensory beings, [B309] and that there may also be intellectual beings which have no relation at all to our faculty of sensory intuition. However, they are completely out of the reach of our concepts of understanding, which are mere forms of thought for our sensory intuition. Therefore what we call a ‘noumenon’ must be understood as being such only in the negative sense.

<pn28>If I take all thought (through the categories) away from empirical knowledge, there remains no knowledge at all of any object. For nothing whatever is thought through mere intuition, and the fact that this affection of sensibility is in me does not establish any relation of this representation to any object. But if I leave out all intuition, the form of thought still remains — that is, the way of determining an object for the multiplicity of a possible intuition. Hence the categories have a wider reach than sensory intuition, in so far as they think objects in general, without regard to the specific mode of intuition (in our case sensibility) in which objects might be given. However, this does not mean that they determine a larger sphere of objects. For we cannot assume that such objects can be given, without presupposing the possibility of a non-sensory mode of intuition — but we have no justification at all for such a presupposition.

<pn29> [B310] I call a concept ‘problematic’, if it has the following characteristics:

• it is not self-contradictory;
• it is connected with other types of knowledge by limiting concepts given in them;
• its objective reality can in no way be known.

The concept of a noumenon is the concept of a thing which is to be thought, not as an object of the senses, but as a thing in itself, and only through a pure understanding. It is certainly not self-contradictory, since we cannot stipulate that sensibility is the only possible mode of intuition.

<pn30> Further, this concept is necessary, in order to prevent sensory intuition from extending to things in themselves, and so to limit the objective validity of sensory knowledge. Everything else, which sensory knowledge does not reach, is called ‘noumena’, precisely so as to indicate that sensory knowledge cannot extend its territory over everything which the understanding can think.

<pn31> However, we ultimately have no insight at all into how such noumena are possible, and the circumference which lies outside the sphere of appearances is empty (for us, at least). That is, we have an understanding which extends itself beyond this sphere problematically. On the other hand, we do not have any intuition, or even the concept of a possible intuition, which could give us objects outside the field of sensibility, and enable the understanding to be used assertorically outside this field. Thus the concept of a noumenon is merely a limiting concept [B311] to curb the pretensions of sensibility, and it is therefore only of negative use. However, it is not arbitrarily thought up. It is intimately bound up with the limitation of sensibility, though without being able to establish anything positive outside the circumference of the sphere of sensibility.

<pn32> It is therefore completely illegitimate to divide objects into phenomena and noumena, and the world into a sensory world and an intellectual world, in the positive sense. However, it is perfectly admissible to divide concepts into those that are sensible and those that are intellectual, since we cannot determine any object for intellectual concepts, and hence pass them off as objectively valid. If we leave the senses out, how will we make it comprehensible that our categories (which would be the only remaining concepts for noumena) still mean anything at all? In order for them to relate to any object, something more must be given than mere unity of thought, namely a possible intuition to which they can be applied.

<pn33> Nevertheless, the concept of a noumenon, provided it is taken in the merely problematic sense, remains not only permissible, but actually indispensable, as a concept which sets limits to sensibility. But in this case, a noumenon is not a special intelligible object for our understanding. Rather, the problem is the nature of an understanding to which it could belong. For it would have to know its object, not discursively through categories, [B312] but intuitively through a non-sensory intuition — and we cannot form the least representation of how this is possible.

<pn34> Now through the concept of a noumenon, our understanding acquires a negative extension. In other words, our understanding is not limited by sensibility, but instead it limits sensibility by giving the name ‘noumena’ to things as they are in themselves, and not considered as appearances. But in doing so it also sets limits to itself, since it cannot know noumena through the categories, and so it can think them only by calling them an ‘unknown something’.

<pn35> In the writings of modern philosophers, I find a use of the expressions ‘sensible world’ and ‘intelligible world’* which departs radically from their meanings in antiquity.

