Preamble: The Distinctive Features of All Metaphysical Knowledge

§ 1. Of the Sources of Metaphysics.

§ 1. The Sources of Metaphysics.

IF it becomes desirable to formulate any cognition as science, it will be necessary first to determine accurately those peculiar features which no other science has in common with it, constituting its characteristics; otherwise the boundaries of all sciences become confused, and none of them can be treated thoroughly according to its nature.

If we want to develop any body of knowledge as a science, we must first identify its distinctive features precisely. These are the features it shares with no other science. Otherwise, the boundaries between all sciences become confused, and none can be studied thoroughly according to its nature.

The characteristics of a science may consist of a simple difference of object, or of the sources of cognition, or of the kind of cognition, or perhaps of all three conjointly. On this, therefore, depends the idea of a possible science and its territory.

A science may be distinguished simply by its subject, its sources of knowledge, its kind of knowledge, or perhaps all three together. The idea of a possible science and its scope therefore depend on these differences.

First, as concerns the sources of metaphysical cognition, its very concept implies that they cannot be empirical. Its principles (including not only its maxims but its basic notions) must never be derived from experience. It must not be physical but metaphysical knowledge, viz., knowledge lying beyond experience. It can therefore have for its basis neither external experience, which is the source of physics proper, nor internal, which is the basis of empirical psychology. It is therefore a priori knowledge, coming from pure Understanding and pure Reason.

First, consider the sources of metaphysical knowledge. The very concept of metaphysics implies that its sources cannot be empirical. Its principles, including both its rules and its basic concepts, must never come from experience. Metaphysical knowledge must not be physical knowledge. It must be knowledge that lies beyond experience. It therefore cannot be based on external experience, which is the source of physics proper. Nor can it be based on internal experience, which is the basis of empirical psychology. Metaphysical knowledge is therefore a priori knowledge, coming from pure understanding and pure reason.

But so far Metaphysics would not be distinguish able from pure Mathematics; it must therefore be called pure philosophical cognition; and for the meaning of this term I refer to the Critique of the Pure Reason (II. "Method of Transcendentalism," Chap. I., Sec. i), where the distinction between these two employments of the reason is sufficiently explained. So far concerning the sources of metaphysical cognition.

But so far, metaphysics cannot be distinguished from pure mathematics. It must therefore be called pure philosophical cognition. For the meaning of this term, I refer the reader to the Critique of the Pure Reason (II. "Method of Transcendentalism," Chap. I., Sec. i). There, the distinction between these two uses of reason is explained sufficiently. This concludes my discussion of the sources of metaphysical cognition.

§ 2. Concerning the Kind of Cognition which can alone be called Metaphysical.

§ 2. On the Kind of Knowledge That Alone Can Be Called Metaphysical.

a. Of the Distinction between Analytical and Synthetical Judgments in general.—The peculiarity of its sources demands that metaphysical cognition must consist of nothing but a priori judgments. But whatever be their origin, or their logical form, there is a distinction in judgments, as to their content, according to which they are either merely explicative, adding nothing to the content of the cognition, or expansive, increasing the given cognition: the former may be called analytical, the latter synthetical, judgments.

a. The Distinction between Analytic and Synthetic Judgments in General. The distinctive nature of its sources requires metaphysical knowledge to consist entirely of a priori judgments. But judgments differ in content, whatever their origin or logical form. Some merely explain what is already known, adding nothing to it. Others expand what is already known, increasing our knowledge. The first kind may be called analytic judgments, the second synthetic judgments.

Analytical judgments express nothing in the predicate but what has been already actually thought in the concept of the subject, though not so distinctly or with the same (full) consciousness. When I say: All bodies are extended, I have not amplified in the least my concept of body, but have only analysed it, as extension was really thought to belong to that concept before the judgment was made, though it was not expressed; this judgment is therefore analytical. On the contrary, this judgment, All bodies have weight, contains in its predicate something not actually thought in the general concept of the body; it amplifies my knowledge by adding something to my concept, and must therefore be called synthetical.

In an analytic judgment, the predicate expresses only what is already thought in the concept of the subject. But it may not have been thought as clearly or with the same full awareness. When I say, “All bodies are extended,” I have not added anything to my concept of body. I have only analyzed it. Extension was already thought to belong to that concept before I made the judgment, though it was not expressed. This judgment is therefore analytic. By contrast, the judgment “All bodies have weight” says something in its predicate that is not already thought in the general concept of body. It adds something to my concept and thus increases my knowledge. It must therefore be called synthetic.

b. The Common Principle of all Analytical Judgments is the Law of Contradiction.—All analytical judgments depend wholly on the law of Contradiction, and are in their nature a priori cognitions, whether the concepts that supply them with matter be empirical or not. For the predicate of an affirmative analytical judgment is already contained in the concept of the subject, of which it cannot be denied without contradiction. In the same way its opposite is necessarily denied of the subject in an analytical, but negative, judgment, by the same law of contradiction. Such is the nature of the judgments: all bodies are extended, and no bodies are unextended (i.e., simple).

b. The Common Principle of All Analytical Judgments Is the Law of Contradiction. All analytical judgments depend entirely on the law of contradiction. By their nature, they are a priori knowledge, whether or not the concepts they draw on are empirical. In an affirmative analytical judgment, the predicate is already contained in the concept of the subject. Denying the predicate of the subject would therefore be a contradiction. Similarly, in a negative analytical judgment, the same law of contradiction necessarily rules out the opposite predicate. The following judgments are examples: all bodies are extended, and no bodies are unextended (that is, simple).

