The Transcendental Problem, Part 2

§ 14.

§ 14.

NATURE is the existence of things, so far as it is determined according to universal laws. Should nature signify the existence of things in themselves, we could never cognise it either a priori or a posteriori. Not a priori, for how can we know what belongs to things in themselves, since this never can be done by the dissection of our concepts (in analytical judgments)? We do not want to know what is contained in our concept of a thing (for the [concept describes what] belongs to its logical being), but what is in the actuality of the thing superadded to our concept, and by what the thing itself is determined in its existence outside the concept. Our understanding, and the conditions on which alone it can connect the determinations of things in their existence, do not prescribe any rule to things themselves; these do not conform to our understanding, but it must conform itself to them; they must therefore be first given us in order to gather these determinations from them, wherefore they would not be cognised a priori.

Nature is the existence of things insofar as universal laws determine that existence. If nature meant the existence of things in themselves, we could never know nature either a priori or a posteriori. We could not know it a priori, because how can we know what belongs to things in themselves? We can never do this by analyzing our concepts (in analytical judgments). We do not want to know what our concept of a thing contains. That describes what belongs to the thing’s logical being. We want to know what exists in the thing’s actual reality beyond our concept. We also want to know what determines the thing’s existence outside the concept. Our understanding can connect the properties of things in their existence only under certain conditions. But neither our understanding nor those conditions prescribe any rule to things themselves. Things do not conform to our understanding. Rather, our understanding must conform to them. Things must therefore first be given to us so that we can learn their properties from them. For that reason, we could not know those properties a priori.

A cognition of the nature of things in themselves a posteriori would be equally impossible. For, if experience is to teach us laws, to which the existence of things is subject, these laws, if they regard things in themselves, must belong to them of necessity even outside our experience. But experience teaches us what exists and how it exists, but never that it must necessarily exist so and not otherwise. Experience therefore can never teach us the nature of things in themselves.

It would be equally impossible to learn the nature of things in themselves from experience. Suppose experience could teach us laws governing the existence of things. If these laws concerned things in themselves, they would necessarily apply even outside our experience. But experience teaches us what exists and how it exists. It never teaches us that things must necessarily exist as they do and not otherwise. Therefore, experience can never teach us the nature of things in themselves.

§ 15. We nevertheless actually possess a pure science of nature in which are propounded, a priori and with all the necessity requisite to apodeictical propositions, laws to which nature is subject. I need only call to witness that propaedeutic of natural science which, under the title of the universal Science of Nature, precedes all Physics (which is founded upon empirical principles). In it we have Mathematics applied to appearance, and also merely discursive principles (or those derived from concepts), which constitute the philosophical part of the pure cognition of nature. But there are several things in it, which are not quite pure and independent of empirical sources: such as the concept of motion, that of impenetrability (upon which the empirical concept of matter rests), that of inertia, and many others, which prevent its being called a perfectly pure science of nature. Besides, it only refers to objects of the external sense, and therefore does not give an example of a universal science of nature, in the strict sense, for such a science must reduce nature in general, whether it regards the object of the external or that of the internal sense (the object of Physics as well as Psychology), to universal laws. But among the principles of this universal physics there are a few which actually have the required universality; for instance, the propositions that "substance is permanent," and that "every event is determined by a cause according to constant laws," etc. These are actually universal laws of nature, which subsist completely a priori. There is then in fact a pure science of nature, and the question arises, How is it possible?

§ 15. Nevertheless, we do possess a pure science of nature. It sets out laws to which nature is subject, a priori and with all the necessity required for apodeictic propositions. As evidence, I need only point to the introduction to natural science called the universal Science of Nature. It comes before all Physics, which is based on empirical principles. In this introductory science, mathematics is applied to appearances. It also contains purely discursive principles, or principles derived from concepts. These constitute the philosophical part of pure knowledge of nature. But several things in this science are not entirely pure and independent of empirical sources. These include the concepts of motion, impenetrability, inertia, and many others. The empirical concept of matter rests on the concept of impenetrability. These concepts prevent the universal Science of Nature from being called a perfectly pure science of nature. Besides, this science deals only with objects of external sense. It therefore does not provide an example of a universal science of nature in the strict sense. Such a science must bring nature in general under universal laws. It must do so whether nature concerns objects of external sense or of internal sense, the objects of Physics or Psychology. But a few principles of this universal physics do have the required universality. Examples are the propositions that "substance is permanent," and that "every event is determined by a cause according to constant laws," etc. These are genuine universal laws of nature that hold entirely a priori. A pure science of nature does therefore exist, and the question arises: How is it possible?

§ 16. The word "nature" assumes yet another meaning, which determines the object, whereas in the former sense it only denotes the conformity to law [Gesetzmässigkeit] of the determinations of the existence of things generally. If we consider it materialiter (i.e., in the matter that forms its objects) "nature is the complex of all the objects of experience." And with this only are we now concerned, for besides, things which can never be objects of experience, if they must be cognised as to their nature, would oblige us to have recourse to concepts whose meaning could never be given in concreto (by any example of possible experience). Consequently we must form for ourselves a list of concepts of their nature, the reality whereof (i.e., whether they actually refer to objects, or are mere creations of thought) could never be determined. The cognition of what cannot be an object of experience would be hyperphysical, and with things hyperphysical we are here not concerned, but only with the cognition of nature, the actuality of which can be confirmed by experience, though it [the cognition of nature] is possible a priori and precedes all experience.

§ 16. The word "nature" has another meaning that specifies the object. In the earlier sense, it refers only to the lawfulness [Gesetzmässigkeit] of the determinations of things’ existence in general. If we consider nature materialiter (that is, in terms of the matter that makes up its objects), "nature is the totality of all objects of experience." We are concerned only with nature in this sense. Suppose we had to know the nature of things that can never be objects of experience. We would then have to use concepts whose meaning could never be shown in concrete terms (by any example of possible experience). We would therefore have to make a list of concepts of the nature of such things. We could never determine the reality of these concepts, that is, whether they actually refer to objects or are merely creations of thought. Knowledge of what cannot be an object of experience would be hyperphysical. We are not concerned here with hyperphysical things. We are concerned only with knowledge of nature. The actuality of this knowledge can be confirmed by experience, though the knowledge is possible a priori and precedes all experience.

§ 17. The formal [aspect] of nature in this narrower sense is therefore the conformity to law of all the objects of experience, and so far as it is cognised a priori, their necessary conformity. But it has just been shown that the laws of nature can never be cognised a priori in objects so far as they are considered not in reference to possible experience, but as things in themselves. And our inquiry here extends not to things in themselves (the properties of which we pass by), but to things as objects of possible experience, and the complex of these is what we properly designate as nature. And now I ask, when the possibility of a cognition of nature a priori is in question, whether it is better to arrange the problem thus: How can we cognise a priori that things as objects of experience necessarily conform to law? or thus: How is it possible to cognise a priori the necessary conformity to law of experience itself as regards all its objects generally?

§ 17. The formal aspect of nature in this narrower sense is therefore the conformity of all objects of experience to law. Insofar as we know this conformity a priori, we know it to be necessary. But we have just shown that we can never know the laws of nature a priori when we consider objects as things in themselves rather than in relation to possible experience. Our inquiry here does not concern things in themselves, whose properties we leave aside. Instead, it concerns things as objects of possible experience. The whole collection of these objects is what we properly call nature. Now the question is how we can know nature a priori. Is it better to frame the problem this way: How can we know a priori that things, as objects of experience, necessarily conform to law? Or is it better to frame it this way: How can we know a priori that experience itself necessarily conforms to law with respect to all its objects in general?

Closely considered, the solution of the problem, represented in either way, amounts, with regard to the pure cognition of nature (which is the point of the question at issue), entirely to the same thing. For the subjective laws, under which alone an empirical cognition of things is possible, hold good of these things, as Objects of possible experience (not as things in themselves, which are not considered here). Either of the following statements means quite the same:

On close examination, either way of presenting the solution comes to exactly the same thing for pure knowledge of nature. That knowledge is what the question is about. For the subjective laws that alone make empirical knowledge of things possible also apply to those things as objects of possible experience. They do not apply to things as they are in themselves, which are not considered here. The following two statements mean exactly the same thing:

A judgment of observation can never rank as experience, without the law, that "whenever an event is observed, it is always referred to some antecedent, which it follows according to a universal rule."

A judgment based on observation can never count as experience without this law: "Whenever an event is observed, it is always linked to something earlier, which the event follows according to a universal rule."

"Everything, of which experience teaches that it happens, must have a cause."

"Everything that experience shows to happen must have a cause."

It is, however, more commendable to choose the first formula. For we can a priori and previous to all given objects have a cognition of those conditions, on which alone experience is possible, but never of the laws to which things may in themselves be subject, without reference to possible experience. We cannot therefore study the nature of things a priori otherwise than by investigating the conditions and the universal (though subjective) laws, under which alone such a cognition as experience (as to mere form) is possible, and we determine accordingly the possibility of things, as objects of experience. For if I should choose the second formula, and seek the conditions a priori, on which nature as an object of experience is possible, I might easily fall into error, and fancy that I was speaking of nature as a thing in itself, and then move round in endless circles, in a vain search for laws concerning things of which nothing is given me.

It is better, however, to choose the first formula. We can know a priori, before any objects are given to us, the conditions that alone make experience possible. But we can never know a priori the laws that things may obey in themselves, apart from possible experience. Therefore, we can study the nature of things a priori only by examining the conditions that make experience possible. We must also examine the universal, though subjective, laws that make experience possible as a form of knowledge. These conditions and laws concern only the form of experience. In this way, we determine how things are possible as objects of experience. For if I chose the second formula, I would look for the a priori conditions that make nature possible as an object of experience. I might then easily make a mistake and imagine that I was speaking of nature as a thing in itself. I would then go around in endless circles, searching in vain for laws about things of which nothing is given to me.

Accordingly we shall here be concerned with experience only, and the universal conditions of its possibility which are given a priori. Thence we shall determine nature as the whole object of all possible experience. I think it will be understood that I here do not mean the rules of the observation of a nature that is already given, for these already presuppose experience. I do not mean how (through experience) we can study the laws of nature; for these would not then be laws a priori, and would yield us no pure science of nature; but [I mean to ask] how the conditions a priori of the possibility of experience are at the same time the sources from which all the universal laws of nature must be derived.

We will therefore be concerned only with experience and the universal conditions that make it possible and are given a priori. From these conditions, we will determine nature as the whole object of all possible experience. I do not mean the rules for observing a nature already given to us, since such rules already presuppose experience. Nor do I mean to ask how we can study the laws of nature through experience. Those laws would not then be a priori, and they would not give us a pure science of nature. Instead, I mean to ask how the a priori conditions that make experience possible are also the sources from which all universal laws of nature must be derived.