<pn36> I admit that the modern usage does not cause any difficulty; but it consists of nothing other than mere empty playing with words. What it amounts to is that some philosophers have taken to calling the sum of appearances the ‘sensible world’ in so far as it is intuited, and the ‘intelligible world’ in so far as its interconnectedness is thought through general laws of understanding.

<pn37> [B313] On this account, practical astronomy would give us a representation of the sensible world, in that it merely reports observations of the starry heavens; whereas theoretical astronomy would give us a representation of the intelligible world, by explaining these observations in terms of the Copernican system, or Newton’s laws of gravitation. But twisting words in this way is merely a sophistical let-out. It is an attempt to worm one’s way out of a difficult question by distorting the meaning of the question so as to makes things easier for oneself.

<pn38> There is no question that understanding and reason are applicable to appearances. But the point at issue is whether or not they are also applicable when their object is not an appearance, but a noumenon. And their object is taken as being a noumenon when it is thought as being intrinsically nothing other than intelligible —in other words, it is thought as being given to the understanding alone, and not to the senses at all. So the point at issue is whether, in addition to the empirical use of the understanding (and Newton’s representation of the structure of the universe is still empirical), there could not also be a transcendental use of the understanding, which has the noumenon as its object. I have given a negative answer to this question.

<pn39> So when I say that the senses represent objects to us as they appear, and the understanding represents them to us as they are, the second half of this statement is to be taken merely in an empirical, and not in a transcendental sense. In other words, objects must be represented to us as objects of experience through the holistic interconnection of appearances, [B314] and not as they might be without their relation to possible experience, and hence to sense in general, and hence as objects of pure understanding. Objects divorced from experience will always remain unknown to us. It will even remain unknown to us whether such a transcendental or miraculous knowledge is possible at all, at least as a kind of knowledge which comes under the categories we are subject to.

<pn40> As far as we are concerned, understanding and sensibility can determine objects only in connection with each other. If we separate them, we have intuitions without concepts, or concepts without intuitions. In both cases, these are representations which we cannot relate to any determinate object.

<pn41> If, despite all these explanations, you still have reservations about renouncing the purely transcendental use of the categories, you should test them through any synthetic proposition. For an analytic proposition does not take the understanding any further. Since the understanding deals only with what it has already thought in the concept, it leaves it undecided whether the concept has an intrinsic relation to objects, or whether it merely signifies the unity of thought in general — which takes absolutely no account of the way an object might be given. In its analytic use, it is enough for the understanding to know what is contained in the concept before it, and it is irrelevant what the concept itself might apply to.

<pn42> So the test must be conducted with [B315] any axiom which is both synthetic, and supposedly transcendental. To give just a couple of examples:

• everything that exists, exists either as a substance, or as a determination inhering in a substance; or
• everything contingent exists as the effect of another thing, namely its cause.

Now the question I ask is this: where will you get this synthetic axiom from, since the concepts are to be valid of things in themselves (noumena), and not just in relation to possible experience? Where is the third thing, which a synthetic proposition always requires, in order to join together the concepts it contains, given that they have no logical (analytic) affinity? You will never be able to prove your proposition, and what is more, you will never even be able to justify the possibility of a pure assertion like this, without appealing to the empirical use of the understanding, and thus completely renouncing your claim that the judgment is pure and independent of the senses.

<pn43> So the concept of pure and merely intelligible objects is completely devoid of any axioms for its application, since we cannot think of any way in which such objects might be given to us. The mere thought of their existence, taken in the problematic sense, does indeed keep a place open for them. However, like an empty space, its only function is to limit the empirical axioms. It does not contain or reveal any object of knowledge outside the sphere of these axioms.

<pa1> The Paralogisms of Pure Reason

[B399] A logical paralogism consists in the formal invalidity of a rational inference, whatever its content. By contrast, a transcendental paralogism has a transcendental ground for drawing a formally invalid conclusion. So a fallacy of this sort will be grounded in the nature of human reason, and will lead to an illusion which is compelling, but not inescapable.