For this very reason all analytical judgments are a priori even when the concepts are empirical, as, for example, Gold is a yellow metal; for to know this I require no experience beyond my concept of gold as a yellow metal: it is, in fact, the very concept, and I need only analyse it, without looking beyond it elsewhere.

For this reason, all analytic judgments are a priori, even when the concepts come from experience. Take the example, “Gold is a yellow metal.” To know this, I need no experience beyond my concept of gold as a yellow metal. Being a yellow metal is part of the concept itself. I only need to analyze the concept, without looking elsewhere.

c. Synthetical Judgments require a different Principle from the Law of Contradiction.—There are synthetical a posteriori judgments of empirical origin; but there are also others which are proved to be certain a priori, and which spring from pure Understanding and Reason. Yet they both agree in this, that they cannot possibly spring from the principle of analysis, viz., the law of contradiction, alone; they require a quite different principle, though, from whatever they may be deduced, they must be subject to the law of contradiction, which must never be violated, even though everything cannot be deduced from it. I shall first classify synthetical judgments.

c. Synthetic Judgments Require a Principle Other Than the Law of Contradiction. Some synthetic judgments are a posteriori, based on experience. Others are known with certainty a priori and arise from pure understanding and reason. But neither kind can possibly arise from the principle of analysis, the law of contradiction, alone. Both require a quite different principle. Yet, whatever principle they are derived from, they must obey the law of contradiction. This law must never be violated, even though not everything can be derived from it. I shall first classify synthetic judgments.

1. Empirical Judgments are always synthetical. For it would be absurd to base an analytical judgment on experience, as our concept suffices for the purpose without requiring any testimony from experience. That body is extended, is a judgment established a priori, and not an empirical judgment. For before appealing to experience, we already have all the conditions of the judgment in the concept, from which we have but to elicit the predicate according to the law of contradiction, and thereby to become conscious of the necessity of the judgment, which experience could not even teach us.

1. Empirical judgments are always synthetic. It would be absurd to base an analytic judgment on experience. Our concept alone is enough for an analytic judgment, without any evidence from experience. The judgment that a body is extended is established a priori, not through experience. Before turning to experience, we already have everything needed for the judgment in the concept. We only need to draw out the predicate according to the law of contradiction. In doing so, we become aware that the judgment is necessary. Experience could not even teach us that the judgment is necessary.

2. Mathematical Judgments are all synthetical. This fact seems hitherto to have altogether escaped the observation of those who have analysed human reason; it even seems directly opposed to all their conjectures, though incontestably certain, and most important in its consequences. For as it was found that the conclusions of mathematicians all proceed according to the law of contradiction (as is demanded by all apodeictic certainty), men persuaded themselves that the fundamental principles were known from the same law. This was a great mistake, for a synthetical proposition can indeed be comprehended according to the law of contradiction, but only by presupposing another synthetical proposition from which it follows, but never in itself.

2. All mathematical judgments are synthetic. This fact seems to have escaped the notice of those who have analyzed human reason. It even seems directly opposed to all their conjectures, though it is unquestionably certain and has very important consequences. For people found that all mathematicians’ conclusions follow the law of contradiction, as required for absolute certainty. They therefore convinced themselves that the fundamental principles were also known through that law. This was a great mistake. A synthetic proposition can indeed be understood through the law of contradiction, but only if another synthetic proposition is presupposed. The proposition must follow from that other proposition. It can never be understood through the law of contradiction on its own.

First of all, we must observe that all proper mathematical judgments are a priori, and not empirical, because they carry with them necessity, which cannot be obtained from experience. But if this be not conceded to me, very good; I shall confine my assertion to pure Mathematics, the very notion of which implies that it contains pure a priori and not empirical cognitions.

First, we must note that all mathematical judgments, strictly speaking, are a priori, not empirical. This is because they carry necessity with them, and necessity cannot come from experience. But if this is not granted, very well. I will limit my claim to pure Mathematics. The very idea of pure Mathematics implies that it contains pure a priori knowledge, not empirical knowledge.

It might at first be thought that the proposition 7 + 5 = 12 is a mere analytical judgment, following from the concept of the sum of seven and five, according to the law of contradiction. But on closer examination it appears that the concept of the sum of 7 + 5 contains merely their union in a single number, without its being at all thought what the particular number is that unites them. The concept of twelve is by no means thought by merely thinking of the combination of seven and five; and analyse this possible sum as we may, we shall not discover twelve in the concept. We must go beyond these concepts, by calling to our aid some concrete image (Anschauung), i.e., either our five fingers, or five points (as Segner has it in his Arithmetic), and we must add successively the units of the five, given in some concrete image (Anschauung), to the concept of seven. Hence our concept is really amplified by the proposition 7 + 5 = 12, and we add to the first a second, not thought in it. Arithmetical judgments are therefore synthetical, and the more plainly according as we take larger numbers; for in such cases it is clear that, however closely we analyse our concepts without calling visual images (Anschauung) to our aid, we can never find the sum by such mere dissection.

At first, we might think that the proposition 7 + 5 = 12 is merely an analytic judgment. It might seem to follow from the concept of the sum of seven and five, according to the law of contradiction. But on closer examination, the concept of the sum of 7 + 5 contains only their union in a single number. It does not tell us which particular number unites them. Simply thinking of seven and five combined does not give us the concept of twelve. However we analyze this possible sum, we will not discover twelve in the concept. We must go beyond these concepts by using a concrete image (Anschauung). We might use our five fingers, or five points, as Segner does in his Arithmetic. We must then add the five units, given in a concrete image (Anschauung), one by one to the concept of seven. So the proposition 7 + 5 = 12 really expands our concept. We add a second concept to the first, one that was not already contained in it. Arithmetic judgments are therefore synthetic. This becomes even clearer when we use larger numbers. In such cases, no matter how closely we analyze our concepts, we can never find the sum by analysis alone. We must call on visual images (Anschauung) to help us.

