I.2.2. The Antinomy of Pure Reason: Cosmological Ideas and the Four Conflicts

We have shown in the introduction to this part of our work that all transcendental illusion of pure reason rests on dialectical inferences whose schema is supplied by logic in the three formal species of syllogisms—just as the categories find their logical schema in the four functions of all judgments. The first type of these pseudo-rational inferences deals with the unconditioned unity of the subjective conditions of all representations in general (of the subject or soul), in correspondence with the categorical syllogisms, the major premiss of which is a principle asserting the relation of a predicate to a subject. The second type of dialectical argument follows the analogy of the hypothetical syllogisms. It has as its content the unconditioned unity of the objective conditions in the [field of] appearance. In similar fashion, the third type, which will be dealt with in the next chapter, has as its theme the unconditioned unity of the objective conditions of the possibility of objects in general.

But there is one point that calls for special notice. Transcendental paralogism produced a purely one-sided illusion in regard to the idea of the subject of our thought. No illusion which will even in the slightest degree support the opposing assertion is caused by the concepts of reason. Consequently, although transcendental paralogism, in spite of a favouring illusion, cannot disclaim the radical defect through which in the fiery ordeal of critical investigation it dwindles into mere semblance, such advantage as it offers is altogether on the side of pneumatism.

A completely different situation arises when reason is applied to the objective synthesis of appearances. For in this domain, however it may endeavour to establish its principle of unconditioned unity, and though it indeed does so with great though illusory appearance of success, it soon falls into such contradictions that it is constrained, in this cosmological field, to desist from any such pretensions.

We have here presented to us a new phenomenon of human reason—an entirely natural antithetic, in which there is no need of making subtle enquiries or of laying snares for the unwary, but into which reason of itself quite unavoidably falls. It certainly guards reason from the slumber of fictitious conviction such as is generated by a purely one-sided illusion, but at the same time subjects it to the temptation either of abandoning itself to a sceptical despair, or of assuming an obstinate attitude, dogmatically committing itself to certain assertions, and refusing to grant a fair hearing to the arguments for the counter-position. Either attitude is the death of sound philosophy, although the former might perhaps be entitled the euthanasia of pure reason.

Before considering the various forms of opposition and dissension to which this conflict or antinomy of the laws of pure reason gives rise, we may offer a few remarks in explanation and justification of the method which we propose to employ in the treatment of this subject. I entitle all transcendental ideas, in so far as they refer to absolute totality in the synthesis of appearances, cosmical concepts, partly because this unconditioned totality also underlies the concept—itself only an idea—of the world-whole; partly because they concern only the synthesis of appearances, therefore only empirical synthesis. When, on the contrary, the absolute totality is that of the synthesis of the conditions of all possible things in general, it gives rise to an ideal of pure reason which, though it may indeed stand in a certain relation to the cosmical concept, is quite distinct from it. Accordingly, just as the paralogisms of pure reason formed the basis of a dialectical psychology, so the antinomy of pure reason will exhibit to us the transcendental principles of a pretended pure rational cosmology. But it will not do so in order to show this science to be valid and to adopt it. As the title, conflict of reason, suffices to show, this pretended science can be exhibited only in its bedazzling but false illusoriness, as an idea which can never be reconciled with appearances.