§ 18. In the first place we must state that, while all judgments of experience (Erfahrungsurtheile) are empirical (i.e., have their ground in immediate sense perception), vice versa, all empirical judgments (empirische Urtheile) are not judgments of experience, but, besides the empirical, and in general besides what is given to the sensuous intuition, particular concepts must yet be superadded—concepts which have their origin quite a priori in the pure understanding, and under which every perception must be first of all subsumed and then by their means changed into experience.¹¹

§ 18. First, we must note that all judgments of experience (Erfahrungsurtheile) are empirical. That is, they are grounded in immediate sense perception. But not all empirical judgments (empirische Urtheile) are judgments of experience. Certain concepts must also be added to what is empirical, or, more generally, to what is given through sensory intuition. These concepts originate entirely a priori in the pure understanding. Every perception must first be brought under these concepts and then transformed into experience by means of them.¹¹

Empirical judgments, so far as they have objective validity, are judgments of experience; but those which are only subjectively valid, I name mere judgments of perception. The latter require no pure concept of the understanding, but only the logical connexion of perception in a thinking subject. But the former always require, besides the representation of the sensuous intuition, particular concepts originally begotten in the understanding, which produce the objective validity of the judgment of experience.

Empirical judgments are judgments of experience insofar as they are objectively valid. But I call those that are only subjectively valid mere judgments of perception. Judgments of perception require no pure concept of the understanding. They require only that a thinking subject logically connect perceptions. But judgments of experience always require more than a representation of sensory intuition. They also require particular concepts that originate in the understanding. These concepts give judgments of experience their objective validity.

All our judgments are at first merely judgments of perception; they hold good only for us (i.e., for our subject), and we do not till afterwards give them a new reference (to an object), and desire that they shall always hold good for us and in the same way for everybody else; for when a judgment agrees with an object, all judgments concerning the same object must likewise agree among themselves, and thus the objective validity of the judgment of experience signifies nothing else than its necessary universality of application. And conversely when we have reason to consider a judgment necessarily universal (which never depends upon perception, but upon the pure concept of the understanding, under which the perception is subsumed), we must consider it objective also, that is, that it expresses not merely a reference of our perception to a subject, but a quality of the object. For there would be no reason for the judgments of other men necessarily agreeing with mine, if it were not the unity of the object to which they all refer, and with which they accord; hence they must all agree with one another.

All our judgments are initially judgments of perception. They hold true only for us (that is, for us as subjects). Only later do we relate these judgments to an object. We then expect them always to hold true for us and equally for everyone else. For when a judgment agrees with an object, all judgments about the same object must also agree with one another. Thus, the objective validity of a judgment of experience means nothing more than that it must apply universally. Conversely, when we have reason to consider a judgment necessarily universal, we must also consider it objective. Necessary universality never depends on perception. It depends on the pure concept of the understanding under which the perception falls. To call a judgment objective means that it expresses a quality of the object, not merely a relation between our perception and a subject. For other people’s judgments would have no reason to necessarily agree with mine if they did not all refer to and agree with the same object. Hence all these judgments must agree with one another.

§ 19. Therefore objective validity and necessary universality (for everybody) are equivalent terms, and though we do not know the object in itself, yet when we consider a judgment as universal, and also necessary, we understand it to have objective validity. By this judgment we cognise the object (though it remains unknown as it is in itself) by the universal and necessary connexion of the given perceptions. As this is the case with all objects of sense, judgments of experience take their objective validity not from the immediate cognition of the object (which is impossible), but from the condition of universal validity in empirical judgments, which, as already said, never rests upon empirical, or, in short, sensuous conditions, but upon a pure concept of the understanding. The object always remains unknown in itself; but when by the concept of the understanding the connexion of the representations of the object, which are given to our sensibility, is determined as universally valid, the object is determined by this relation, and it is the judgment that is objective.

§ 19. Therefore, objective validity and necessary universality (for everyone) mean the same thing. Although we do not know the object as it is in itself, we understand a judgment to be objectively valid when we regard it as universal and necessary. Through such a judgment, we know the object by the universal and necessary connection between the perceptions given to us. Yet the object remains unknown as it is in itself. This is true of all objects of the senses. Judgments of experience therefore get their objective validity not from direct knowledge of the object, which is impossible, but from the condition that empirical judgments must be universally valid. As already noted, this condition never rests on empirical or, in short, sensory conditions. It rests instead on a pure concept of the understanding. The object always remains unknown in itself. But a concept of the understanding determines the connection between the representations of the object given to our senses as universally valid. The object is determined by this relation, and it is the judgment that is objective.

To illustrate the matter: When we say, "the room is warm, sugar sweet, and wormwood bitter"¹²—we have only subjectively valid judgments. I do not at all expect that I or any other person shall always find it as I now do; each of these sentences only expresses a relation of two sensations to the same subject, to myself, and that only in my present state of perception; consequently they are not valid of the object. Such are judgments of perception. Judgments of experience are of quite a different nature. What experience teaches me under certain circumstances, it must always teach me and everybody; and its validity is not limited to the subject nor to its state at a particular time. Hence I pronounce all such judgments as being objectively valid. For instance, when I say the air is elastic, this judgment is as yet a judgment of perception only—I do nothing but refer two of my sensations to one another. But, if I would have it called a judgment of experience, I require this connexion to stand under a condition, which makes it universally valid. I desire therefore that I and everybody else should always connect necessarily the same perceptions under the same circumstances.

To illustrate the point, when we say, "the room is warm, sugar sweet, and wormwood bitter"¹², these judgments are valid only for the person making them. I do not expect that I or anyone else will always find these things as I do now. Each sentence expresses only a relation between two sensations in the same person, namely myself. And it expresses that relation only as I perceive it now. These judgments are therefore not valid for the objects themselves. They are judgments of perception. Judgments of experience are quite different. What experience teaches me under certain circumstances, it must always teach me and everyone else. Its validity is not limited to one person or to that person's state at a particular time. I therefore call all such judgments objectively valid. For example, when I say that the air is elastic, this is still only a judgment of perception. I am merely relating two of my sensations to each other. But if I want to call it a judgment of experience, I require the connection to meet a condition that makes it universally valid. I therefore want everyone, including myself, to connect the same perceptions necessarily under the same circumstances, every time.

§ 20. We must consequently analyse experience in order to see what is contained in this product of the senses and of the understanding, and how the judgment of experience itself is possible. The foundation is the intuition of which I become conscious, i.e., perception (perceptio), which pertains merely to the senses. But in the next place, there are acts of judging (which belong only to the understanding). But this judging may be twofold—first, I may merely compare perceptions and connect them in a particular state of my consciousness; or, secondly, I may connect them in consciousness generally. The former judgment is merely a judgment of perception, and of subjective validity only: it is merely a connexion of perceptions in my mental state, without reference to the object. Hence it is not, as is commonly imagined, enough for experience to compare perceptions and to connect them in consciousness through judgment; there arises no universality and necessity, for which alone judgments can become objectively valid and be called experience.

§ 20. We must therefore analyze experience to see what this product of the senses and the understanding contains. We must also see how a judgment of experience is possible. Its foundation is an intuition of which I become conscious, that is, a perception (perceptio). Perception belongs only to the senses. Next come acts of judgment, which belong only to the understanding. But judgment can take two forms. First, I may simply compare perceptions and connect them in a particular state of my consciousness. Second, I may connect them in consciousness generally. The first kind is merely a judgment of perception and is valid only subjectively. It merely connects perceptions in my mental state, without reference to the object. So, contrary to common belief, experience requires more than comparing perceptions and connecting them through judgment in consciousness. This alone produces no universality or necessity. Only through universality and necessity can judgments be objectively valid and be called experience.

Quite another judgment therefore is required before perception can become experience. The given intuition must be subsumed under a concept, which determines the form of judging in general relatively to the intuition, connects its empirical consciousness in consciousness generally, and thereby procures universal validity for empirical judgments. A concept of this nature is a pure a priori concept of the Understanding, which does nothing but determine for an intuition the general way in which it can be used for judgments. Let the concept be that of cause, then it determines the intuition which is subsumed under it, e.g., that of air, relative to judgments in general, viz., the concept of air serves with regard to its expansion in the relation of antecedent to consequent in a hypothetical judgment. The concept of cause accordingly is a pure concept of the understanding, which is totally disparate from all possible perception, and only serves to determine the representation subsumed under it, relatively to judgments in general, and so to make a universally valid judgment possible.

A quite different judgment is therefore needed before perception can become experience. The given intuition must be brought under a concept. This concept determines how judgments in general are formed in relation to the intuition. It connects empirical consciousness of the intuition with consciousness in general. It thereby gives empirical judgments universal validity. A concept of this kind is a pure a priori concept of the understanding. It does nothing but determine how an intuition can be used in judgments generally. Take the concept of cause. It determines how an intuition brought under it, such as the intuition of air, relates to judgments in general. For example, the concept of air serves as the antecedent to its expansion as the consequent in a hypothetical judgment. The concept of cause is therefore a pure concept of the understanding, entirely different from all possible perception. It serves only to determine how the representation brought under it relates to judgments in general. In this way, it makes a universally valid judgment possible.

Before, therefore, a judgment of perception can become a judgment of experience, it is requisite that the perception should be subsumed under some such a concept of the understanding; for instance, air ranks under the concept of causes, which determines our judgment about it in regard to its expansion as hypothetical.¹³ Thereby the expansion of the air is represented not as merely belonging to the perception of the air in my present state or in several states of mine, or in the state of perception of others, but as belonging to it necessarily. The judgment, "the air is elastic," becomes universally valid, and a judgment of experience, only by certain judgments preceding it, which subsume the intuition of air under the concept of cause and effect: and they thereby determine the perceptions not merely as regards one another in me, but relatively to the form of judging in general, which is here hypothetical, and in this way they render the empirical judgment universally valid.

Therefore, before a judgment of perception can become a judgment of experience, the perception must fall under a concept of the understanding. For example, air falls under the concept of cause. This concept makes our judgment about the expansion of air hypothetical.¹³ The expansion of air is thereby represented as necessarily belonging to air. It is not represented as merely belonging to my perception of air in my present state, in several of my states, or in others’ states of perception. The judgment, "the air is elastic," becomes universally valid and a judgment of experience only through certain prior judgments. These judgments bring the intuition of air under the concept of cause and effect. They thus determine how the perceptions relate, not merely to one another in me, but to the form of judgment in general. Here that form is hypothetical. In this way, the prior judgments make the empirical judgment universally valid.

If all our synthetical judgments are analysed so far as they are objectively valid, it will be found that they never consist of mere intuitions connected only (as is commonly believed) by comparison into a judgment; but that they would be impossible were not a pure concept of the understanding superadded to the concepts abstracted from intuition, under which concept these latter are subsumed, and in this manner only combined into an objectively valid judgment. Even the judgments of pure mathematics in their simplest axioms are not exempt from this condition. The principle, "a straight line is the shortest between two points," presupposes that the line is subsumed under the concept of quantity, which certainly is no mere intuition, but has its seat in the understanding alone, and serves to determine the intuition (of the line) with regard to the judgments which may be made about it, relatively to their quantity, that is, to plurality (as judicia plurativa).¹⁴ For under them it is understood that in a given intuition there is contained a plurality of homogenous parts.