All principles of geometry are no less analytical. That a straight line is the shortest path between two points, is a synthetical proposition. For my concept of straight contains nothing of quantity, but only a quality. The attribute of shortness is therefore altogether additional, and cannot be obtained by any analysis of the concept. Here, too, visualisation (Anschauung) must come to aid us. It alone makes the synthesis possible.

All the principles of geometry are equally analytical. The claim that a straight line is the shortest path between two points is a synthetic proposition. My concept of a straight line contains nothing about quantity, only a quality. Shortness is therefore an entirely new attribute. It cannot be found by analyzing the concept of a straight line. Here, too, visualization (Anschauung) must help us. Visualization alone makes the synthesis possible.

Some other principles, assumed by geometers, are indeed actually analytical, and depend on the law of contradiction; but they only serve, as identical propositions, as a method of concatenation, and not as principles, e.g., a = a, the whole is equal to itself, or a + b > a, the whole is greater than its part. And yet even these, though they are recognised as valid from mere concepts, are only admitted in mathematics, because they can be represented in some visual form (Anschauung). What usually makes us believe that the predicate of such apodeictic⁸ judgments is already contained in our concept, and that the judgment is therefore analytical, is the duplicity of the expression, requesting us to think a certain predicate as of necessity implied in the thought of a given concept, which necessity attaches to the concept. But the question is not what we are requested to join in thought to the given concept, but what we actually think together with and in it, though obscurely; and so it appears that the predicate belongs to these concepts necessarily indeed, yet not directly but indirectly by an added visualisation (Anschauung).

Some other principles used by geometers are indeed analytic and depend on the law of contradiction. But, as statements of identity, they serve only to link steps in an argument, not as foundational principles. Examples are a = a, the whole is equal to itself, and a + b > a, the whole is greater than its part. Yet even these are admitted in mathematics only because they can be represented in a visual form (Anschauung), though their validity is recognized from concepts alone. We usually believe that the predicate of such apodeictic⁸ judgments is already contained in our concept. We therefore believe that the judgment is analytic. The usual cause of this belief is an ambiguity in the wording. It asks us to think of a certain predicate as necessarily implied when we think of a given concept. This necessity is attached to the concept. But the question is not what we are asked to connect in thought with the given concept. It is what we actually think along with and within that concept, however obscurely. This shows that the predicate does indeed belong to these concepts necessarily. It belongs to them, however, not directly but indirectly, through an added visualization (Anschauung).

§ 3. A Remark on the General Division of Judgments into Analytical and Synthetical.

§ 3. A Note on the General Division of Judgments into Analytic and Synthetic.

This division is indispensable, as concerns the Critique of human understanding, and therefore deserves to be called classical, though otherwise it is of little use, but this is the reason why dogmatic philosophers, who always seek the sources of metaphysical judgments in Metaphysics itself, and not apart from it, in the pure laws of reason generally, altogether neglected this apparently obvious distinction. Thus the celebrated Wolf, and his acute follower Baumgarten, came to seek the proof of the principle of Sufficient Reason, which is clearly synthetical, in the principle of Contradiction. In Locke's Essay, however, I find an indication of my division. For in the fourth book (chap. iii. § 9, seq.), having discussed the various connexions of representations in judgments, and their sources, one of which he makes "identity and contradiction" (analytical judgments), and another the coexistence of representations in a subject, he confesses (§ 10) that our a priori knowledge of the latter is very narrow, and almost nothing. But in his remarks on this species of cognition, there is so little of what is definite, and reduced to rules, that we cannot wonder if no one, not even Hume, was led to make investigations concerning this sort of judgments. For such general and yet definite principles are not easily learned from other men, who have had them obscurely in their minds. We must hit on them first by our own reflexion, then we find them elsewhere, where we could not possibly have found them at first, because the authors themselves did not know that such an idea lay at the basis of their observations. Men who never think independently have nevertheless the acuteness to discover everything, after it has been once shown them, in what was said long since, though no one ever saw it there before.

This division is indispensable to the critique of human understanding, and therefore deserves to be called classical, though otherwise it is of little use. Yet dogmatic philosophers entirely neglected this apparently obvious distinction. They always look for the sources of metaphysical judgments in metaphysics itself, rather than outside it, in the pure laws of reason generally. Thus the celebrated Wolf and his perceptive follower Baumgarten sought to prove the principle of Sufficient Reason through the principle of Contradiction, although the former is clearly synthetic. In Locke's Essay, however, I find a hint of my division. In the fourth book (chap. iii. § 9, seq.), he discusses the various connections between representations in judgments and their sources. One source he calls "identity and contradiction" (analytical judgments). Another is the coexistence of representations in a subject. He admits (§ 10) that our a priori knowledge of the latter is very limited, almost nonexistent. But his remarks on this kind of knowledge are so vague and lacking in rules that it is no wonder no one, not even Hume, was led to investigate judgments of this kind. General principles that are also definite are not easily learned from others who have held them only vaguely in mind. We must first discover such principles through our own reflection. Then we find them elsewhere, where we could not possibly have found them at first. For the authors themselves did not know that such an idea lay behind their observations. People who never think independently are nevertheless clever enough to discover everything, once it has been shown to them, in what was said long ago, even though no one had ever seen it there before.

§ 4. The General Question of the Prolegomena.—Is Metaphysics at all Possible?

§ 4. The General Question of the Prolegomena: Is Metaphysics Possible at All?