In proceeding to enumerate these ideas with systematic precision according to a principle, we must bear in mind two points. In the first place we must recognise that pure and transcendental concepts can issue only from the understanding. Reason does not really generate any concept. The most it can do is to free a concept of understanding from the unavoidable limitations of possible experience, and so to endeavour to extend it beyond the limits of the empirical, though still, indeed, in terms of its relation to the empirical. This is achieved in the following manner. For a given conditioned, reason demands on the side of the conditions—to which as the conditions of synthetic unity the understanding subjects all appearances—absolute totality, and in so doing converts the category into a transcendental idea. For only by carrying the empirical synthesis as far as the unconditioned is it enabled to render it absolutely complete; and the unconditioned is never to be met with in experience, but only in the idea. Reason makes this demand in accordance with the principle that if the conditioned is given, the entire sum of conditions, and consequently the absolutely unconditioned (through which alone the conditioned has been possible) is also given. The transcendental ideas are thus, in the first place, simply categories extended to the unconditioned, and can be reduced to a table arranged according to the [fourfold] headings of the latter. In the second place, not all categories are fitted for such employment, but only those in which the synthesis constitutes a series of conditions subordinated to, not co-ordinated with, one another, and generative of a [given] conditioned. Absolute totality is demanded by reason only in so far as the ascending series of conditions relates to a given conditioned. It is not demanded in regard to the descending line of consequences, nor in reference to the aggregate of co-ordinated conditions of these consequences. For in the case of the given conditioned, conditions are presupposed, and are considered as given together with it. On the other hand, since consequences do not make their conditions possible, but rather presuppose them, we are not called upon, when we advance to consequences or descend from a given condition to the conditioned, to consider whether the series does or does not cease; the question as to the totality of the series is not in any way a presupposition of reason.

Thus we necessarily think time as having completely elapsed up to the given moment, and as being itself given in this completed form. This holds true, even though such completely elapsed time is not determinable by us. But since the future is not the condition of our attaining to the present, it is a matter of entire indifference, in our comprehension of the latter, how we may think of future time, whether as coming to an end or as flowing on to infinity. We have, as it were, the series m, n, o, in which n is given as conditioned by m, and at the same time as being the condition of o. The series ascends from the conditioned n to m (l, k, i, etc.), and also descends from the condition n to the conditioned o (p, q, r, etc.). Now I must presuppose the first series in order to be able to view n as given. According to reason, with its demand for totality of conditions, n is possible only by means of that series. Its possibility does not, however, rest upon the subsequent series, o, p, q, r. This latter series may not therefore be regarded as given, but only as allowing of being given (dabilis).

I propose to name the synthesis of a series which begins, on the side of the conditions, from the condition which stands nearest to the given appearance and so passes to the more remote conditions, the regressive synthesis; and that which advances, on the side of the conditioned, from the first consequence to the more distant, the progressive. The first proceeds in antecedentia, the second in consequentia. The cosmological ideas deal, therefore, with the totality of the regressive synthesis proceeding in antecedentia, not in consequentia. The problem of pure reason suggested by the progressive form of totality is gratuitous and unnecessary, since the raising of it is not required for the complete comprehension of what is given in appearance. For that we require to consider only the grounds, not the consequences.

In arranging the table of ideas in accordance with the table of categories, we first take the two original quanta of all our intuition, time and space. Time is in itself a series, and indeed the formal condition of all series. In it, in regard to a given present, the antecedents can be a priori distinguished as conditions (the past) from the consequents (the future). The transcendental idea of the absolute totality of the series of conditions of any given conditioned therefore refers only to all past time; and in conformity with the idea of reason past time, as condition of the given moment, is necessarily thought as being given in its entirety. Now in space, taken in and by itself, there is no distinction between progress and regress. For as its parts are co-existent, it is an aggregate, not a series. The present moment can be regarded only as conditioned by past time, never as conditioning it, because this moment comes into existence only through past time, or rather through the passing of the preceding time. But as the parts of space are co-ordinated with, not subordinated to, one another, one part is not the condition of the possibility of another; and unlike time, space does not in itself constitute a series. Nevertheless the synthesis of the manifold parts of space, by means of which we apprehend space, is successive, taking place in time and containing a series. And since in this series of the aggregated spaces (as for instance of the feet in a rood) of the given space, those which are thought in extension of the given space are always the condition of the limits of the given space, the measuring of a space is also to be regarded as a synthesis of a series of the conditions of a given conditioned, only with this difference that the side of the conditions is not in itself distinct from that of the conditioned, and that in space regressus and progressus would therefore seem to be one and the same. Inasmuch as one part of space is not given through the others but only limited by them, we must consider each space, in so far as it is limited, as being also conditioned, in that it presupposes another space as the condition of its limits, and so on. In respect of limitation the advance in space is thus also a regress, and the transcendental idea of the absolute totality of the synthesis in the series of conditions likewise applies to space. I can as legitimately enquire regarding the absolute totality of appearance in space as of that in past time. Whether an answer to this question is ever possible, is a point which will be decided later.