<pa2> Now we come to a concept which was not included in the earlier general list of transcendental concepts. Yet it must be included in their number, but without altering the table in any way, or admitting it to be defective. This is the concept (or judgment, if you prefer) ‘I think’. You will easily see that it is the vehicle of all concepts in general, and hence also of the transcendental concepts. So it is always conceived along with them, and is therefore just as transcendental as they are.

<pa3> However, it does not belong to a section on its own, since its only function is to present every thought as belonging to consciousness. [B400] Nevertheless, however pure it is of the empirical (the impression of the senses), it also has the function of distinguishing two kinds of object arising from the nature of our faculty of representation: I, as thinking, am an object of inner sense, and I am called ‘soul’; and whatever is an object of outer sense is called ‘body’.

<pa4> Hence the expression ‘I’ (as a thinking being) already identifies the object of that branch of psychology which can be called the rational doctrine of the soul — provided that I do not seek to know any more about the soul than can be deduced from this concept ‘I’ in so far as it accompanies all thought, and independently of all experience (which defines me more closely and as a concrete individual).

<pa5> The rational doctrine of the soul is actually an undertaking of this kind. For it would no longer be a rational, but an empirical doctrine of the soul, if the slightest empirical element of my thought — any particular perception of my inner state — contaminated the cognitive criteria of this science. So we already have before us a candidate for a genuine science, built up on the single proposition: ‘I think.’ Here it is fully appropriate, and in accordance with the nature of a transcendental philosophy, that we should investigate whether or not at has any basis.

<pa6> One should not be deflected by the objection that this very proposition, which expresses the perception of itself, involves my having an inner experience, and hence that the rational [B401] doctrine of the soul which is to be built on it will never be pure, but partly grounded on an empirical principle. For this inner perception is nothing beyond the mere apperception ‘I think’, which even makes all transcendental concepts possible, since what is said in them is ‘I think substance’, ‘I think cause’, etc.

<pa7> For inner experience in general and its possibility (or perception in general and its relation to other perception, provided that no particular distinction between them, or determination, is empirically given) cannot be considered as empirical knowledge. Rather, it must be considered as knowledge of the empirical in general, and it belongs to the investigation of the possibility of any experience, which certainly is transcendental. But rational psychology would immediately degenerate into an empirical psychology if the slightest object of perception (if only pleasure or displeasure, for example) were added to the general representation of self-consciousness.

<pa8> [B402] Here we simply have to follow the leading-thread of the categories, except that here the first to be given is a thing, namely I, as thinking being. So we shall not alter the internal order of the categories as presented in their earlier table. Instead, we shall follow their sequence in reverse order, starting with the category of substance, through which a thing is represented in itself. So the following is the structure of the topics covered by the rational doctrine of the soul, from which everything else it may contain must be derived:

<pa11> [B403] All the concepts of the pure doctrine of the soul derive from these elements, merely by combining them, and without any need whatever to appeal to any other principle. This substance, simply as the object of inner sense, yields the concept of immateriality; as simple substance, that of incorruptibility; its identity as an intellectual substance yields personality; all these three elements together yield spirituality; the relation to objects in space yields interaction with bodies; and hence it represents thinking substance as the principle of life in matter, i.e. as soul (anima), and as the ground of animality; and animality limited to spirituality yields immortality.

<pa12> Now related to these concepts, there are four Paralogisms of a transcendental doctrine of the soul, which is wrongly held to be a science of pure reason about the nature of our thinking being. The only foundation [B404] we can lay for this science is the representation ‘I’, which is simple, and in itself wholly devoid of content. One cannot even say that it is a concept, but merely a consciousness which accompanies all concepts. Through this I, or he, or it (the thing) which thinks, nothing more is represented than a transcendental subject of the thoughts, = x. It is known only through the thoughts which are its predicates, and we can never have the least concept of it in separation from them. This is why we constantly go round in a circle, in that we must always already use the representation of it in order to make any judgment about it. We cannot get round this embarrassment, because consciousness in itself is not so much a representation which marks out a particular object, but it is rather a form of representation in general, in so far as representation is to be called knowledge. For this representation is the only thing of which I can say that I think anything through it.

