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Hume’s challenge to speculative metaphysics exerted a strong influence on subsequent philosophy, and was taken up in a systematic way by the famous German philosopher Immanuel Kant, first in his mammoth and highly complex Critique of Pure Reason (1781), and then in the Prolegomena (1783), which was intended as a more popular abstract of that work. The full title of the ‘Prolegomena’ (‘Preamble’ or ‘Preliminary Remarks’) is Prolegomena to any future metaphysics which will be able to present itself as a science (Prolegomena zu einer jeden künftigen Metaphysik die als Wissenschaft wird auftreten können); the question Kant addresses is ‘whether such a thing as metaphysics is even possible at all’.

Hume had convinced Kant that previous attempts to ascend beyond the empirical world and describe the supposed ultimate nature of reality (e.g. the theory of substance proposed by Leibniz (see above, extract 5)) were doomed to failure. Kant condemned such vain aspirations in a famous metaphor: ‘the light dove, cleaving the air in her free flight, might imagine [absurdly] that flight would be easier still in empty space’.¹ There is, for Kant, no possible description of the world which can free itself from some reference to experience. But Kant argues that in experiencing the world, the mind is already armed with certain fundamental categories of understanding; these are a priori, but not in the traditional sense of being wholly abstract and independent of experience; rather they constitute the preconditions for all possible experience (see above, Part I, extract 8).

In the following set of extracts Kant argues that we do already possess knowledge that is both a priori and also genuinely informative or synthetic.² To begin with, he argues that a priori mathematical judgements (e.g. that 7 + 5 = 12) are synthetic, since we cannot arrive at the concept of twelve merely by reflection on the notions of seven and five.³ Second, and more important, he takes up Hume’s challenge with respect to scientific knowledge (Hume had argued, extract 7 above, that we can never know any causal connections a priori). For Kant, the principle that every event has a cause is synthetic; yet it is a priori in the sense of being presupposed by experience (Kant argues elsewhere that we could not even begin to classify sets of perceptions as constituting genuine events unless the mind had the power to interpret the world in terms of causal frameworks).⁴

So there is, after all, room for a genuine metaphysics – not one which fruitlessly attempts to speculate about what lies beyond experience, but one which instead analyses and systematically lays out all the a priori concepts of the understanding which the mind necessarily employs in processing and interpreting the data of experience (see penultimate paragraph of extracts below). Though Kant does from time to time talk of a hidden world beyond experience, a world of what he calls noumena or ‘Things in Themselves’, he makes it clear that there can be no valid philosophical speculation about what such an independent reality might be like; human reason, when it operates properly, is necessarily confined to phenomena – to the world as experienced. The confusions and pretensions of traditional metaphysics arose from its attempt to describe the supposed nature of reality ‘in itself’; the new ‘critical’ metaphysics, mapping out the necessary preconditions for human experience, can hope to provide instead ‘definite and perfect knowledge’. It has, Kant concludes, the kind of validity and authority which modern astronomy has when compared to the pretensions of fortune-telling or astrology.

The distinction between analytic and synthetic judgements.

Metaphysical knowledge must contain simply judgements a priori; so much is demanded by the speciality of its sources. But judgements, let them have what origin they may, or let them even as regards logical form be constituted as they may, possess a distinction according to their content, by virtue of which they are either simply explanatory and contribute nothing to the content of a cognition, or they are extensive, and enlarge the given cognition; the first may be termed analytic, and the second synthetic judgements.

Analytic judgements say nothing in the predicate but what was already thought in the conception of the subject, though perhaps not so clearly, or with the same degree of consciousness. When I say, all bodies are extended, I do not thereby enlarge my conception of a body in the least, but simply analyse it, inasmuch as extension, although not expressly stated, was already thought in that conception; the judgement is, in other words, analytic. On the other hand, the proposition ‘some bodies are heavy’ contains something in the predicate which was not already thought in the general conception of a body; it enlarges, that is to say, my knowledge, in so far as it adds something to my conception; and must therefore be termed a synthetic judgement.

The common principle of all analytic judgements is the principle of contradiction.