Were a metaphysics, which could maintain its place as a science, really in existence; could we say, here is metaphysics, learn it, and it will convince you irresistibly and irrevocably of its truth: this question would be useless, and there would only remain that other question (which would rather be a test of our acuteness, than a proof of the existence of the thing itself), "How is the science possible, and how does reason come to attain it?" But human reason has not been so fortunate in this case. There is no single book to which you can point as you do to Euclid, and say: This is Metaphysics; here you may find the noblest objects of this science, the knowledge of a highest Being, and of a future existence, proved from principles of pure reason. We can be shown indeed many judgments, demonstrably certain, and never questioned; but these are all analytical, and rather concern the materials and the scaffolding for Metaphysics, than the extension of knowledge, which is our proper object in studying it (§ 2). Even supposing you produce synthetical judgments (such as the law of Sufficient Reason, which you have never proved, as you ought to, from pure reason a priori, though we gladly concede its truth), you lapse when they come to be employed for your principal object, into such doubtful assertions, that in all ages one Metaphysics has contradicted another, either in its assertions, or their proofs, and thus has itself destroyed its own claim to lasting assent. Nay, the very attempts to set up such a science are the main cause of the early appearance of scepticism, a mental attitude in which reason treats itself with such violence that it could never have arisen save from complete despair of ever satisfying our most important aspirations. For long before men began to inquire into nature methodically, they consulted abstract reason, which had to some extent been exercised by means of ordinary experience; for reason is ever present, while laws of nature must usually be discovered with labor. So Metaphysics floated to the surface, like foam, which dissolved the moment it was scooped off. But immediately there appeared a new supply on the surface, to be ever eagerly gathered up by some, while others, instead of seeking in the depths the cause of the phenomenon, thought they showed their wisdom by ridiculing the idle labor of their neighbors.

If a metaphysics existed that could hold its place as a science, we could say: Here is metaphysics. Learn it, and it will convince you of its truth beyond resistance or doubt. In that case, this question would be unnecessary. Only another question would remain: “How is the science possible, and how does reason come to attain it?” That question would test our insight rather than prove that the science exists. But human reason has not been so fortunate in this case. There is no single book we can point to as we do to Euclid and say: This is Metaphysics. Here you can find its noblest objects, knowledge of a highest Being and a future existence, proved from principles of pure reason. We can indeed be shown many judgments that are demonstrably certain and have never been questioned. But these are all analytical. They concern the materials and scaffolding for Metaphysics, rather than the expansion of knowledge. Yet expanding knowledge is our proper aim in studying it (§ 2). Suppose you do produce synthetic judgments, such as the law of Sufficient Reason. You have never proved this law from pure reason a priori, as you should have, though we gladly grant its truth. Even so, when you apply such judgments to your main aim, you fall into doubtful assertions. In every age, one Metaphysics has contradicted another, either in its assertions or in their proofs. Metaphysics has therefore destroyed its own claim to lasting assent. Indeed, the very attempts to establish such a science are the main cause of the early appearance of scepticism. In this state of mind, reason treats itself so violently that scepticism could only have arisen from complete despair of ever satisfying our most important aspirations. Long before people began to study nature methodically, they consulted abstract reason. Reason had already been exercised to some extent through ordinary experience. For reason is always present, while the laws of nature usually take work to discover. So Metaphysics floated to the surface like foam, dissolving as soon as it was scooped up. But a fresh supply immediately appeared on the surface. Some people were always eager to gather it up. Others, instead of looking in the depths for the cause of the phenomenon, thought they showed their wisdom by mocking their neighbors’ idle labor.

The essential and distinguishing feature of pure mathematical cognition among all other a priori cognitions is, that it cannot at all proceed from concepts, but only by means of the construction of concepts (see Critique II., Method of Transcendentalism, chap. I., sect. 1). As therefore in its judgments it must proceed beyond the concept to that which its corresponding visualisation (Anschauung) contains, these judgments neither can, nor ought to, arise analytically, by dissecting the concept, but are all synthetical.

Pure mathematical cognition differs from all other a priori cognition in one essential way. It cannot proceed from concepts alone, but only by constructing them (see Critique II., Method of Transcendentalism, chap. I., sect. 1). Therefore, mathematical judgments must go beyond the concept to what its corresponding intuition (Anschauung) contains. These judgments cannot and should not arise analytically, by breaking down the concept. They are all synthetic.

I cannot refrain from pointing out the disadvantage resulting to philosophy from the neglect of this easy and apparently insignificant observation. Hume being prompted (a task worthy of a philosopher) to cast his eye over the whole field of a priori cognitions in which human understanding claims such mighty possessions, heedlessly severed from it a whole, and indeed its most valuable, province, viz., pure mathematics; for he thought its nature, or, so to speak, the state-constitution of this empire, depended on totally different principles, namely, on the law of contradiction alone; and although he did not divide Judgments in this manner formally and universally as I have done here, what he said was equivalent to this: that mathematics contains only analytical, but metaphysics synthetical, a priori judgments. In this, however, he was greatly mistaken, and the mistake had a decidedly injurious effect upon his whole conception. But for this, he would have extended his question concerning the origin of our synthetical judgments far beyond the metaphysical concept of Causality, and included in it the possibility of mathematics a priori also, for this latter he must have assumed to be equally synthetical. And then he could not have based his metaphysical judgments on mere experience without subjecting the axioms of mathematics equally to experience, a thing which he was far too acute to do. The good company into which metaphysics would thus have been brought, would have saved it from the danger of a contemptuous ill-treatment, for the thrust intended for it must have reached mathematics, which was not and could not have been Hume's intention. Thus that acute man would have been led into considerations which must needs be similar to those that now occupy us, but which would have gained inestimably by his inimitably elegant style.