If we analyze all our synthetic judgments insofar as they are objectively valid, we will find something important. Such judgments never consist merely of intuitions joined into a judgment by comparison, as is commonly believed. Rather, they would be impossible without a pure concept of the understanding added to the concepts abstracted from intuition. Those concepts are subsumed under the pure concept. Only in this way are they combined into an objectively valid judgment. Even the simplest axioms of pure mathematics are subject to this condition. The principle, "a straight line is the shortest between two points," presupposes that the line is subsumed under the concept of quantity. Quantity is certainly not a mere intuition. It belongs to the understanding alone and serves to determine the intuition of the line. It determines the intuition with respect to the judgments that may be made about the line in terms of quantity. That is, it determines the intuition with respect to judgments about plurality (as judicia plurativa).¹⁴ For such judgments imply that a given intuition contains a plurality of homogeneous parts.

§ 21. To prove, then, the possibility of experience so far as it rests upon pure concepts of the understanding a priori, we must first represent what belongs to judgments in general and the various functions of the understanding, in a complete table. For the pure concepts of the understanding must run parallel to these functions, as such concepts are nothing more than concepts of intuitions in general, so far as these are determined by one or other of these functions of judging, in themselves, that is, necessarily and universally. Hereby also the a priori principles of the possibility of all experience, as of an objectively valid empirical cognition, will be precisely determined. For they are nothing but propositions by which all perception is (under certain universal conditions of intuition) subsumed under those pure concepts of the understanding.

§ 21. To prove that experience is possible insofar as it rests on pure a priori concepts of the understanding, we must first make a complete table. This table must show what belongs to judgments in general and the various functions of the understanding. The pure concepts of the understanding must correspond to these functions. For these pure concepts are nothing more than concepts of intuitions in general, insofar as the intuitions are determined in themselves by one or another of these functions of judgment. That is, they are determined necessarily and universally. The table will also define precisely the a priori principles that make all experience possible as objectively valid empirical knowledge. These principles are simply statements that place all perception under those pure concepts of the understanding, subject to certain universal conditions of intuition.

§ 21a. In order to comprise the whole matter in one idea, it is first necessary to remind the reader that we are discussing not the origin of experience, but of that which lies in experience. The former pertains to empirical psychology, and would even then never be adequately explained without the latter, which belongs to the Critique of cognition, and particularly of the understanding.

§ 21a. To sum up the whole matter in one idea, I must first remind the reader of our subject. We are discussing not the origin of experience, but the origin of what lies in experience. The origin of experience belongs to empirical psychology. But it could never be adequately explained without an account of the origin of what lies in experience. That account belongs to the critique of cognition, especially of the understanding.

Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments, which the understanding forms alone from sensuous intuitions, are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in the sensuous intuition, while in the other the judgments must express what experience in general, and not what the mere perception (which possesses only subjective validity) contains. The judgment of experience must therefore add to the sensuous intuition and its logical connexion in a judgment (after it has been rendered universal by comparison) something that determines the synthetical judgment as necessary and therefore as universally valid. This can be nothing else than that concept which represents the intuition as determined in itself with regard to one form of judgment rather than another, viz., a concept of that synthetical unity of intuitions which can only be represented by a given logical function of judgments.

Experience consists of intuitions, which belong to sensibility, and judgments, which are entirely the work of the understanding. But the judgments the understanding forms from sensory intuitions alone are far from being judgments of experience. In the first case, the judgment connects perceptions only as they are given in sensory intuition. In the second, the judgment must express what experience in general contains, not what mere perception contains. Mere perception has only subjective validity. A judgment of experience must therefore add something to sensory intuition and its logical connection in a judgment. This addition must be made after the judgment has been made universal through comparison. It must establish that the synthetic judgment is necessary and therefore universally valid. This addition can only be a concept that represents the intuition as determined in itself by one form of judgment rather than another. It is a concept of the synthetic unity of intuitions. This unity can be represented only by a given logical function of judgments.

§ 22. The sum of the matter is this: the business of the senses is to intuite—that of the understanding is to think. But thinking is uniting representations in one consciousness. This union originates either merely relative to the subject, and is accidental and subjective, or is absolute, and is necessary or objective. The union of representations in one consciousness is judgment. Thinking therefore is the same as judging, or referring representations to judgments in general. Hence judgments are either merely subjective, when representations are referred to a consciousness in one subject only, and united in it, or objective, when they are united in a consciousness generally, that is, necessarily. The logical functions of all judgments are but various modes of uniting representations in consciousness. But if they serve for concepts, they are concepts of their necessary union in a consciousness, and so principles of objectively valid judgments. This union in a consciousness is either analytical, by identity, or synthetical, by the combination and addition of various representations one to another. Experience consists in the synthetical connexion of phenomena (perceptions) in consciousness, so far as this connexion is necessary. Hence the pure concepts of the understanding are those under which all perceptions must be subsumed ere they can serve for judgments of experience, in which the synthetical unity of the perceptions is represented as necessary and universally valid.¹⁵

§ 22. The point is this: the senses provide intuitions, while the understanding thinks. Thinking means uniting representations in one consciousness. This union arises either only in relation to the subject and is accidental and subjective, or absolutely and is necessary or objective. The union of representations in one consciousness is judgment. Thinking is therefore the same as judging, or relating representations to judgments in general. Hence judgments are merely subjective when representations are related to the consciousness of only one subject and united there. Judgments are objective when representations are united in a consciousness in general, that is, necessarily. The logical functions of all judgments are simply different ways of uniting representations in consciousness. But when these functions serve as concepts, they are concepts of the necessary union of representations in a consciousness. They are therefore principles of objectively valid judgments. This union in a consciousness is either analytic, through identity, or synthetic, through the combination and addition of different representations to one another. Experience consists in the synthetic connection of phenomena (perceptions) in consciousness, insofar as this connection is necessary. Hence the pure concepts of the understanding are those under which all perceptions must be subsumed before they can serve for judgments of experience. In such judgments, the synthetic unity of the perceptions is represented as necessary and universally valid.¹⁵

§ 23. Judgments, when considered merely as the condition of the union of given representations in a consciousness, are rules. These rules, so far as they represent the union as necessary, are rules a priori, and so far as they cannot be deduced from higher rules, are fundamental principles. But in regard to the possibility of all experience, merely in relation to the form of thinking in it, no conditions of judgments of experience are higher than those which bring the phenomena, according to the various form of their intuition, under pure concepts of the understanding, and render the empirical judgment objectively valid. These concepts are therefore the a priori principles of possible experience.

§ 23. Judgments can be considered simply as conditions for joining given representations in consciousness. Considered in this way, judgments are rules. To the extent that these rules represent the connection as necessary, they are a priori rules. To the extent that they cannot be derived from higher rules, they are fundamental principles. But, as far as the possibility of all experience and the form of thought in it are concerned, no conditions for judgments of experience are higher than the following. These conditions bring appearances under pure concepts of the understanding according to the different forms in which the appearances are intuited. They also make empirical judgments objectively valid. These concepts are therefore the a priori principles of possible experience.

The principles of possible experience are then at the same time universal laws of nature, which can be cognised a priori. And thus the problem in our second question, "How is the pure Science of Nature possible?" is solved. For the system which is required for the form of a science is to be met with in perfection here, because, beyond the above-mentioned formal conditions of all judgments in general offered in logic, no others are possible, and these constitute a logical system. The concepts grounded thereupon, which contain the a priori conditions of all synthetical and necessary judgments, accordingly constitute a transcendental system. Finally the principles, by means of which all phenomena are subsumed under these concepts, constitute a physical¹⁶ system, that is, a system of nature, which precedes all empirical cognition of nature, makes it even possible, and hence may in strictness be denominated the universal and pure science of nature.

The principles of possible experience are also universal laws of nature that can be known a priori. This solves the problem raised in our second question: "How is the pure Science of Nature possible?" The system needed to give a science its form is present here in perfect form. Logic provides the formal conditions of all judgments in general. No other such conditions are possible, and these conditions constitute a logical system. The concepts based on those conditions contain the a priori conditions of all synthetic and necessary judgments. These concepts therefore constitute a transcendental system. Finally, the principles that bring all phenomena under these concepts constitute a physical¹⁶ system, or a system of nature. This system precedes all empirical knowledge of nature and even makes such knowledge possible. It may therefore, strictly speaking, be called the universal and pure science of nature.

§ 24. The first one¹⁷ of the physiological principles subsumes all phenomena, as intuitions in space and time, under the concept of Quantity, and is so far a principle of the application of Mathematics to experience. The second one subsumes the empirical element, viz., sensation which denotes the real in intuitions, not indeed directly under the concept of quantity, because sensation is not an intuition that contains either space or time, though it places the respective object into both. But still there is between reality (sense-representation) and the zero, or total void of intuition in time, a difference which has a quantity. For between every given degree of light and of darkness, between every degree of heat and of absolute cold, between every degree of weight and of absolute lightness, between every degree of occupied space and of totally void space, diminishing degrees can be conceived, in the same manner as between consciousness and total unconsciousness (the darkness of a psychological blank) ever diminishing degrees obtain. Hence there is no perception that can prove an absolute absence of it; for instance, no psychological darkness that cannot be considered as a kind of consciousness. This occurs in all cases of sensation, and so the understanding can anticipate even sensations, which constitute the peculiar quality of empirical representations (appearances), by means of the principle: "that they all have (consequently that what is real in all phenomena has) a degree." Here is the second application of mathematics (mathesis intensorum) to the science of nature.

§ 24. The first¹⁷ of the physiological principles brings all phenomena, as intuitions in space and time, under the concept of quantity. In this respect, it is a principle for applying mathematics to experience. The second principle concerns the empirical element, namely sensation, which represents what is real in intuitions. It does not bring sensation directly under the concept of quantity. For sensation is not an intuition containing either space or time, though it places its object in both. But there is a measurable difference between reality (sense representation) and zero, or the complete absence of intuition in time. For we can conceive of diminishing degrees between any given degree of light and darkness, or heat and absolute cold. The same is true between any degree of weight and absolute lightness, or occupied space and completely empty space. Likewise, there are ever-diminishing degrees between consciousness and total unconsciousness (the darkness of a psychological blank). So no perception can prove its own complete absence. For example, no psychological darkness is so complete that it cannot be considered a kind of consciousness. This holds for all sensation. Sensations make up the distinctive quality of empirical representations (appearances). Even so, the understanding can anticipate sensations through the principle: "that they all have (and therefore that what is real in all phenomena has) a degree." Here is the second application of mathematics (mathesis intensorum) to the science of nature.

§ 25. Anent the relation of appearances merely with a view to their existence, the determination is not mathematical but dynamical, and can never be objectively valid, consequently never fit for experience, if it does not come under a priori principles by which the cognition of experience relative to appearances becomes even possible. Hence appearances must be subsumed under the concept of Substance, which is the foundation of all determination of existence, as a concept of the thing itself; or secondly—so far as, a succession is found among phenomena, that is, an event—under the concept of an Effect with reference to Cause; or lastly—so far as coexistence is to be known objectively, that is, by a judgment of experience—under the concept of Community (action and reaction).¹⁸ Thus a priori principles form the basis of objectively valid, though empirical judgments, that is, of the possibility of experience so far as it must connect objects as existing in nature. These principles are the proper laws of nature, which may be termed dynamical.