<pa13> But right from the start, it must seem strange that the precondition of my thinking in general (which is therefore merely a quality of my subject) should at the same time be valid for everything which thinks. It must also seem strange that we can presume to use what seems to be an empirical proposition as the foundation for a necessary and universal judgment — namely that everything which thinks is constituted in the same way as the expression of self-consciousness asserts of me. [B405] But the reason for this lies in the fact that we must necessarily attribute to things apriori all the properties which constitute the preconditions under which alone we can think them. Now I can have no representation at all of thinking being through any outer experience, but only through self-consciousness. So such objects are nothing more than the carrying across of this my consciousness to other things, since this is the only way they can be represented as thinking beings. However, in this case the proposition ‘I think’ is taken as merely problematic — not in the sense that it might contain the perception of something existent (the Cartesian cogito ergo sum), but because of its mere possibility. The purpose is to see what properties might flow from as simple a proposition as this to its subject (whether or not such a subject exists).

<pa14> If our pure rational knowledge of thinking being in general were grounded in anything more than the cogito — if we also had recourse to observations about the play of our thoughts, and the natural laws of the thinking self to be drawn from them — then this would give rise to an empirical psychology, which would be a sort of natural science of inner sense. It might perhaps explain the appearances of inner sense, but it could never serve to reveal any properties which do not belong to any possible experience (e.g. those of the simple), [B406] nor could it provide a necessary demonstration of what belongs to the nature of thinking being in general. Consequently, it would not be a rational psychology.

<pa15> Now the proposition ‘I think’ (taken problematically) contains the form of every judgment of the understanding in general, and accompanies all the categories as their vehicle. So it is clear that the conclusions from it can contain only a transcendental use of the understanding. This use excludes any admixture of experience, and (as I have shown above), already at the very start we can form no optimistic concept of its progress. So I shall follow it through all the topics of the pure doctrine of the soul with a critical eye. However, for the sake of brevity, I shall proceed to examine them in an uninterrupted sequence.

<pa16> First of all, the following general observation may make us more acutely aware of this kind of reasoning. I do not know any object merely through thinking it, but I can know any object only through determining a given intuition by reference to the unity of consciousness, in which all thinking consists. Thus I do not know myself by being conscious of myself as thinking, but only when I am conscious to myself of the intuition of my self as determined in relation to the function of thought. So all modes of self-consciousness in thought [B407] (taken in itself) are not yet concepts-of-understanding of objects (categories), but are mere functions, which do not provide thought with any object at all for it to know, and hence do not provide my self as an object either. The object is not the consciousness of that which determines, but only the consciousness of the determinable self, that is, of my inner intuition (in so far as its multiplicity can be unified in accordance with the universal precondition of the unity of apperception in thought).

<pa17> 1. Now in all judgments, I am always the determining subject of the relation which the judgment consists in. But it is a deductively necessary, and indeed an analytic proposition that the I which I think must always be taken as the subject of thought, and not as something which can be considered merely as a predicate attached to the thought. However, this does not mean that I, as object, am for myself a self-subsistent being, or substance. This claim goes too far, since it requires data which are not met with at all in thought, and perhaps more than I will ever meet with (in thought) quite generally (in so far as I consider that which thinks merely as such).

<pa18> 2. It is already contained in the concept of thought (and hence it is an analytic proposition) that the I of apperception (and therefore in every thought) is singular, and cannot be broken up into a multiplicity of subjects. Consequently it denotes a logically simple subject. However, this [B408] does not mean that the thinking I is a simple substance, since that would be a synthetic proposition. The concept of substance always relates to intuitions; and since in my case these can only be sensory, it therefore lies completely outside the scope of the understanding and its thinking. And it is essentially only the understanding which is referred to here, when it is said that the I in thought is simple. In cases other than that of the self, it requires much paraphernalia to discern substance from what is given in intuition, let alone to discern whether it too could be simple (as with the parts of matter). So it would be miraculous if, in this case, which involves the poorest representation of all, substance were given to me so directly, as if through some sort of revelation.