All analytic judgements are based entirely on the principle of contradiction, and are by their nature cognitions a priori, whether the conceptions serving as their matter be empirical or not. For inasmuch as the predicate of an affirmative analytic judgement is previously thought in the conception of the subject, it cannot without contradiction be denied of it; in the same way, its contrary, in a negative analytic judgement, must necessarily be denied of the subject, likewise in accordance with the principle of contradiction. It is thus with the propositions ‘every body is extended’; ‘no body is unextended’. For this reason all analytic propositions are judgements a priori, although their conceptions may be empirical. Let us take as an instance the proposition ‘gold is a yellow metal’. Now, to know this, I require no further experience beyond my conception of gold, which contains the propositions that this body is yellow and a metal, for this constitutes precisely my conception, and therefore I have only to dissect it, without needing to look around for anything elsewhere.

Synthetic judgements demand a principle other than that of contradiction.

There are synthetic judgements a posteriori whose origin is empirical; but there are also others of an a priori certainty that spring from the Understanding and the Reason. But both are alike in this, that they can never have their source solely in the axiom of analysis, viz., the principle of contradiction; they require an altogether different principle, notwithstanding that whatever principle they may be deduced from, they must always conform to the principle of contradiction, for nothing can be opposed to this principle, although not everything can be deduced from it. I will first of all bring synthetic judgements under certain classes.

(1) Judgements of experience are always synthetic. It would be absurd to found an analytic judgement on experience, as it is unnecessary to go beyond my own conception in order to construct the judgement, and therefore the confirmation of experience is unnecessary to it. That a body is extended is a proposition possessing a priori certainty, and no judgement of experience. For before I go to experience I have all the conditions of my judgement already present in the conception, out of which I simply draw the predicate in accordance with the principle of contradiction, and thereby at the same time the necessity of the judgement may be known, a point which experience could never teach me.

(2) Mathematical judgements are in their entirety synthetic. This truth seems hitherto to have altogether escaped the analysts of human Reason; indeed, to be directly opposed to all their suppositions, although it is indisputably certain and very important in its consequences. For, because it was found that the conclusions of mathematicians all proceed according to the principle of contradiction (which the nature of every demonstrative certainty demands), it was concluded that the axioms were also known through the principle of contradiction, which was a great error; for though a synthetic proposition can be viewed in the light of the above principle, it can only be so by presupposing another synthetic proposition from which it is derived, but never by itself.

It must be first of all remarked that essentially mathematical propositions are always a priori, and never empirical, because they involve necessity, which cannot be inferred from experience. Should anyone be unwilling to admit this, I will limit my assertion to pure mathematics, the very conception of which itself brings with it the fact that it contains nothing empirical, but simply pure knowledge a priori.

At first sight, one might be disposed to think the proposition 7 + 5 = 12 merely analytic, resulting from the conception of a sum of seven and five, according to the principle of contradiction. But more closely considered it will be found that the conception of the sum of 7 and 5 comprises nothing beyond the union of two numbers in a single one, and that therein nothing whatever is thought as to what the single number is that combines both the others. The conception of twelve is by no means already thought, when I think merely of the union of seven and five, and I may dissect my conception of such a possible sum as long as I please, without discovering therein the number twelve. One must leave these conceptions, and call to one’s aid an intuition corresponding to one or other of them, as for instance one’s five fingers … and so gradually add the units of the five given in intuition to the conception of the seven. One’s conception is therefore really enlarged by the proposition 7 + 5 = 12; to the first a new one being added, that was in no way thought in the former; in other words, arithmetical propositions are always synthetic, a truth which is more apparent when we take rather larger numbers, for we must then be clearly convinced, that turn and twist our conceptions as we may, without calling intuition to our aid, we shall never find the sum required, by the mere dissection of them …

How is knowledge possible from pure reason?

We have already seen the important distinction between analytic and synthetic judgements. The possibility of analytic propositions can be very easily conceived, for they are based simply on the principle of contradiction. The possibility of synthetic propositions a posteriori, i.e., of such as are derived from experience, requires no particular explanation, for experience is nothing more than a continual adding together (synthesis) of perceptions. There remains, then, only synthetic propositions a priori, the possibility of which has yet to be sought for, or examined, because it must rest on other principles than that of contradiction.

But we do not require to search out the possibility of such propositions, that is, to ask whether they are possible, for there are enough of them, actually given, and with unquestionable certainty; and as the method we are here following is analytic, we shall assume at the outset that such synthetic but pure knowledge from Reason, is real; but thereupon we must investigate the ground of this possibility and proceed to ask – how is this knowledge possible? in order that, from the principles of its possibility, we may be in a position to determine the conditions, the scope, and limits of its use. The proper problem, on which everything turns, when expressed with scholastic precision, will accordingly stand thus: how are synthetic propositions a priori possible?