§ 25. When appearances are related solely with respect to their existence, their determination is not mathematical but dynamical. This determination can never be objectively valid, and therefore can never serve experience, unless it comes under a priori principles. These principles make empirical knowledge of appearances possible in the first place. Appearances must therefore come under the concept of Substance, understood as the thing itself. Substance is the basis for all determination of existence. Second, insofar as there is a succession among phenomena, that is, an event, appearances must come under the concept of an Effect in relation to a Cause. Finally, insofar as coexistence is to be known objectively, that is, through a judgment of experience, appearances must come under the concept of Community (action and reaction).¹⁸ Thus a priori principles underlie objectively valid, though empirical, judgments. In other words, they underlie the possibility of experience insofar as experience must connect objects as existing in nature. These principles are the laws of nature proper, which may be called dynamical.

Finally the cognition of the agreement and connexion not only of appearances among themselves in experience, but of their relation to experience in general, belongs to the judgments of experience. This relation contains either their agreement with the formal conditions, which the understanding cognises, or their coherence with the materials of the senses and of perception, or combines both into one concept. Consequently it contains Possibility, Actuality, and Necessity according to universal laws of nature; and this constitutes the physical doctrine of method, or the distinction of truth and of hypotheses, and the bounds of the certainty of the latter.

Finally, judgments of experience involve knowing how appearances agree and connect with one another in experience. They also involve knowing how appearances relate to experience in general. This relation involves their agreement with the formal conditions recognized by the understanding, or their coherence with the material provided by the senses and perception. It may also combine both in a single concept. Consequently, this relation involves possibility, actuality, and necessity according to universal laws of nature. This constitutes the physical doctrine of method: the distinction between truth and hypotheses, and the limits of certainty for hypotheses.

§ 26. The third table of Principles drawn from the nature of the understanding itself after the critical method, shows an inherent perfection, which raises it far above every other table which has hitherto though in vain been tried or may yet be tried by analysing the objects themselves dogmatically. It exhibits all synthetical a priori principles completely and according to one principle, viz., the faculty of judging in general, constituting the essence of experience as regards the understanding, so that we can be certain that there are no more such principles, a satisfaction such as can never be attained by the dogmatical method. Yet is this not all: there is a still greater merit in it.

§ 26. The third table of principles is derived from the nature of the understanding itself, using the critical method. It has an inherent perfection that places it far above every other table. This includes every table that has been attempted so far, though in vain, or that might yet be attempted by dogmatically analyzing objects themselves. The third table presents all synthetic a priori principles completely and according to a single principle: the faculty of judgment in general. This faculty constitutes the essence of experience as it concerns the understanding. The table therefore assures us that there are no more such principles. The dogmatic method can never give us this assurance. But this is not all. The table has a still greater merit.

We must carefully bear in mind the proof which shows the possibility of this cognition a priori, and at the same time limits all such principles to a condition which must never be lost sight of, if we desire it not to be misunderstood, and extended in use beyond the original sense which the understanding attaches to it. This limit is that they contain nothing but the conditions of possible experience in general so far as it is subjected to laws a priori. Consequently I do not say, that things in themselves possess a quantity, that their actuality possesses a degree, their existence a connexion of accidents in a substance, etc. This nobody can prove, because such a synthetical connexion from mere concepts, without any reference to sensuous intuition on the one side, or connexion of it in a possible experience on the other, is absolutely impossible. The essential limitation of the concepts in these principles then is: That all things stand necessarily a priori under the afore-mentioned conditions, as objects of experience only.

We must carefully keep in mind the proof that shows how this a priori knowledge is possible. At the same time, the proof limits all such principles to a condition we must never forget. Otherwise, we risk misunderstanding these principles and applying them beyond the meaning the understanding originally gives them. The limit is this: the principles contain only the conditions of possible experience in general, insofar as experience is subject to a priori laws. Consequently, I do not say that things in themselves have a quantity, or that their actuality has a degree. Nor do I say that their existence involves a connection of accidents in a substance, and so on. Nobody can prove this. A synthetic connection based on concepts alone is absolutely impossible without reference to sensory intuition or to its connection in a possible experience. The essential limitation of the concepts in these principles is therefore this: all things necessarily fall a priori under the conditions mentioned above, but only as objects of experience.

Hence there follows secondly a specifically peculiar mode of proof of these principles: they are not directly referred to appearances and to their relations, but to the possibility of experience, of which appearances constitute the matter only, not the form. Thus they are referred to objectively and universally valid synthetical propositions, in which we distinguish judgments of experience from those of perception. This takes place because appearances, as mere intuitions, occupying a part of space and time, come under the concept of Quantity, which unites their multiplicity a priori according to rules synthetically. Again, so far as the perception contains, besides intuition, sensibility, and between the latter and nothing (i.e., the total disappearance of sensibility), there is an ever decreasing transition, it is apparent that that which is in appearances must have a degree, so far as it (viz., the perception) does not itself occupy any part of space or of time.¹⁹ Still the transition to actuality from empty time or empty space is only possible in time; consequently though sensibility, as the quality of empirical intuition, can never be cognised a priori, by its specific difference from other sensibilities, yet it can, in a possible experience in general, as a quantity of perception be intensely distinguished from every other similar perception. Hence the application of mathematics to nature, as regards the sensuous intuition by which nature is given to us, becomes possible and is thus determined.

A second consequence follows: these principles have a distinctive mode of proof. They do not refer directly to appearances and their relations, but to the possibility of experience. Appearances provide only the matter of experience, not its form. Thus the principles refer to synthetic propositions that are objectively and universally valid. These propositions distinguish judgments of experience from judgments of perception. This is because appearances, as mere intuitions occupying parts of space and time, fall under the concept of Quantity. This concept combines their multiplicity in advance, or a priori, synthetically and according to rules. Perception, however, contains sensibility as well as intuition. Sensibility can gradually decrease until it reaches nothing, meaning its complete disappearance. So what is present in appearances must have a degree, insofar as perception itself occupies no part of space or time.¹⁹ Still, the transition from empty time or empty space to actuality is possible only in time. Consequently, sensibility, as the quality of empirical intuition, can never be known a priori by its specific difference from other sensibilities. Yet in any possible experience, sensibility can be distinguished in intensity from every other similar perception, as a quantity of perception. The application of mathematics to nature thus becomes possible and is determined in this way. This applies to the sensible intuition through which nature is given to us.

Above all, the reader must pay attention to the mode of proof of the principles which occur under the title of Analogies of experience. For these do not refer to the genesis of intuitions, as do the principles of applied mathematics, but to the connexion of their existence in experience; and this can be nothing but the determination of their existence in time according to necessary laws, under which alone the connexion is objectively valid, and thus becomes experience. The proof therefore does not turn on the synthetical unity in the connexion of things in themselves, but merely of perceptions, and of these not in regard to their matter, but to the determination of time and of the relation of their existence in it, according to universal laws. If the empirical determination in relative time is indeed objectively valid (i.e., experience), these universal laws contain the necessary determination of existence in time generally (viz., according to a rule of the understanding a priori).

Above all, pay attention to how the principles called the Analogies of experience are proved. Unlike the principles of applied mathematics, they do not concern how intuitions arise. They concern the connection between the existence of intuitions in experience. This connection can only be the determination of their existence in time according to necessary laws. Only under these laws is the connection objectively valid and so becomes experience. The proof therefore concerns the synthetic unity in the connection of perceptions, not of things in themselves. It concerns perceptions not in respect of their content, but in respect of their determination in time. It also concerns how their existence relates to time, according to universal laws. If the empirical determination in relative time is indeed objectively valid (that is, if it is experience), these universal laws contain the necessary determination of existence in time generally. This determination follows an a priori rule of the understanding.

In these Prolegomena I cannot further descant on the subject, but my reader (who has probably been long accustomed to consider experience a mere empirical synthesis of perceptions, and hence not considered that it goes much beyond them, as it imparts to empirical judgments universal validity, and for that purpose requires a pure and a priori unity of the understanding) is recommended to pay special attention to this distinction of experience from a mere aggregate of perceptions, and to judge the mode of proof from this point of view.

In these Prolegomena, I cannot discuss the subject further. My reader has probably long been accustomed to thinking of experience as merely an empirical synthesis of perceptions. The reader may therefore not have considered that experience goes much beyond these perceptions. Experience gives empirical judgments universal validity, and for this purpose it requires a pure and a priori unity of the understanding. I recommend that the reader pay special attention to the distinction between experience and a mere collection of perceptions. The reader should also judge the method of proof from this point of view.

§ 27. Now we are prepared to remove Hume's doubt. He justly maintains, that we cannot comprehend by reason the possibility of Causality, that is, of the reference of the existence of one thing to the existence of another, which is necessitated by the former. I add, that we comprehend just as little the concept of Subsistence, that is, the necessity that at the foundation of the existence of things there lies a subject which cannot itself be a predicate of any other thing; nay, we cannot even form a notion of the possibility of such a thing (though we can point out examples of its use in experience). The very same in comprehensibility affects the Community of things, as we cannot comprehend how from the state of one thing an inference to the state of quite another thing beyond it, and vice versa, can be drawn, and how substances which have each their own separate existence should depend upon one another necessarily. But I am very far from holding these concepts to be derived merely from experience, and the necessity represented in them, to be imaginary and a mere illusion produced in us by long habit. On the contrary, I have amply shown, that they and the theorems derived from them are firmly established a priori, or before all experience, and have their undoubted objective value, though only with regard to experience.

§ 27. We are now ready to resolve Hume's doubt. He rightly maintains that reason cannot understand how Causality is possible. Causality is the relation in which the existence of one thing makes the existence of another necessary. I add that we understand the concept of Subsistence just as little. Subsistence is the necessity that, underlying the existence of things, there is a subject that cannot itself be a predicate of anything else. Indeed, we cannot even conceive how such a thing is possible (though we can give examples of its use in experience). The Community of things is just as incomprehensible. We cannot understand how the state of one thing allows us to infer the state of another, separate thing, or vice versa. Nor can we understand how substances, each with its own separate existence, should necessarily depend on one another. But I am far from claiming that these concepts come merely from experience. Nor do I claim that the necessity they represent is imaginary, a mere illusion produced in us by long habit. On the contrary, I have shown at length that these concepts and the principles derived from them are firmly established a priori, or before all experience. They also have unquestionable objective validity, though only in relation to experience.

§ 28. Though I have no notion of such a connexion of things in themselves, that they can either exist as substances, or act as causes, or stand in community with others (as parts of a real whole), and I can just as little conceive such properties in appearances as such (because those concepts contain nothing that lies in the appearances, but only what the understanding alone must think): we have yet a notion of such a connexion of representations in our understanding, and in judgments generally; consisting in this that representations appear in one sort of judgments as subject in relation to predicates, in another as reason in relation to consequences, and in a third as parts, which constitute together a total possible cognition. Besides we cognise a priori that without considering the representation of an object as determined in some of these respects, we can have no valid cognition of the object, and, if we should occupy ourselves about the object in itself, there is no possible attribute, by which I could know that it is determined under any of these aspects, that is, under the concept either of substance, or of cause, or (in relation to other substances) of community, for I have no notion of the possibility of such a connexion of existence. But the question is not how things in themselves, but how the empirical cognition of things is determined, as regards the above aspects of judgments in general, that is, how things, as objects of experience, can and shall be subsumed under these concepts of the understanding. And then it is clear, that I completely comprehend not only the possibility, but also the necessity of subsuming all phenomena under these concepts, that is, of using them for principles of the possibility of experience.