I cannot help pointing out the harm philosophy has suffered from neglecting this simple and apparently insignificant observation. Hume set out to survey the whole field of a priori knowledge, where human understanding claims such vast possessions. This was a task worthy of a philosopher. Yet he carelessly cut off an entire part of that field, and indeed its most valuable part: pure mathematics. He thought that its nature, or, so to speak, the constitution of this empire, rested on entirely different principles. He believed it rested on the law of contradiction alone. He did not formally and universally divide judgments as I have done here. But what he said amounted to the same thing: mathematics contains only analytical a priori judgments, while metaphysics contains synthetical a priori judgments. On this point, however, he was greatly mistaken, and the mistake seriously harmed his whole conception. Without this mistake, Hume would have taken his question about the origin of our synthetical judgments much further. He would have looked beyond the metaphysical concept of Causality and included the possibility of a priori mathematics. For he would have had to regard its judgments as synthetical too. Then he could not have based his metaphysical judgments on mere experience without also making the axioms of mathematics dependent on experience. He was far too perceptive to do that. The company of mathematics would have saved metaphysics from the danger of contemptuous treatment. Any blow aimed at metaphysics would also have struck mathematics, and that was not and could not have been Hume's intention. In this way, that perceptive man would have been led to consider questions necessarily similar to those that now occupy us. His inimitably elegant style would have added immeasurably to their value.

Metaphysical judgments, properly so called, are all synthetical. We must distinguish judgments pertaining to metaphysics from metaphysical judgments properly so called. Many of the former are analytical, but they only afford the means for metaphysical judgments, which are the whole end of the science, and which are always synthetical. For if there be concepts pertaining to metaphysics (as, for example, that of substance), the judgments springing from simple analysis of them also pertain to metaphysics, as, for example, substance is that which only exists as subject; and by means of several such analytical judgments, we seek to approach the definition of the concept. But as the analysis of a pure concept of the understanding pertaining to metaphysics, does not proceed in any different manner from the dissection of any other, even empirical, concepts, not pertaining to metaphysics (such as: air is an elastic fluid, the elasticity of which is not destroyed by any known degree of cold), it follows that the concept indeed, but not the analytical judgment, is properly metaphysical. This science has something peculiar in the production of its a priori cognitions, which must therefore be distinguished from the features it has in common with other rational knowledge. Thus the judgment, that all the substance in things is permanent, is a synthetical and properly metaphysical judgment.

All metaphysical judgments, properly speaking, are synthetic. We must distinguish judgments that concern metaphysics from metaphysical judgments properly so called. Many judgments that concern metaphysics are analytic. But they only provide the means for making metaphysical judgments. These judgments are the whole aim of the science, and they are always synthetic. For example, substance is a concept that concerns metaphysics. Judgments that come from simply analyzing that concept also concern metaphysics. One such judgment is that substance is what exists only as a subject. We use several such analytic judgments to approach a definition of the concept. But analyzing a pure concept of the understanding that concerns metaphysics is no different from analyzing any other concept. This holds even for empirical concepts that do not concern metaphysics. For example, air is an elastic fluid whose elasticity is not destroyed by any known degree of cold. So the concept, but not the analytic judgment, is properly metaphysical. Metaphysics produces a priori knowledge in a distinctive way. This feature must therefore be distinguished from those it shares with other kinds of rational knowledge. For example, the judgment that all substance in things is permanent is synthetic and properly metaphysical.

If the a priori principles, which constitute the materials of metaphysics, have first been collected according to fixed principles, then their analysis will be of great value; it might be taught as a particular part (as a philosophia definitiva), containing nothing but analytical judgments pertaining to metaphysics, and could be treated separately from the synthetical which constitute metaphysics proper. For indeed these analyses are not elsewhere of much value, except in metaphysics, i.e., as regards the synthetical judgments, which are to be generated by these previously analysed concepts.

If the a priori principles that form the materials of metaphysics are first collected according to fixed principles, analyzing them will be very valuable. This analysis might be taught as a separate part of philosophy (a philosophia definitiva). It would contain only analytic judgments concerning metaphysics. It could be treated separately from the synthetic judgments that constitute metaphysics proper. For these analyses are not of much value elsewhere. Their value lies in metaphysics, with regard to the synthetic judgments to be produced from these previously analyzed concepts.

The conclusion drawn in this section then is, that metaphysics is properly concerned with synethetical propositions a priori, and these alone constitute its end, for which it indeed requires various dissections of its concepts, viz., of its analytical judgments, but wherein the procedure is not different from that in every other kind of knowledge, in which we merely seek to render our concepts distinct by analysis. But the generation of a priori cognition by concrete images as well as by concepts, in fine of synthetical propositions a priori in philosophical cognition, constitutes the essential subject of Metaphysics.

The conclusion of this section is that metaphysics is properly concerned with synthetic a priori propositions. These alone are its goal. To reach this goal, metaphysics must analyze its concepts through analytic judgments. But this analysis is no different from that used in every other kind of knowledge to clarify concepts. The essential subject of metaphysics, however, is the production of a priori knowledge through concrete images as well as concepts. In short, its subject is the production of synthetic a priori propositions in philosophical knowledge.

Weary therefore as well of dogmatism, which teaches us nothing, as of scepticism, which does not even promise us anything, not even the quiet state of a contented ignorance; disquieted by the importance of knowledge so much needed; and lastly, rendered suspicious by long experience of all knowledge which we believe we possess, or which offers itself, under the title of pure reason: there remains but one critical question on the answer to which our future procedure depends, viz., Is Metaphysics at all possible? But this question must be answered not by sceptical objections to the asseverations of some actual system of metaphysics (for we do not as yet admit such a thing to exist), but from the conception, as yet only problematical, of a science of this sort.