<pa19> 3. The proposition of the identity of my self in all multiplicities of which I am conscious also lies in the concepts themselves, and is therefore an analytic proposition. However, this identity of the subject which I can be conscious of in all its representations has nothing to do with the intuition of the subject, through which it is given as an object. So the proposition cannot denote the identity of the person, meaning consciousness of the identity of one’s own substance as a thinking being through all its changing states. To prove this would require various [B409] synthetic judgments based on the given intuition; and it cannot be achieved merely by analysis of the analytic proposition ‘I think’.

<pa20> 4. I distinguish my own existence, as that of a thinking being, from other things external to me (which include my body). This is also an analytic proposition, since other things are those which I think as distinct from me. However, this gives me no means of knowing whether this consciousness of my self is possible at all without things external to me, through which representations are given to me; and hence whether I could exist simply as a thinking being (without being a human).

<pa21> So nothing at all to do with my knowledge of my self as an object has been achieved through the analysis of the consciousness of my self in thought in general. The logical exposition of thought in general is wrongly taken as a metaphysical determination of the object.

<pa22> A bigger, indeed the only stumbling-block for my whole critique would be if it were possible to prove apriori that all thinking beings are simple substances in themselves. It would follow from this same ground of proof that, as such, they necessarily have personality, and are conscious of their existence separate from all matter. For in this way we would have made just one step beyond the world of the senses, and would have set foot in the territory of noumena. Then no-one could deny us [B410] the authority to expand further into this territory, to cultivate it, and, depending on each person’s good fortune, to take possession of it.

<pa23> For the proposition ‘Every thinking being is, as such, a simple substance’ is a synthetic apriori proposition, for two reasons. First, it goes beyond the concept on which it is based, and adds to thought in general the way in which it exists. Second, it adds to that concept a predicate (that of simplicity) which cannot be given in any experience at all. But if this were allowed, synthetic apriori propositions would not be feasible and admissible merely in relation to objects of possible experience, and indeed as principles of the possibility of this experience itself (which is what I have asserted), but would also be able to reach out to things in general and in themselves. This consequence would put an end to this whole critique, and would tell us to leave everything as it was in antiquity. However, this danger is not so great here, when one gets closer to the heart of things.

<pa24> In the methodology of rational psychology, there is an overarching paralogism, which can be set out in the following syllogism:

The major premise refers to a being which can be thought universally and in every respect, and so this includes how it might be given in intuition. But the minor premise refers to it only in so far as it considers itself, as subject, relative to thought and the unity of consciousness, and not also in connection with the intuition through which it is given to thought as object. So the conclusion is arrived at through the sophism of figure of speech, and hence fallaciously.*

<pa26> [B412] It will become absolutely clear that this reduction of the famous argument to a paralogism is perfectly correct, if you refer back to the General Remark on the Systematic Representation of the Principles, and to the section on Noumena. There I proved that the concept of a thing which can exist independently as a subject, and not just as a predicate, includes no objective reality at all. In other words, you could not know whether, in general, any object could correspond to it, since you would have no insight into the possibility of such a mode of existing. Consequently, it provides no knowledge at all.

<pa27> So if it is to be called a substance, and denote an object which can be given (i.e. if it is to be an item of knowledge), it must be grounded in a persisting intuition. Such an intuition is the indispensable precondition of the objective reality of a concept, since it is that through which alone the object is given. Now in [B413] inner intuition we have nothing at all which persists, since the I is only the consciousness of my thought. So as long as we confine ourselves merely to thought, we also lack the necessary precondition for applying the concept of substance (i.e. the concept of a self-subsistent subject) to itself as a thinking being. The simplicity of the substance, which is involved in this concept, is also completely lost along with its objective reality. It turns into nothing more than a logical and qualitative unity of self-consciousness in thought in general, and the subject could equally well be composite or not.

<pa28>