§ 28. I have no idea of how things in themselves could be connected in these ways. They might exist as substances, act as causes, or stand in community with one another as parts of a real whole. Nor can I conceive of such properties in appearances as such. These concepts contain nothing found in appearances, but only what the understanding alone must think. Yet we do have an idea of such connections among representations in our understanding and in judgments generally. In one kind of judgment, representations appear as subjects in relation to predicates. In another, they appear as grounds in relation to consequences. In a third, they appear as parts that together make up a complete possible cognition. Moreover, we know a priori that we cannot have valid cognition of an object without considering its representation as determined in some of these ways. And if we were concerned with the object in itself, no possible attribute could tell me whether it was determined in any of these ways. That is, no attribute could tell me whether it fell under the concept of substance, cause, or community with other substances. For I have no idea of how such a connection among things that exist is possible. But the question is not how things in themselves are determined. It is how empirical cognition of things is determined with respect to these features of judgments in general. In other words, how can and must things, as objects of experience, be brought under these concepts of the understanding? In that case, it is clear that I fully understand both the possibility and the necessity of bringing all phenomena under these concepts. That is, I understand why we can and must use these concepts as principles of the possibility of experience.

§ 29. When making an experiment with Hume's problematical concept (his crux metaphysicorum), the concept of cause, we have, in the first place, given a priori, by means of logic, the form of a conditional judgment in general, i.e., we have one given cognition as antecedent and another as consequence. But it is possible, that in perception we may meet with a rule of relation, which runs thus: that a certain phenomenon is constantly followed by another (though not conversely), and this is a case for me to use the hypothetical judgment, and, for instance, to say, it the sun shines long enough upon a body, it grows warm. Here there is indeed as yet no necessity of connexion, or concept of cause. But I proceed and say, that if this proposition, which is merely a subjective connexion of perceptions, is to be a judgment of experience, it must be considered as necessary and universally valid. Such a proposition would be, "the sun is by its light the cause of heat." The empirical rule is now considered as a law, and as valid not merely of appearances but valid of them for the purposes of a possible experience which requires universal and therefore necessarily valid rules. I therefore easily comprehend the concept of cause, as a concept necessarily belonging to the mere form of experience, and its possibility as a synthetical union of perceptions in consciousness generally; but I do not at all comprehend the possibility of a thing generally as a cause, because the concept of cause denotes a condition not at all belonging to things, but to experience. It is nothing in fact but an objectively valid cognition of appearances and of their succession, so far as the antecedent can be conjoined with the consequent according to the rule of hypothetical judgments.

§ 29. Let us examine Hume's difficult concept of cause, his crux metaphysicorum. First, logic gives us a priori the general form of a conditional judgment. In such a judgment, one given item of knowledge is the antecedent and another is the consequence. In perception, we may encounter a rule of relation: one phenomenon is constantly followed by another, though not the other way around. This is a case in which I can use a hypothetical judgment. For example, I can say that if the sun shines long enough on a body, the body grows warm. So far, there is no necessary connection and no concept of cause. But I go on to say that this proposition is merely a subjective connection between perceptions. If it is to become a judgment of experience, it must be regarded as necessary and universally valid. Such a proposition would be, "the sun is by its light the cause of heat." The empirical rule is now regarded as a law. It is valid not merely for appearances, but for appearances as objects of possible experience. Possible experience requires universal and therefore necessarily valid rules. I can therefore easily understand the concept of cause as necessarily belonging to the mere form of experience. I can also understand how it is possible as a synthetic union of perceptions in consciousness generally. But I cannot understand at all how a thing in general can be a cause. The concept of cause denotes a condition that belongs not to things at all, but to experience. In fact, it is nothing but objectively valid knowledge of appearances and their succession. This knowledge holds insofar as the antecedent can be joined to the consequent according to the rule of hypothetical judgments.

§ 30. Hence if the pure concepts of the understanding do not refer to objects of experience but to things in themselves (noumena), they have no signification whatever. They serve, as it were, only to decipher appearances, that we may be able to read them as experience. The principles which arise from their reference to the sensible world, only serve our understanding for empirical use. Beyond this they are arbitrary combinations, without objective reality, and we can neither cognise their possibility a priori, nor verify their reference to objects, let alone make it intelligible by any example; because examples can only be borrowed from some possible experience, consequently the objects of these concepts can be found nowhere but in a possible experience.

§ 30. Therefore, if the pure concepts of the understanding refer to things in themselves (noumena) rather than objects of experience, they have no meaning at all. They serve only to decipher appearances, so that we can read them as experience. The principles that arise from applying these concepts to the sensible world serve our understanding only in its empirical use. Beyond this use, they are arbitrary combinations with no objective reality. We can neither know their possibility a priori nor verify that they refer to objects. Still less can we make their reference to objects intelligible by an example. For examples can come only from possible experience. Consequently, the objects of these concepts can be found nowhere except in a possible experience.

This complete (though to its originator unexpected) solution of Hume's problem rescues for the pure concepts of the understanding their a priori origin, and for the universal laws of nature their validity, as laws of the understanding, yet in such a way as to limit their use to experience, because their possibility depends solely on the reference of the understanding to experience, but with a completely reversed mode of connexion which never occurred to Hume, not by deriving them from experience, but by deriving experience from them.

This complete solution to Hume's problem was unexpected even by Hume himself. It restores the a priori origin of the pure concepts of the understanding. It also restores the validity of the universal laws of nature as laws of the understanding. Yet it limits their use to experience, because their possibility depends solely on the understanding's relation to experience. But the connection is the reverse of what Hume thought. The concepts and laws are not derived from experience. Instead, experience is derived from them.

This is therefore the result of all our foregoing inquiries: "All synthetical principles a priori are nothing more than principles of possible experience, and can never be referred to things in themselves, but to appearances as objects of experience. And hence pure mathematics as well as a pure science of nature can never be referred to anything more than mere appearances, and can only represent either that which makes experience generally possible, or else that which, as it is derived from these principles, must always be capable of being represented in some possible experience.

This is the result of all our inquiries so far: "All synthetic a priori principles are only principles of possible experience. They can never apply to things in themselves, but only to appearances as objects of experience. Therefore, pure mathematics and a pure science of nature can apply only to appearances. They can represent only what makes experience possible in general. Or they can represent what follows from these principles and must always be capable of being represented in some possible experience.

§ 31. And thus we have at last something definite, upon which to depend in all metaphysical enterprises, which have hitherto, boldly enough but always at random, attempted everything without discrimination. That the aim of their exertions should be so near, struck neither the dogmatical thinkers nor those who, confident in their supposed sound common sense, started with concepts and principles of pure reason (which were legitimate and natural, but destined for mere empirical use) in quest of fields of knowledge, to which they neither knew nor could know any determinate bounds, because they had never reflected nor were able to reflect on the nature or even on the possibility of such a pure understanding.

§ 31. And so we finally have something definite to rely on in all metaphysical inquiries. Until now, these inquiries have boldly attempted everything without distinction, but always at random. Neither dogmatic thinkers nor those who trusted their supposed sound common sense realized how close they were to their goal. Both groups began with concepts and principles of pure reason. These were legitimate and natural, but intended only for empirical use. They used them to seek fields of knowledge whose precise limits they neither knew nor could know. For they had never reflected, nor were they able to reflect, on the nature or even the possibility of such a pure understanding.

Many a naturalist of pure reason (by which I mean the man who believes he can decide in matters of metaphysics without any science) may pretend, that he long ago by the prophetic spirit of his sound sense, not only suspected, but knew and comprehended, what is here propounded with so much ado, or, if he likes, with prolix and pedantic pomp: "that with all our reason we can never reach beyond the field of experience." But when he is questioned about his rational principles individually, he must grant, that there are many of them which he has not taken from experience, and which are therefore independent of it and valid a priori. How then and on what grounds will he restrain both himself and the dogmatist, who makes use of these concepts and principles beyond all possible experience, because they are recognised to be independent of it? And even he, this adept in sound sense, in spite of all his assumed and cheaply acquired wisdom, is not exempt from wandering inadvertently beyond objects of experience into the field of chimeras. He is often deeply enough involved in them, though in announcing everything as mere probability, rational conjecture, or analogy, he gives by his popular language a color to his groundless pretensions.

Many a naturalist of pure reason may claim that he understood the point presented here long ago. By a naturalist of pure reason, I mean someone who believes he can settle metaphysical questions without any science. He may claim that, through the prophetic power of his sound common sense, he not only suspected but knew and understood this point. It is presented here with so much fuss, or, if he prefers, with long-winded, pedantic pomp: "With all our reason, we can never reach beyond the field of experience." But when questioned about his individual rational principles, he must admit that he did not derive many of them from experience. Those principles are therefore independent of experience and valid a priori. How, then, and on what grounds, will he restrain both himself and the dogmatist? The dogmatist uses these concepts and principles beyond all possible experience, because they are recognized as independent of experience. Even this expert in common sense is not immune to straying unwittingly beyond objects of experience into the realm of fantasies. His supposed, cheaply acquired wisdom does not protect him. He is often deeply entangled in such fantasies. Yet he calls everything mere probability, rational conjecture, or analogy. In this way, his popular language gives an air of credibility to his groundless claims.

§ 32. Since the oldest days of philosophy inquirers into pure reason have conceived, besides the things of sense, or appearances (phenomena), which make up the sensible world, certain creations of the understanding (Verstandeswesen), called noumena, which should constitute an intelligible world. And as appearance and illusion were by those men identified (a thing which we may well excuse in an undeveloped epoch), actuality was only conceded to the creations of thought.

§ 32. Since the earliest days of philosophy, people studying pure reason have imagined certain beings of the understanding (Verstandeswesen), called noumena. These were supposed to make up an intelligible world, distinct from the sensible world of things we perceive, or appearances (phenomena). These thinkers confused appearance with illusion, a mistake we can readily excuse in an undeveloped age. Because of this confusion, they granted reality only to beings conceived by thought.

And we indeed, rightly considering objects of sense as mere appearances, confess thereby that they are based upon a thing in itself, though we know not this thing in its internal constitution, but only know its appearances, viz., the way in which our senses are affected by this unknown something. The understanding therefore, by assuming appearances, grants the existence of things in themselves also, and so far we may say, that the representation of such things as form the basis of phenomena, consequently of mere creations of the understanding, is not only admissible, but unavoidable.

We rightly regard objects of sense as mere appearances. In doing so, we acknowledge that they are based on a thing in itself. We do not know the inner nature of this thing, but only its appearances. These are the ways our senses are affected by this unknown something. By accepting appearances, then, the understanding also admits that things in themselves exist. So we may say that representing things as the basis of phenomena is not only permissible but unavoidable. Such representations are therefore mere creations of the understanding.