We are therefore weary of dogmatism, which teaches us nothing. We are also weary of skepticism, which promises us nothing, not even the peace of contented ignorance. We are troubled by the importance of the knowledge we so badly need. Finally, long experience has made us suspicious of all knowledge we believe we possess or that is offered as pure reason. So only one critical question remains, and our future course depends on the answer: Is metaphysics possible at all? We must not answer this question by raising skeptical objections to the claims of some existing system of metaphysics. We do not yet accept that any such system exists. Instead, we must answer it by considering the idea of such a science, whose possibility is still in question.

In the Critique of Pure Reason I have treated this question synthetically, by making inquiries into pure reason itself, and endeavoring in this source to determine the elements as well as the laws of its pure use according to principles. The task is difficult, and requires a resolute reader to penetrate by degrees into a system, based on no data except reason itself, and which therefore seeks, without resting upon any fact, to unfold knowledge from its original germs. Prolegomena, however, are designed for preparatory exercises; they are intended rather to point out what we have to do in order if possible to actualise a science, than to propound it. They must therefore rest upon something already known as trustworthy, from which we can set out with confidence, and ascend to sources as yet unknown, the discovery of which will not only explain to us what we knew, but exhibit a sphere of many cognitions which all spring from the same sources. The method of Prolegomena, especially of those designed as a preparation for future metaphysics, is consequently analytical.

In the Critique of Pure Reason, I approached this question synthetically by examining pure reason itself. I tried to identify both the elements of its pure use and the laws governing it according to principles. This is a difficult task. It requires a determined reader to work gradually into a system based on nothing but reason itself. The system therefore seeks to develop knowledge from its original seeds, without relying on any facts. Prolegomena, however, are meant as preparation. Rather than presenting a science, they aim to show what we must do to establish one, if possible. They must therefore start from something already known to be reliable. From that starting point, we can work our way up with confidence to sources that are still unknown. Discovering these sources will not only explain what we already knew. It will also reveal a range of knowledge that all comes from the same sources. The method of Prolegomena is therefore analytical, especially when they prepare the way for future metaphysics.

But it happens fortunately, that though we cannot assume metaphysics to be an actual science, we can say with confidence that certain pure a priori synthetical cognitions, pure Mathematics and pure Physics are actual and given; for both contain propositions, which are thoroughly recognised as apodeictically certain, partly by mere reason, partly by general consent arising from experience, and yet as independent of experience. We have therefore some at least uncontested synthetical knowledge a priori, and need not ask whether it be possible, for it is actual, but how it is possible, in order that we may deduce from the principle which makes the given cognitions possible the possibility of all the rest.

Fortunately, although we cannot assume that metaphysics is an established science, we can confidently say that some pure a priori synthetic knowledge exists. Pure Mathematics and pure Physics are examples. Both contain propositions recognized as necessarily certain, some by reason alone and others by general agreement based on experience. Yet these propositions are recognized as independent of experience. We therefore have at least some undisputed synthetic knowledge a priori. We need not ask whether such knowledge is possible, because it exists. Instead, we must ask how it is possible. That will allow us to derive the possibility of all other such knowledge from the principle that makes this existing knowledge possible.

The General Problem: How is Cognition from Pure Reason Possible?

The General Problem: How Is Knowledge from Pure Reason Possible?

§ 5. We have above learned the significant distinction between analytical and synthetical judgments. The possibility of analytical propositions was easily comprehended, being entirely founded on the law of Contradiction. The possibility of synthetical a posteriori judgments, of those which are gathered from experience, also requires no particular explanation; for experience is nothing but a continual synthesis of perceptions. There remain therefore only synthetical propositions a priori, of which the possibility must be sought or investigated, because they must depend upon other principles than the law of contradiction.

§ 5. We have already learned the important distinction between analytic and synthetic judgments. The possibility of analytic propositions was easy to understand, since they rest entirely on the law of contradiction. The possibility of synthetic a posteriori judgments, those drawn from experience, also needs no special explanation. For experience is nothing but a continuous synthesis of perceptions. Only synthetic a priori propositions remain. We must investigate how they are possible, because they must depend on principles other than the law of contradiction.

But here we need not first establish the possibility of such propositions so as to ask whether they are possible. For there are enough of them which indeed are of undoubted certainty, and as our present method is analytical, we shall start from the fact, that such synthetical but purely rational cognition actually exists; but we must now inquire into the reason of this possibility, and ask, how such cognition is possible, in order that we may from the principles of its possibility be enabled to determine the conditions of its use, its sphere and its limits. The proper problem upon which all depends, when expressed with scholastic precision, is therefore:

But here we do not need to establish whether such propositions are possible. Enough of them are unquestionably certain. Since our present method is analytical, we will start from the fact that synthetic knowledge based purely on reason exists. But we must now investigate what makes this knowledge possible and ask how it is possible. From the principles that make it possible, we can then determine the conditions for its use, its scope, and its limits. The central problem on which everything depends, stated with scholarly precision, is therefore:

How are Synthetic Propositions a priori possible?

How are synthetic a priori propositions possible?