Secondly, reality in space, i.e. matter, is a conditioned. Its internal conditions are its parts, and the parts of these parts its remote conditions. There thus occurs a regressive synthesis, the absolute totality of which is demanded by reason. This can be obtained only by a completed division in virtue of which the reality of matter vanishes either into nothing or into what is no longer matter—namely, the simple. Here also, then, we have a series of conditions, and an advance to the unconditioned.

Thirdly, as regards the categories of real relation between appearances, that of substance with its accidents is not adapted to being a transcendental idea. That is to say, in it reason finds no ground for proceeding regressively to conditions. Accidents, in so far as they inhere in one and the same substance, are co-ordinated with each other, and do not constitute a series. Even in their relation to substance they are not really subordinated to it, but are the mode of existence of the substance itself. What in this category may still, however, seem to be an idea of transcendental reason, is the concept of the substantial. But since this means no more than the concept of object in general, which subsists in so far as we think in it merely the transcendental subject apart from all predicates, whereas we are here dealing with the unconditioned only as it may exist in the series of appearances, it is evident that the substantial cannot be a member of that series. This is also true of substances in community. They are mere aggregates, and contain nothing on which to base a series. For we cannot say of them, as we can of spaces, whose limits are never determined in and by themselves but only through some other space, that they are subordinated to each other as conditions of the possibility of one another. There thus remains only the category of causality. It presents a series of causes of a given effect such that we can proceed to ascend from the latter as the conditioned to the former as conditions, and so to answer the question of reason.

Fourthly, the concepts of the possible, the actual, and the necessary do not lead to any series, save in so far as the accidental in existence must always be regarded as conditioned, and as pointing in conformity with the rule of the understanding to a condition under which it is necessary, and this latter in turn to a higher condition, until reason finally attains unconditioned necessity in the totality of the series.

When we thus select out those categories which necessarily lead to a series in the synthesis of the manifold, we find that there are but four cosmological ideas, corresponding to the four titles of the categories:

There are several points which here call for notice. In the first place, the idea of absolute totality concerns only the exposition of appearances, and does not therefore refer to the pure concept, such as the understanding may form, of a totality of things in general. Appearances are here regarded as given; what reason demands is the absolute completeness of the conditions of their possibility, in so far as these conditions constitute a series. What reason prescribes is therefore an absolutely (that is to say, in every respect) complete synthesis, whereby the appearance may be exhibited in accordance with the laws of understanding.

Secondly, what reason is really seeking in this serial, regressively continued, synthesis of conditions, is solely the unconditioned. What it aims at is, as it were, such a completeness in the series of premisses as will dispense with the need of presupposing other premisses. This unconditioned is always contained in the absolute totality of the series as represented in imagination. But this absolutely complete synthesis is again only an idea; for we cannot know, at least at the start of this enquiry, whether such a synthesis is possible in the case of appearance. If we represent everything exclusively through pure concepts of understanding, and apart from conditions of sensible intuition, we can indeed at once assert that for a given conditioned, the whole series of conditions subordinated to each other is likewise given. The former is given only through the latter. When, however, it is with appearances that we are dealing, we find a special limitation due to the manner in which conditions are given, namely, through the successive synthesis of the manifold of intuition—a synthesis which has to be made complete through the regress. Whether this completeness is sensibly possible is a further problem; the idea of it lies in reason, independently alike of the possibility or of the impossibility of our connecting with it any adequate empirical concepts. Since, then, the unconditioned is necessarily contained in the absolute totality of the regressive synthesis of the manifold in the [field of] appearance—the synthesis being executed in accordance with those categories which represent appearance as a series of conditions to a given conditioned—reason here adopts the method of starting from the idea of totality, though what it really has in view is the unconditioned, whether of the entire series or of a part of it. Meantime, also, it leaves undecided whether and how this totality is attainable.