Our critical deduction by no means excludes things of that sort (noumena), but rather limits the principles of the Aesthetic (the science of the sensibility) to this, that they shall not extend to all things, as everything would then be turned into mere appearance, but that they shall only hold good of objects of possible experience. Hereby then objects of the understanding are granted, but with the inculcation of this rule which admits of no exception: "that we neither know nor can know anything at all definite of these pure objects of the understanding, because our pure concepts of the understanding as well as our pure intuitions extend to nothing but objects of possible experience, consequently to mere things of sense, and as soon as we leave this sphere these concepts retain no meaning whatever."

Our critical deduction does not rule out things of that kind (noumena). Instead, it limits the principles of the Aesthetic (the science of sensibility) to objects of possible experience. These principles must not apply to all things, because everything would then become mere appearance. Objects of the understanding are therefore admitted, but with a rule that allows no exceptions: "We neither know nor can know anything definite about these pure objects of the understanding. This is because our pure concepts of the understanding and our pure intuitions apply only to objects of possible experience, and therefore only to things of sense. As soon as we leave this sphere, these concepts have no meaning at all."

§ 33. There is indeed something seductive in our pure concepts of the understanding, which tempts us to a transcendent use, —a use which transcends all possible experience. Not only are our concepts of substance, of power, of action, of reality, and others, quite independent of experience, containing nothing of sense appearance, and so apparently applicable to things in themselves (noumena), but, what strengthens this conjecture, they contain a necessity of determination in themselves, which experience never attains. The concept of cause implies a rule, according to which one state follows another necessarily; but experience can only show us, that one state of things often, or at most, commonly, follows another, and therefore affords neither strict universality, nor necessity.

§ 33. There is something seductive about our pure concepts of the understanding. They tempt us to use them in a transcendent way, beyond all possible experience. Our concepts of substance, power, action, reality, and others are entirely independent of experience. They contain nothing from appearances given through the senses. They therefore seem applicable to things in themselves (noumena). Another point strengthens this conjecture: these concepts contain a necessity of determination that experience never reaches. The concept of cause implies a rule under which one state necessarily follows another. But experience can show us only that one state of things often, or at most commonly, follows another. Experience therefore provides neither strict universality nor necessity.

Hence the Categories seem to have a deeper meaning and import than can be exhausted by their empirical use, and so the understanding inadvertently adds for itself to the house of experience a much more extensive wing, which it fills with nothing but creatures of thought, without ever observing that it has transgressed with its otherwise lawful concepts the bounds of their use.

The Categories therefore seem to have a deeper meaning and significance than their use in experience can fully express. So the understanding inadvertently adds a much larger wing to the house of experience. It fills this wing with nothing but creatures of thought. Yet it never notices that it has used its otherwise legitimate concepts beyond their proper bounds.

§ 34. Two important, and even indispensable, though very dry, investigations had therefore become indispensable in the Critique of Pure Reason,—viz., the two chapters "Vom Schematismus der reinen Verstandsbegriffe," and "Vom Grunde der Unterscheidung aller Verstandesbegriffe überhaupt in Phänomena und Noumena." In the former it is shown, that the senses furnish not the pure concepts of the understanding in concreto, but only the schedule for their use, and that the object conformable to it occurs only in experience (as the product of the understanding from materials of the sensibility). In the latter it is shown, that, although our pure concepts of the understanding and our principles are independent of experience, and despite of the apparently greater sphere of their use, still nothing whatever can be thought by them beyond the field of experience, because they can do nothing but merely determine the logical form of the judgment relatively to given intuitions. But as there is no intuition at all beyond the field of the sensibility, these pure concepts, as they cannot possibly be exhibited in concreto, are void of all meaning; consequently all these noumena, together with their complex, the intelligible world,²⁰ are nothing but representation of a problem, of which the object in itself is possible, but the solution, from the nature of our understanding, totally impossible. For our understanding is not a faculty of intuition, but of the connexion of given intuitions in experience. Experience must therefore contain all the objects for our concepts; but beyond it no concepts have any significance, as there is no intuition that might offer them a foundation.

§ 34. Two important and even indispensable investigations were therefore needed in the Critique of Pure Reason, though both were very dry. They are the chapters "Vom Schematismus der reinen Verstandsbegriffe" and "Vom Grunde der Unterscheidung aller Verstandesbegriffe überhaupt in Phänomena und Noumena." The first shows that the senses do not give us the pure concepts of the understanding in concrete form. Instead, they give us only a schema for using them. An object conforming to that schema occurs only in experience, as a product of the understanding from materials provided by sensibility. The second chapter shows that our pure concepts of the understanding and our principles are independent of experience. It also shows that, despite their apparently wider range of use, they cannot be used to think anything beyond experience. This is because they can only determine the logical form of a judgment in relation to given intuitions. But there is no intuition at all beyond the field of sensibility. So these pure concepts have no meaning when they cannot possibly be presented in concrete form. Consequently, all these noumena, together with their whole, the intelligible world,²⁰ are nothing but the representation of a problem. The object of this problem is possible in itself, but the nature of our understanding makes its solution totally impossible. For our understanding is not a faculty of intuition. It is a faculty for connecting given intuitions in experience. Experience must therefore contain all the objects for our concepts. Beyond experience, no concepts have any significance, because there is no intuition to provide them with a foundation.

§ 35. The imagination may perhaps be forgiven for occasional vagaries, and for not keeping carefully within the limits of experience, since it gains life and vigor by such flights, and since it is always easier to moderate its boldness, than to stimulate its languor. But the understanding which ought to think can never be forgiven for indulging in vagaries; for we depend upon it alone for assistance to set bounds, when necessary, to the vagaries of the imagination.

§ 35. The imagination may perhaps be forgiven for occasionally wandering beyond the limits of experience. Such flights give it life and vigor. And it is always easier to restrain its boldness than to stir it from sluggishness. But the understanding, whose task is to think, can never be forgiven for wandering. For we depend on the understanding alone to set limits on the imagination’s wandering when necessary.

But the understanding begins its aberrations very innocently and modestly. It first elucidates the elementary cognitions, which inhere in it prior to all experience, but yet must always have their application in experience. It gradually drops these limits, and what is there to prevent it, as it has quite freely derived its principles from itself? And then it proceeds first to newly-imagined powers in nature, then to beings, outside nature; in short to a world, for whose construction the materials cannot be wanting, because fertile fiction furnishes them abundantly, and though not confirmed, is never refuted, by experience. This is the reason that young thinkers are so partial to metaphysics of the truly dogmatical kind, and often sacrifice to it their time and their talents, which might be otherwise better employed.

But the understanding begins to go astray quite innocently and modestly. It first explains the basic knowledge it possesses before all experience. Yet this knowledge must always be applied to experience. Gradually, the understanding abandons these limits. And what is to stop it, since it has derived its principles quite freely from itself? It then moves on, first to newly imagined powers in nature, and then to beings outside nature. In short, it constructs a world whose materials can never be lacking. Imagination supplies them abundantly, and although experience does not confirm them, it never refutes them either. This is why young thinkers are so drawn to truly dogmatic metaphysics. They often devote their time and talents to it, though they might put both to better use elsewhere.

But there is no use in trying to moderate these fruitless endeavors of pure reason by all manner of cautions as to the difficulties of solving questions so occult, by complaints of the limits of our reason, and by degrading our assertions into mere conjectures. For if their impossibility is not distinctly shown, and reason's cognition of its own essence does not become a true science, in which the field of its right use is distinguished, so to say, with mathematical certainty from that of its worthless and idle use, these fruitless efforts will never be abandoned for good.

But warnings about the difficulty of solving such obscure questions cannot restrain these fruitless efforts of pure reason. Nor can complaints about the limits of our reason, or the downgrading of our claims to mere guesses. For these fruitless efforts will never be abandoned for good unless their impossibility is clearly shown. Reason’s knowledge of its own nature must also become a true science. This science must distinguish the proper use of reason from its worthless and idle use with, so to speak, mathematical certainty.

§ 36. How is Nature itself possible?

§ 36. How is nature itself possible?

This question—the highest point that transcendental philosophy can ever reach, and to which, as its boundary and completion, it must proceed—properly contains two questions.

This question is the highest point that transcendental philosophy can ever reach. Transcendental philosophy must reach it as its boundary and completion. The question actually contains two questions.

First: How is nature at all possible in the material sense, by intuition, considered as the totality of appearances; how are space, time, and that which fills both—the object of sensation, in general possible? The answer is: By means of the constitution of our Sensibility, according to which it is specifically affected by objects, which are in themselves unknown to it, and totally distinct from those phenomena. This answer is given in the Critique itself in the transcendental Aesthetic, and in these Prolegomena by the solution of the first general problem.

First: How is nature possible at all in the material sense, through intuition, as the totality of appearances? How are space, time, and what fills both, namely the object of sensation, possible at all? The answer lies in the constitution of our sensibility. Our sensibility is affected in a specific way by objects. These objects are unknown to sensibility in themselves and are entirely distinct from the appearances. This answer is given in the transcendental Aesthetic of the Critique itself. It is also given in these Prolegomena through the solution to the first general problem.

Secondly: How is nature possible in the formal sense, as the totality of the rules, under which all phenomena must come, in order to be thought as connected in experience? The answer must be this: It is only possible by means of the constitution of our Understanding, according to which all the above representations of the sensibility are necessarily referred to a consciousness, and by which the peculiar way in which we think (viz., by rules), and hence experience also, are possible, but must be clearly distinguished from an insight into the objects in themselves. This answer is given in the Critique itself in the transcendental Logic, and in these Prolegomena, in the course of the solution of the second main problem.

Secondly: How is nature possible in the formal sense? That is, how is nature possible as the totality of rules under which all phenomena must fall to be thought of as connected in experience? The answer must be this: Nature is possible only because of the structure of our understanding. Because of this structure, all the representations of sensibility mentioned above must be related to a consciousness. This structure also makes possible our distinctive way of thinking, namely, thinking by rules, and thus makes experience possible too. But experience must be clearly distinguished from insight into objects in themselves. This answer is given in the transcendental Logic of the Critique itself. It is also given in these Prolegomena, in the course of the solution to the second main problem.

But how this peculiar property of our sensibility itself is possible, or that of our understanding and of the apperception which is necessarily its basis and that of all thinking, cannot be further analysed or answered, because it is of them that we are in need for all our answers and for all our thinking about objects.

But we cannot explain how this particular property of our sensibility is possible. Nor can we explain how the corresponding properties of our understanding and our apperception are possible. Apperception is necessarily the basis of both our understanding and all thinking. We cannot analyze or explain these properties further because we need them for all our answers and all our thinking about objects.

There are many laws of nature, which we can only know by means of experience; but conformity to law in the connexion of appearances, i.e., in nature in general, we cannot discover by any experience, because experience itself requires laws which are a priori at the basis of its possibility.

There are many laws of nature that we can know only through experience. But no experience can reveal that appearances are connected according to laws, that is, that nature in general follows laws. This is because experience itself is possible only if laws are already in place a priori.