… Upon the solution of this problem, the standing or falling of metaphysics, in other words, its very existence, entirely depends. Let any one lay down assertions, however plausible, with regard to it, pile up conclusions upon conclusions to the point of overwhelming, if he has not been able first to answer satisfactorily the above question, I have a right to say: It is all vain, baseless philosophy, and false wisdom. You speak through pure Reason, and claim to create a priori cognitions, inasmuch as you pretend not merely to dissect given conceptions but new connections which do not rest on the principle of contradiction, and which you think you conceive quite independently of all experience. How do you arrive at them, and how will you justify yourself in such pretensions? …

How is pure mathematics possible?

Pure mathematics is only possible as synthetic knowledge a priori in so far as it refers simply to objects of sense, whose empirical intuition has for its foundation a pure intuition a priori (that of time and space). Such intuition is able to serve as a foundation because it is nothing more than the pure form of sensibility itself, that precedes the real appearance of objects, in that it makes them in the first place possible. This faculty of intuiting a priori does not concern the matter of the phenomenon … for that constitutes the empirical element therein, but only its form, space and time …

To contribute something to the explanation and confirmation of the above, we have only to consider the ordinary and necessary procedure of geometricians. All the proofs of complete likeness between two figures turn finally on the fact of their covering each other – in other words the possibility of substituting one, in every point, for the other; and this is obviously nothing else but a synthetic proposition, resting on immediate intuition. Now this intuition must be given pure and a priori, for otherwise the proposition in question could not count as demonstratively certain, but would possess only empirical certainty (in the latter case, we would only be able to say that it has always been so observed, or it is valid only in so far as our perception has hitherto extended) …

How is pure natural science possible?

Although all the judgements of experience are empirical (i.e. have their ground in the immediate perception of sense), on the other hand all empirical judgements are not judgements of experience. Beyond the empirical, and beyond the given sense-intuition generally, special conceptions must be added, which have their origin entirely a priori in the pure understanding. Every perception is primarily subsumed under these conceptions, and it is only by means of them that it can be transformed into experience …

Let us now attempt a solution of Hume’s problematical conception … namely the conception of Cause. First, there is given me a priori, by means of logic, the form of a conditioned judgement generally (one cognition as antecedent, the other as consequent). But it is possible that in the perception, a rule of the relation may be met with which will say that on the occurrence of a given phenomenon another always follows (though not conversely). This would be a case of making use of the hypothetical judgement – to say, for instance, if a body is illuminated long enough by the sun it will become warm. There is certainly no necessity of connection here, in other words, no conception of cause. But to continue: if the above proposition, which is merely a subjective connection of perception, is to be a proposition of experience, it must be regarded as necessary and universally valid. Such a proposition would run: sun is, through its light, the cause of heat. The above empirical rule is now looked upon as law, and indeed not just as valid of phenomena, but valid of them in relation to a possible experience – which requires thoroughly, and therefore necessarily, valid rules. I perfectly understand, then, the conception of cause as a conception necessarily belonging to the mere form of experience, and its possibility as a synthetic union of perceptions, in a consciousness in general. But the possibility of a thing in general as a cause I do not understand, because the conception of cause does not refer at all to things, but only indicates the condition attaching to experience: that this can only be an objectively valid knowledge of phenomena, and their sequence in time, in so far as their antecedent can be united to the consequent according to the rule of hypothetical judgements.

Hence, the pure conceptions of the understanding have no meaning whatever, when they quit the objects of experience and refer to things in themselves (noumena). They serve, as it were, to spell out phenomena, that these may be able to be read as experience. The axioms arising from their relation to the world of sense, only serve our understanding for use in experience. Beyond this, are only arbitrary combinations, destitute of objective reality, and the possibility of which can neither be known a priori, nor their reference to objects be confirmed, or even made intelligible by an example, because all examples are borrowed from some possible experience, and consequently the objects of those conceptions are nothing but what may be met with in a possible experience.

This complete solution of Hume’s problem, although it turns out to be contrary to the opinion of its originator, preserves for the pure conceptions of the understanding their origin a priori, and for the universal laws of Nature their validity as laws of the understanding, but in such a manner that their use is limited to experience, because their possibility has its basis, solely, in the reference of the understanding to experience; not because they are derived from experience, but because experience is derived from them, which completely reversed mode of connection never occurred to Hume.