For the sake of popularity I have above expressed this problem somewhat differently, as an inquiry into purely rational cognition, which I could do for once without detriment to the desired comprehension, because, as we have only to do here with metaphysics and its sources, the reader will, I hope, after the fore going remarks, keep in mind that when we speak of purely rational cognition, we do not mean analytical, but synthetical cognition.⁹

To make the problem more accessible, I described it above somewhat differently, as an inquiry into purely rational knowledge. I could do this without harming understanding in this instance. For here we are concerned only with metaphysics and its sources. So I hope that, after my earlier remarks, the reader will remember what I mean by purely rational knowledge. I mean synthetic knowledge, not analytic knowledge.⁹

Metaphysics stands or falls with the solution of this problem: its very existence depends upon it. Let any one make metaphysical assertions with ever so much plausibility, let him overwhelm us with conclusions, if he has not previously proved able to answer this question satisfactorily, I have a right to say: this is all vain baseless philosophy and false wisdom. You speak through pure reason, and claim, as it were to create cognitions a priori by not only dissecting given concepts, but also by asserting connexions which do not rest upon the law of contradiction, and which you believe you conceive quite independently of all experience; how do you arrive at this, and how will you justify your pretensions? An appeal to the consent of the common sense of mankind cannot be allowed; for that is a witness whose authority depends merely upon rumor. Says Horace:

Metaphysics stands or falls with the solution to this problem. Its very existence depends on that solution. Someone may make metaphysical claims, however plausible, and overwhelm us with conclusions. But if that person has not first proved able to answer this question satisfactorily, I have a right to say: this is all empty, baseless philosophy and false wisdom. You speak through pure reason and claim, as it were, to create knowledge a priori. You do this not only by analyzing given concepts, but also by asserting connections that do not rest on the law of contradiction. You believe you understand these connections quite independently of all experience. How do you arrive at this knowledge, and how will you justify your claims? You cannot appeal to the agreement of humanity's common sense. That witness's authority rests merely on hearsay. As Horace says:

"Quodcunque ostendis mihi sic, incredulus odi."

"Whatever you show me this way, I disbelieve and hate."

"To all that which thou provest me thus, I refuse to give credence."

"I refuse to believe anything you prove to me in this way."

The answer to this question, though indispensable, is difficult; and though the principal reason that it was not made long ago is, that the possibility of the question never occurred to anybody, there is yet another reason, which is this that a satisfactory answer to this one question requires a much more persistent, profound, and painstaking reflexion, than the most diffuse work on Metaphysics, which on its first appearance promised immortality to its author. And every intelligent reader, when he carefully reflects what this problem requires, must at first be struck with its difficulty, and would regard it as insoluble and even impossible, did there not actually exist pure synthetical cognitions a priori. This actually happened to David Hume, though he did not conceive the question in its entire universality as is done here, and as must be done, should the answer be decisive for all Metaphysics. For how is it possible, says that acute man, that when a concept is given me, I can go beyond it and connect with it another, which is not contained in it, in such a manner as if the latter necessarily belonged to the former? Nothing but experience can furnish us with such connexions (thus he concluded from the difficulty which he took to be an impossibility), and all that vaunted necessity, or, what is the same thing, all cognition assumed to be a priori, is nothing but a long habit of accepting something as true, and hence of mistaking subjective necessity for objective.

The answer to this question is essential, but difficult. The main reason it was not given long ago is that no one thought the question could be asked. But there is another reason. A satisfactory answer requires far more sustained, deep, and careful thought than even the longest work on Metaphysics. Such a work might have promised its author immortality when it first appeared. Every intelligent reader who carefully considers what this problem demands must at first be struck by its difficulty. Indeed, the reader would consider it insoluble and even impossible if pure synthetic a priori knowledge did not actually exist. This is what happened to David Hume. However, he did not conceive the question in its full generality, as we do here. The question must be understood in this general way if the answer is to be decisive for all Metaphysics. For, as that perceptive man asked, how can I go beyond a given concept and connect it to another concept not contained in it? How can I do this as if the second concept necessarily belonged to the first? Hume concluded that only experience can provide such connections. He drew this conclusion because he took the difficulty to be an impossibility. He also concluded that all this much praised necessity, or, in other words, all knowledge assumed to be a priori, is merely a long habit of accepting something as true. We therefore mistake subjective necessity for objective necessity.

Should my reader complain of the difficulty and the trouble which I occasion him in the solution of this problem, he is at liberty to solve it himself in an easier way. Perhaps he will then feel under obligation to the person who has undertaken for him a labor of so profound research, and will rather be surprised at the facility with which, considering the nature of the subject, the solution has been attained. Yet it has cost years of work to solve the problem in its whole universality (using the term in the mathematical sense, viz., for that which is sufficient for all cases), and finally to exhibit it in the analytical form, as the reader finds it here.

If readers complain about the difficulty and trouble this problem gives them, they are free to solve it more easily themselves. Perhaps they will then feel grateful to the person who undertook such deep research for them. Instead of complaining, they may be surprised at how easily the solution was reached, given the nature of the subject. Yet solving the problem in its full generality took years of work. I use “generality” in the mathematical sense, meaning what is sufficient for all cases. It also took years to present the solution in the analytical form readers find here.

All metaphysicians are therefore solemnly and legally suspended from their occupations till they shall have answered in a satisfactory manner the question, "How are synthetic cognitions a priori possible?" For the answer contains which they must show when they have anything to offer in the name of pure reason. But if they do not possess these credentials, they can expect nothing else of reasonable people, who have been deceived so often, than to be dismissed without further ado.

All metaphysicians are therefore formally and legally suspended from their work until they satisfactorily answer the question, "How are synthetic cognitions a priori possible?" The answer contains the credentials they must show whenever they offer anything in the name of pure reason. But if they lack these credentials, they can only expect reasonable people to dismiss them without further discussion. After all, reasonable people have been deceived so often.