The possibility of experience in general is therefore at the same time the universal law of nature, and the principles of the experience are the very laws of nature. For we do not know nature but as the totality of appearances, i.e., of representations in us, and hence we can only derive the laws of its connexion from the principles of their connexion in us, that is, from the conditions of their necessary union in consciousness, which constitutes the possibility of experience.

The possibility of experience in general is therefore also the universal law of nature. The principles of experience are the very laws of nature. For we know nature only as the totality of appearances, that is, of representations within us. So we can derive the laws connecting appearances only from the principles that connect these representations within us. These principles are the conditions under which representations are necessarily united in consciousness. This union makes experience possible.

Even the main proposition expounded throughout this section—that universal laws of nature can be distinctly cognised a priori—leads naturally to the proposition: that the highest legislation of nature must lie in ourselves, i.e., in our understanding, and that we must not seek the universal laws of nature in nature by means of experience, but conversely must seek nature, as to its universal conformity to law, in the conditions of the possibility of experience, which lie in our sensibility and in our understanding. For how were it otherwise possible to know a priori these laws, as they are not rules of analytical cognition, but truly synthetical extensions of it?

The main proposition developed throughout this section is that universal laws of nature can be known clearly a priori. This leads naturally to another proposition: the highest legislation of nature must lie in ourselves, that is, in our understanding. We must not seek the universal laws of nature in nature through experience. Instead, we must seek nature, insofar as it conforms to universal laws, in the conditions that make experience possible. These conditions lie in our sensibility and our understanding. For how else could we know these laws a priori? They are not rules of analytic knowledge, but genuinely synthetic extensions of knowledge.

Such a necessary agreement of the principles of possible experience with the laws of the possibility of nature, can only proceed from one of two reasons: either these laws are drawn from nature by means of experience, or conversely nature is derived from the laws of the possibility of experience in general, and is quite the same as the mere universal conformity to law of the latter. The former is self-contradictory, for the universal laws of nature can and must be cognised a priori (that is, independent of all experience), and be the foundation of all empirical use of the understanding; the latter alternative therefore alone remains.²¹

There are only two possible reasons why the principles of possible experience necessarily agree with the laws that make nature possible. Either these laws are drawn from nature through experience, or nature is derived from the laws that make experience possible in general. In the latter case, nature is nothing more than the universal conformity of experience to law. The first possibility is self-contradictory. The universal laws of nature can and must be known a priori, that is, independently of all experience. They must also be the foundation for every use of the understanding based on experience. Therefore, only the second possibility remains.²¹

But we must distinguish the empirical laws of nature, which always presuppose particular perceptions, from the pure or universal laws of nature, which, without being based on particular perceptions, contain merely the conditions of their necessary union in experience. In relation to the latter, nature and possible experience are quite the same, and as the conformity to law here depends upon the necessary connexion of appearances in experience (without which we cannot cognise any object whatever in the sensible world), consequently upon the original laws of the understanding, it seems at first strange, but is not the less certain, to say:

But we must distinguish empirical laws of nature from pure or universal laws of nature. Empirical laws always presuppose particular perceptions. Pure or universal laws are not based on particular perceptions. They contain only the conditions under which perceptions must be joined together in experience. With regard to these universal laws, nature and possible experience are exactly the same. The lawful order of nature here depends on the necessary connection of appearances in experience. Without this connection, we cannot know any object in the world of the senses. This lawful order therefore depends on the original laws of the understanding. So the following statement seems strange at first, but it is no less certain:

The understanding does not derive its laws (a priori) from, but prescribes them to, nature.

The understanding does not derive its laws (a priori) from nature. Instead, it prescribes those laws to nature.

§ 37. We shall illustrate this seemingly bold proposition by an example, which will show, that laws, which we discover in objects of sensuous intuition (especially when these laws are cognised as necessary), are commonly held by us to be such as have been placed there by the understanding, in spite of their being similar in all points to the laws of nature, which we ascribe to experience.

§ 37. We will illustrate this seemingly bold claim with an example. The example will show how we commonly regard laws discovered in objects given through the senses. We regard them as laws placed there by the understanding, especially when we recognize them as necessary. This is so even though they are similar in every respect to the laws of nature that we attribute to experience.

§ 38. If we consider the properties of the circle, by which this figure combines so many arbitrary determinations of space in itself, at once in a universal rule, we cannot avoid attributing a constitution (eine Natur) to this geometrical thing. Two right lines, for example, which intersect one another and the circle, howsoever they may be drawn, are always divided so that the rectangle constructed with the segments of the one is equal to that constructed with the segments of the other. The question now is: Does this law lie in the circle or in the understanding, that is, Does this figure, independently of the understanding, contain in itself the ground of the law, or does the understanding, having constructed according to its concepts (according to the quality of the radii) the figure itself, introduce into it this law of the chords cutting one another in geometrical proportion? When we follow the proofs of this law, we soon perceive, that it can only be derived from the condition on which the understanding founds the construction of this figure, and which is that of the equality of the radii. But, if we enlarge this concept, to pursue further the unity of various properties of geometrical figures under common laws, and consider the circle as a conic section, which of course is subject to the same fundamental conditions of construction as other conic sections, we shall find that all the chords which intersect within the ellipse, parabola, and hyperbola, always intersect so that the rectangles of their segments are not indeed equal, but always bear a constant ratio to one another. If we proceed still farther, to the fundamental laws of physical astronomy, we find a physical law of reciprocal attraction diffused over all material nature, the rule of which is: "that it decreases inversely as the square of the distance from each attracting point, i.e., as the spherical surfaces increase, over which this force spreads," which law seems to be necessarily inherent in the very nature of things, and hence is usually propounded as cognisable a priori. Simple as the sources of this law are, merely resting upon the relation of spherical surfaces of different radii, its consequences are so valuable with regard to the variety of their agreement and its regularity, that not only are all possible orbits of the celestial bodies conic sections, but such a relation of these orbits to each other results, that no other law of attraction, than that of the inverse square of the distance, can be imagined as fit for a cosmical system.

§ 38. Consider the properties of a circle. This figure brings so many arbitrary determinations of space together under a single universal rule. We cannot help attributing a nature (eine Natur) to this geometrical object. For example, suppose two straight lines intersect each other and the circle. However they are drawn, they are always divided in the same way: the rectangle formed from the segments of one line equals the rectangle formed from the segments of the other. The question now is: Does this law lie in the circle or in the understanding? Does the figure itself contain the basis of the law, independently of the understanding? Or does the understanding introduce this law of geometrical proportion between intersecting chords into the figure? And does it do so after constructing the figure according to its concepts, that is, according to the properties of the radii? When we examine the proofs of this law, we soon see that it can only be derived from the condition on which the understanding bases its construction of the figure. This condition is the equality of the radii. But suppose we broaden this concept to explore how various properties of geometrical figures are united under common laws. We can then consider the circle as a conic section. The circle is, of course, subject to the same basic conditions of construction as other conic sections. We then find that all chords intersecting within an ellipse, parabola, or hyperbola always intersect in a particular way. The rectangles formed from their segments are not equal, but they always stand in a constant ratio to one another. If we go still further, to the fundamental laws of physical astronomy, we find a physical law of mutual attraction throughout all material nature. Its rule is: "The attraction decreases in inverse proportion to the square of the distance from each attracting point, that is, in proportion to the increase in the spherical surfaces over which the force spreads." This law seems necessarily inherent in the very nature of things. It is therefore usually presented as knowable a priori. The sources of this law are simple. They rest only on the relation between spherical surfaces with different radii. Yet the consequences of the law are valuable because of the variety and regularity of their agreement. Not only are all possible orbits of celestial bodies conic sections, but the relation of these orbits to one another is such that no other law of attraction can be imagined as suitable for a cosmic system. Only the law of the inverse square of the distance will do.

Here accordingly is a nature that rests upon laws which the understanding cognises a priori, and chiefly from the universal principles of the determination of space. Now I ask:

Here, then, is a nature based on laws that the understanding knows a priori, chiefly from the universal principles that determine space. Now I ask:

Do the laws of nature lie in space, and does the understanding learn them by merely endeavoring to find out the enormous wealth of meaning that lies in space; or do they inhere in the understanding and in the way in which it determines space according to the conditions of the synthetical unity in which its concepts are all centred?

Do the laws of nature lie in space? Does the understanding learn them simply by trying to discover the immense wealth of meaning in space? Or do the laws lie in the understanding itself? Do they lie in how the understanding determines space according to the conditions of synthetic unity, in which all its concepts are centered?

Space is something so uniform and as to all particular properties so indeterminate, that we should certainly not seek a store of laws of nature in it. Whereas that which determines space to assume the form of a circle or the figures of a cone and a sphere, is the understanding, so far as it contains the ground of the unity of their constructions.

Space is so uniform and so indeterminate in all its particular properties that we should certainly not look to it for a store of natural laws. Rather, the understanding determines space to take the form of a circle, a cone, or a sphere. It does so insofar as it contains the basis for the unity of their constructions.

The mere universal form of intuition, called space, must therefore be the substratum of all intuitions determinable to particular objects, and in it of course the condition of the possibility and of the variety of these intuitions lies. But the unity of the objects is entirely determined by the understanding, and on conditions which lie in its own nature; and thus the understanding is the origin of the universal order of nature, in that it comprehends all appearances under its own laws, and thereby first constructs, a priori, experience (as to its form), by means of which whatever is to be cognised only by experience, is necessarily subjected to its laws. For we are not now concerned with the nature of things in themselves, which is independent of the conditions both of our sensibility and our understanding, but with nature, as an object of possible experience, and in this case the understanding, whilst it makes experience possible, thereby insists that the sensuous world is either not an object of experience at all, or must be nature [viz., an existence of things, determined according to universal laws²²].

The universal form of intuition alone, called space, must therefore be the basis of all intuitions that can be determined as particular objects. Space, of course, contains the condition that makes these intuitions and their variety possible. But the understanding entirely determines the unity of objects, according to conditions inherent in its own nature. The understanding is therefore the source of the universal order of nature. It brings all appearances under its own laws and thereby first constructs the form of experience a priori. As a result, whatever can be known only through experience is necessarily subject to those laws. For we are not concerned here with the nature of things in themselves, which is independent of the conditions of both our sensibility and our understanding. We are concerned with nature as an object of possible experience. In this case, the understanding makes experience possible and thereby requires that the sensible world either is not an object of experience at all or must be nature [that is, an existence of things determined according to universal laws²²].

APPENDIX TO THE PURE SCIENCE OF NATURE.

APPENDIX TO THE PURE SCIENCE OF NATURE.

§ 39. Of the System of the Categories.

§ 39. The System of Categories.

There can be nothing more desirable to a philosopher, than to be able to derive the scattered multiplicity of the concepts or the principles, which had occurred to him in concrete use, from a principle a priori, and to unite everything in this way in one cognition. He formerly only believed that those things, which remained after a certain abstraction, and seemed by comparison among one another to constitute a particular kind of cognitions, were completely collected; but this was only an Aggregate. Now he knows, that just so many, neither more nor less, can constitute the mode of cognition, and perceives the necessity of his division, which constitutes comprehension; and now only he has attained a System.