The following result of all previous researches follows from the above investigations: ‘All synthetic axioms a priori are nothing more than principles of possible experience’, and can never be referred to things in themselves, but only to phenomena as objects of experience. Hence pure mathematics no less than pure natural science can never refer to anything more than mere phenomena, and only present that which either makes experience in general possible, or which, inasmuch as it is derived from these principles, must always be able to be presented in some possible experience …

From the earliest ages of philosophy, investigators of pure reason have postulated, beyond the sensible essences (phenomena) which constitute the world of sense, special essences of the understanding (noumena) which are supposed to constitute a world of understanding; and since they regarded appearance and illusion as the same thing, which in an undeveloped epoch is to be excused, ascribed reality to the intelligible essence alone.

In fact, when we regard the objects of sense, as is correct, as mere appearances, we thereby at the same time confess that a thing in itself lies at their foundation although we do not know it as it is constituted in itself, but only its appearance, that is, the manner in which our senses are affected by this unknown something. The understanding then, by accepting appearances, admits also the existence of things in themselves, and we may even say that the presentation of such essences as lie at the basis of appearances, in short, mere essences of the understanding, is not only admissible, but unavoidable.

Our critical deduction does not by any means exclude such things (noumena), but rather limits the principles of aesthetic,⁵ in such a way that these should not be extended to all things (which would change everything into mere appearance) but should only be valid of objects of a possible experience. Essences of the understanding are hereby admitted only by the emphasizing of this rule, which admits of no exception, that we know nothing definite whatever of these pure essences of the understanding, neither can we know anything of them, because our pure conceptions of the understanding, no less than our pure intuitions, concern nothing but objects of a possible experience, in short, mere essences of sense; and as soon as we leave these, the above conceptions have not the least significance remaining.

There is indeed something seductive about our pure conceptions of the understanding, namely a temptation to a transcendent use; for so I name that which transcends all possible experience. Not only do our conceptions of substance, force, action, reality, &c., which are entirely independent of experience containing no phenomenon of sense, really seem to concern things in themselves (noumena); but what strengthens this supposition is, that they contain a necessity of determination in themselves, to which experience can never approach. The conception of cause contains a rule, according to which from one state another follows in a necessary manner; but experience only teaches us that often, or at most usually, one state of a thing follows upon another, and can therefore acquire neither strict universality nor necessity.

Hence these conceptions of the understanding seem to have far too much significance and content for mere use in experience to exhaust their entire determination, and the understanding builds in consequence, unobserved, by the side of the house of experience, a much more imposing wing, which it fills with sheer essences of thought, without even noticing that it has overstepped the legitimate bounds of its otherwise correct conceptions …

Solution of the general problem of the Prolegomena: How is metaphysics as a science possible?

Metaphysics, as a natural disposition of Reason is real, but it is also, in itself, dialectical and deceptive … Hence to attempt to draw our principles from it, and in their employment to follow this natural but none the less fallacious illusion can never produce science, but only an empty dialectical art, in which one school may indeed outdo the other, but none can ever attain a justifiable and lasting success. In order that, as science, it may lay claim not merely to deceptive persuasion, but to insight and conviction, a Critique of Reason must exhibit in a complete system the whole stock of conceptions a priori, arranged according to their different sources – the Sensibility, the Understanding, and the Reason; it must present a complete table of these conceptions, together with their analysis and all that can be deduced from them, but more especially the possibility of synthetic knowledge a priori by means of their deduction, the principles of its use, and finally, its boundaries. Thus criticism contains, and it alone contains, the whole plan well tested and approved, indeed all the means whereby metaphysics may be perfected as a science – by other ways and means this is impossible. The question now is not, however, how this business is possible, but only how we are to set about it; how good heads are to be turned from their previous mistaken and fruitless path to a non-deceptive treatment, and how such a combination may be best directed towards the common end.

This much is certain: he who has once tried criticism will be sickened for ever of all the dogmatic trash he was compelled to content himself with before, because his Reason, requiring something, could find nothing better for its occupation. Criticism stands to the ordinary school-metaphysics exactly in the same relation as chemistry to alchemy, or as astronomy to fortune-telling astrology. I guarantee that no one who has comprehended and thought out the conclusions of criticism, even in these Prolegomena, will ever return to the old sophistical pseudo-science. He will rather look forward with a kind of pleasure to a metaphysics, certainly now within his power, which requires no more preparatory discoveries, and which alone can procure for reason permanent satisfaction.