If they on the other hand desire to carry on their business, not as a science, but as an art of wholesome oratory suited to the common sense of man, they cannot in justice be prevented. They will then speak the modest language of a rational belief, they will grant that they are not allowed even to conjecture, far less to know, anything which lies beyond the bounds of all possible experience, but only to assume (not for speculative use, which they must abandon, but for practical purposes only) the existence of something that is possible and even indispensable for the guidance of the understanding and of the will in life. In this manner alone can they be called useful and wise men, and the more so as they renounce the title of metaphysicians; for the latter profess to be speculative philosophers, and since, when judgments a priori are under discussion, poor probabilities cannot be admitted (for what is declared to be known a priori is thereby announced as necessary), such men cannot be permitted to play with conjectures, but their assertions must be either science, or are worth nothing at all.

If, on the other hand, they wish to carry on their work not as a science, but as an art of sound public speaking suited to common sense, no one can fairly stop them. They will then speak modestly of rational belief. They will admit that they cannot even make guesses, much less know anything, about what lies beyond all possible experience. They can only assume the existence of something possible and even indispensable for guiding the understanding and the will in life. They must make this assumption only for practical purposes, not for speculation, which they must give up. Only in this way can they be called useful and wise. They deserve these names all the more if they give up the title of metaphysicians. For metaphysicians claim to be speculative philosophers. When judgments a priori are at issue, mere probabilities cannot be accepted. Whatever is said to be known a priori is thereby claimed to be necessary. So metaphysicians cannot be allowed to play with guesses. Their claims must either be science or be worth nothing at all.

It may be said, that the entire transcendental philosophy, which necessarily precedes all metaphysics, is nothing but the complete solution of the problem here propounded, in systematical order and completeness, and hitherto we have never had any transcendental philosophy; for what goes by its name is properly a part of metaphysics, whereas the former science is intended first to constitute the possibility of the latter, and must therefore precede all metaphysics. And it is not surprising that when a whole science, deprived of all help from other sciences, and consequently in itself quite new, is required to answer a single question satisfactorily, we should find the answer troublesome and difficult, nay even shrouded in obscurity.

It may be said that all of transcendental philosophy is nothing more than a complete, systematic solution to the problem posed here. Transcendental philosophy must come before all metaphysics, and until now we have never had any transcendental philosophy. What goes by that name is really part of metaphysics. Transcendental philosophy, however, is intended first to establish the possibility of metaphysics, and must therefore come before it. So it is not surprising that we find the answer troublesome and difficult, even shrouded in obscurity. For a satisfactory answer to this single question requires a whole science, one that receives no help from other sciences and is therefore entirely new in itself.

As we now proceed to this solution according to the analytical method, in which we assume that such cognitions from pure reasons actually exist, we can only appeal to two sciences of theoretical cognition (which alone is under consideration here), pure mathematics and pure natural science (physics). For these alone can exhibit to us objects in a definite and actualisable form (in der Anschauung), and consequently (if there should occur in them a cognition a priori) can show the truth or conformity of the cognition to the object in concreto, that is, its actuality, from which we could proceed to the reason of its possibility by the analytic method. This facilitates our work greatly for here universal considerations are not only applied to facts, but even start from them, while in a synthetic procedure they must strictly be derived in abstracto from concepts.

We now proceed toward a solution by the analytical method, assuming that knowledge from pure reason actually exists. We can appeal to only two sciences of theoretical knowledge, the only kind considered here: pure mathematics and pure natural science (physics). Only these sciences can present objects to us in a definite form that can be realized in intuition (in der Anschauung). So, if either science contains a priori knowledge, it can show in a concrete case that this knowledge is true, or conforms to its object. In other words, it can show that such knowledge is actual. From there, we can use the analytical method to discover what makes that knowledge possible. This greatly simplifies our work. Here, we not only apply general considerations to facts, but even start from facts. By contrast, a synthetic procedure must derive these considerations strictly from concepts in the abstract.

But, in order to rise from these actual and at the same time well-grounded pure cognitions a priori to such a possible cognition of the same as we are seeking, viz., to metaphysics as a science, we must comprehend that which occasions it, I mean the mere natural, though in spite of its truth not unsuspected, cognition a priori which lies at the bottom of that science, the elaboration of which without any critical investigation of its possibility is commonly called metaphysics. In a word, we must comprehend the natural conditions of such a science as a part of our inquiry, and thus the transcendental problem will be gradually answered by a division into four questions:

But we want to move from these actual and well-founded pure a priori cognitions to another possible cognition: metaphysics as a science. To do this, we must understand what gives rise to metaphysics. I mean the merely natural a priori cognition that underlies it, which is open to suspicion despite its truth. Developing this cognition without critically investigating its possibility is commonly called metaphysics. In short, our inquiry must include the natural conditions of such a science. The transcendental problem will thus be answered gradually by dividing it into four questions:

1. How is pure mathematics possible?

1. How is pure mathematics possible?

2. How is pure natural science possible?

2. How is pure natural science possible?

3. How is metaphysics in general possible?

3. How is metaphysics possible in general?

4. How is metaphysics as a science possible?

4. How is metaphysics possible as a science?

It may be seen that the solution of these problems, though chiefly designed to exhibit the essential matter of the Critique, has yet something peculiar, which for itself alone deserves attention. This is the search for the sources of given sciences in reason itself, so that its faculty of knowing something a priori may by its own deeds be investigated and measured. By this procedure these sciences gain, if not with regard to their contents, yet as to their proper use, and while they throw light on the higher question concerning their common origin, they give, at the same time, an occasion better to explain their own nature.

The solutions to these problems are chiefly meant to present the essential subject of the Critique. Yet they also have a distinctive feature that deserves attention in its own right. They seek the sources of established sciences in reason itself. In this way, reason’s ability to know something a priori can be examined and measured by its own achievements. This procedure benefits the sciences, if not in their content, then in their proper use. As the sciences shed light on the broader question of their common origin, they also provide an opportunity to explain their own nature more clearly.