Nothing could be more desirable to a philosopher than deriving scattered concepts or principles from an a priori principle. These concepts or principles had occurred to the philosopher in practical use. Deriving them in this way unites them all in a single body of knowledge. Previously, the philosopher only believed that everything left after a certain abstraction had been gathered completely. These things seemed, when compared with one another, to form a particular kind of knowledge. But they were only an aggregate. Now the philosopher knows that exactly this many, no more and no fewer, can make up that kind of knowledge. The philosopher also sees why the division must be as it is, and this constitutes comprehension. Only now has the philosopher attained a system.

To search in our daily cognition for the concepts, which do not rest upon particular experience, and yet occur in all cognition of experience, where they as it were constitute the mere form of connexion, presupposes neither greater reflexion nor deeper insight, than to detect in a language the rules of the actual use of words generally, and thus to collect elements for a grammar. In fact both researches are very nearly related, even though we are not able to give a reason why each language has just this and no other formal constitution, and still less why an exact number of such formal determinations in general are found in it.

In our everyday knowledge, we can look for concepts that do not depend on particular experiences. These concepts occur in all knowledge gained from experience, where they provide, so to speak, only the form of connection. Finding them requires no more reflection or insight than identifying the general rules for how words are actually used in a language, and thus gathering the elements of a grammar. In fact, the two inquiries are closely related. Yet we cannot explain why each language has the particular formal structure it does rather than another. Still less can we explain why it has exactly the number of formal features it has.

Aristotle collected ten pure elementary concepts under the name of Categories.²³ To these, which are also called predicaments, he found himself obliged afterwards to add five post-predicaments,²⁴ some of which however (prius, simul, and motus) are contained in the former; but this random collection must be considered (and commended) as a mere hint for future inquirers, not as a regularly developed idea, and hence it has, in the present more advanced state of philosophy, been rejected as quite useless.

Aristotle collected ten pure elementary concepts under the name of Categories.²³ These are also called predicaments. He later found it necessary to add five post-predicaments.²⁴ But some of these (prius, simul, and motus) are already contained in the original categories. This random collection should be regarded, and praised, as merely a suggestion for future researchers, not as a systematically developed idea. For this reason, it has been rejected as quite useless in the present, more advanced state of philosophy.

After long reflexion on the pure elements of human knowledge (those which contain nothing empirical), I at last succeeded in distinguishing with certainty and in separating the pure elementary notions of the Sensibility (space and time) from those of the Understanding. Thus the 7th, 8th, and 9th Categories had to be excluded from the old list. And the others were of no service to me; because there was no principle [in them], on which the understanding could be investigated, measured in its completion, and all the functions, whence its pure concepts arise, determined exhaustively and with precision.

After long reflection on the pure elements of human knowledge (those containing nothing empirical), I finally succeeded in distinguishing and separating two kinds of basic concepts. I could now distinguish with certainty the pure basic concepts of sensibility (space and time) from those of the understanding. The 7th, 8th, and 9th categories therefore had to be removed from the old list. The others were of no use to me either. They contained no principle for investigating the understanding, measuring its completeness, and precisely and exhaustively determining all the functions that give rise to its pure concepts.

But in order to discover such a principle, I looked about for an act of the understanding which comprises all the rest, and is distinguished only by various modifications or phases, in reducing the multiplicity of representation to the unity of thinking in general: I found this act of the understanding to consist in judging. Here then the labors of the logicians were ready at hand, though not yet quite free from defects, and with this help I was enabled to exhibit a complete table of the pure functions of the understanding, which are however undetermined in regard to any object. I finally referred these functions of judging to objects in general, or rather to the condition of determining judgments as objectively valid, and so there arose the pure concepts of the understanding, concerning which I could make certain, that these, and this exact number only, constitute our whole cognition of things from pure understanding. I was justified in calling them by their old name, Categories, while I reserved for myself the liberty of adding, under the title of "Predicables," a complete list of all the concepts deducible from them, by combinations whether among themselves, or with the pure form of the appearance, i.e., space or time, or with its matter, so far as it is not yet empirically determined (viz., the object of sensation in general), as soon as a system of transcendental philosophy should be completed with the construction of which I am engaged in the Critique of Pure Reason itself.

To discover such a principle, I looked for an act of the understanding that includes all the others. The other acts would differ from it only in the ways they reduce the diversity of representations to the unity of thought in general. I found that this act of the understanding is judging. The work of the logicians was already available to me, though it was not yet entirely free of defects. With its help, I was able to present a complete table of the pure functions of the understanding. These functions, however, are not yet determined with respect to any object. Finally, I related these functions of judging to objects in general. More precisely, I related them to the condition for determining that judgments are objectively valid. In this way, I arrived at the pure concepts of the understanding. I could be certain that these concepts, and exactly this number of them, make up all our cognition of things through the pure understanding. I was justified in calling them by their old name, Categories. At the same time, I reserved the freedom to add a complete list of all the concepts that can be derived from them. These concepts can be derived by combining the Categories with one another, with the pure form of appearance, namely space or time, or with the matter of appearance, insofar as it is not yet empirically determined, namely the object of sensation in general. I would add this list under the title "Predicables" once a system of transcendental philosophy had been completed. I am engaged in constructing that system in the Critique of Pure Reason itself.

Now the essential point in this system of Categories, which distinguishes it from the old rhapsodical collection without any principle, and for which alone it deserves to be considered as philosophy, consists in this: that by means of it the true significance of the pure concepts of the understanding and the condition of their use could be precisely determined. For here it became obvious that they are themselves nothing but logical functions, and as such do not produce the least concept of an object, but require some sensuous intuition as a basis. They therefore only serve to determine empirical judgments, which are otherwise undetermined and indifferent as regards all functions of judging, relatively to these functions, thereby procuring them universal validity, and by means of them making judgments of experience in general possible.

The essential point of this system of Categories sets it apart from the old, unsystematic collection, which had no guiding principle. This point alone makes the system worthy of being considered philosophy. The system made it possible to determine precisely the true meaning of the pure concepts of the understanding and the condition for their use. It became clear that these concepts are nothing more than logical functions. As such, they do not produce even the slightest concept of an object. They require some sensuous intuition as a basis. They serve only to determine empirical judgments according to these logical functions. Otherwise, empirical judgments are undetermined and neutral with respect to all functions of judging. By determining them in this way, the pure concepts give empirical judgments universal validity and make judgments of experience possible in general.

Such an insight into the nature of the categories, which limits them at the same time to the mere use of experience, never occurred either to their first author, or to any of his successors; but without this insight (which immediately depends upon their derivation or deduction), they are quite useless and only a miserable list of names, without explanation or rule for their use. Had the ancients ever conceived such a notion, doubtless the whole study of the pure rational knowledge, which under the name of metaphysics has for centuries spoiled many a sound mind, would have reached us in quite another shape, and would have enlightened the human understanding, instead of actually exhausting it in obscure and vain speculations, thereby rendering it unfit for true science.

Neither the first author of the categories nor any of his successors grasped their nature and their limits. Those limits confine the categories to use in experience alone. But without this insight, which depends directly on deriving or deducing the categories, they are completely useless. They are only a miserable list of names, with no explanation or rule for their use. If the ancients had ever grasped this idea, the whole study of pure rational knowledge would undoubtedly have reached us in quite a different form. This study, known as metaphysics, has spoiled many a sound mind over the centuries. Instead, it would have enlightened human understanding. As things stand, metaphysics has exhausted the understanding with obscure and futile speculations, making it unfit for true science.

This system of categories makes all treatment of every object of pure reason itself systematic, and affords a direction or clue how and through what points of inquiry every metaphysical consideration must proceed, in order to be complete; for it exhausts all the possible movements (momenta) of the understanding, among which every concept must be classed. In like manner the table of Principles has been formulated, the completeness of which we can only vouch for by the system of the categories. Even in the division of the concepts,²⁵ which must go beyond the physical application of the understanding, it is always the very same clue, which, as it must always be determined a priori by the same fixed points of the human understanding, always forms a closed circle. There is no doubt that the object of a pure conception either of the understanding or of reason, so far as it is to be estimated philosophically and on a priori principles, can in this way be completely cognised. I could not therefore omit to make use of this clue with regard to one of the most abstract ontological divisions, viz., the various distinctions of "the notions of something and of nothing," and to construct accordingly (Critique, p. 207) a regular and necessary table of their divisions.²⁶

This system of categories makes the treatment of every object of pure reason systematic. It also provides a guide to the questions every metaphysical inquiry must address to be complete. For the system covers all the possible acts (momenta) of the understanding, under which every concept must be classified. The table of Principles was formulated in the same way. Only the system of categories can assure us that the table is complete. The division of concepts²⁵ that must go beyond the physical application of the understanding also follows this same guide. Because the guide must always be determined a priori by the same fixed points of human understanding, it always forms a closed circle. There is no doubt that, in this way, we can completely know the object of a pure concept of either the understanding or reason, insofar as it is to be considered philosophically and on a priori principles. I therefore had to use this guide for one of the most abstract ontological divisions, namely, the various distinctions of "the notions of something and of nothing." Accordingly, I constructed a systematic and necessary table of those divisions (Critique, p. 207).²⁶

And this system, like every other true one founded on a universal principle, shows its inestimable value in this, that it excludes all foreign concepts, which might otherwise intrude among the pure concepts of the understanding, and determines the place of every cognition. Those concepts, which under the name of "concepts of reflexion" have been likewise arranged in a table according to the clue of the categories, intrude, without having any privilege or title to be among the pure concepts of the understanding in Ontology. They are concepts of connexion, and thereby of the objects themselves, whereas the former are only concepts of a mere comparison of concepts already given, hence of quite another nature and use. By my systematic division²⁷ they are saved from this confusion. But the value of my special table of the categories will be still more obvious, when we separate the table of the transcendental concepts of Reason from the concepts of the understanding. The latter being of quite another nature and origin, they must have quite another form than the former. This so necessary separation has never yet been made in any system of metaphysics for, as a rule, these rational concepts all mixed up with the categories, like children of one family, which confusion was unavoidable in the absence of a definite system of categories.

Like every other true system founded on a universal principle, this system shows its inestimable value in two ways. It excludes all foreign concepts that might otherwise intrude among the pure concepts of the understanding. It also determines the place of every cognition. Concepts known as "concepts of reflexion" have likewise been arranged in a table, using the categories as a guide. But these concepts intrude among the pure concepts of the understanding in Ontology, without any right or claim to belong there. The pure concepts of the understanding are concepts of connection and, therefore, of objects themselves. Concepts of reflexion, on the other hand, are only concepts for comparing concepts already given. They are therefore quite different in nature and use. My systematic division²⁷ saves them from this confusion. But the value of my particular table of the categories will be still clearer once we separate the table of transcendental concepts of Reason from the concepts of the understanding. The concepts of the understanding have quite a different nature and origin from those of Reason. They must therefore have quite a different form. This necessary separation has never yet been made in any system of metaphysics. As a rule, concepts of Reason were all mixed up with the categories, like children of one family. Without a definite system of categories, this confusion was unavoidable.