This unconditioned may be conceived in either of two ways. It may be viewed as consisting of the entire series in which all the members without exception are conditioned and only the totality of them is absolutely unconditioned. This regress is to be entitled infinite. Or alternatively, the absolutely unconditioned is only a part of the series—a part to which the other members are subordinated, and which does not itself stand under any other condition.’ On the first view, the series a parte priori is without limits or beginning, 2.e. is infinite, and at the same time is given in its entirety. But the regress in it is never completed, and can only be called potentially infinite. On the second view, there is a first member of the series which in respect of past time is entitled, the beginning of the world, in respect of space, the limit of the world, in respect of the parts of a given limited whole, the simple, in respect of causes, absolute self-activity (freedom), in respect of the existence of alterable things, absolute natural necessity.

We have two expressions, world and nature, which sometimes coincide. The former signifies the mathematical sum-total of all appearances and the totality of their synthesis, alike in the great and in the small, that is, in the advance alike through composition and through division. This same world is entitled nature when it is viewed as a dynamical whole. We are not then concerned with the aggregation in space and time, with a view to determining it as a magnitude, but with the unity in the existence of appearances. In this case the condition of that which happens is entitled the cause. Its unconditioned causality in the [field of] appearance is called freedom, and its conditioned causality is called natural cause in the narrower [adjectival] sense. The conditioned in existence in general is termed contingent and the unconditioned necessary. The unconditioned necessity of appearances may be entitled natural necessity.

The ideas with which we are now dealing I have above entitled cosmological ideas, partly because by the term ‘world’ we mean the sum of all appearances, and it is exclusively to the unconditioned in the appearances that our ideas are directed, partly also because the term ‘world’, in the transcendental sense, signifies the absolute totality of all existing things, and we direct our attention solely to the completeness of the synthesis, even though that is only attainable in the regress to its conditions. Thus despite the objection that these ideas are one and all transcendent, and that although they do not in kind surpass the object, namely, appearances, but are concerned exclusively with the world of sense, not with noumena, they yet carry the synthesis to a degree which transcends all possible experience, I none the less still hold that they may quite appropriately be entitled cosmical concepts In respect of the distinction between the mathematically and the dynamically unconditioned at which the regress aims, I might, however, call the first two concepts cosmical in the narrower sense, as referring to the world of the great and the small, and the other two transcendent concepts of nature. This distinction has no special immediate value; its significance will appear later.

If thetic be the name for any body of dogmatic doctrines, antithetic may be taken as meaning, not dogmatic assertions of the opposite, but the conflict of the doctrines of seemingly dogmatic knowledge (thesis cum antithesi) in which no one assertion can establish superiority over another. The antithetic does not, therefore, deal with one-sided assertions. It treats only of the conflict of the doctrines of reason with one another and the causes of this conflict. The transcendental antithetic is an enquiry into the antinomy of pure reason, its causes and outcome. If in employing the principles of understanding we do not merely apply our reason to objects of experience, but venture to extend these principles beyond the limits of experience, there arise pseudo-rational doctrines which can neither hope for confirmation in experience nor fear refutation by it. Each of them is not only in itself free from contradiction, but finds conditions of its necessity in the very nature of reason—only that, unfortunately, the assertion of the opposite has, on its side, grounds that are just as valid and necessary.

The questions which naturally arise in connection with such a dialectic of pure reason are the following: (1) In what propositions is pure reason unavoidably subject to an antinomy? (2) On what causes does this antinomy depend? (3) Whether and in what way, despite this contradiction, does there still remain open to reason a path to certainty?

A dialectical doctrine of pure reason must therefore be distinguished from all sophistical propositions in two respects. It must not refer to an arbitrary question such as may be raised for some special purpose, but to one which human reason must necessarily encounter in its progress. And secondly, both it and its opposite must involve no mere artificial illusion such as at once vanishes upon detection, but a natural and unavoidable illusion, which even after it has ceased to beguile still continues to delude though not to deceive us, and which though thus capable of being rendered harmless can never be eradicated.

Such dialectical doctrine relates not to the unity of understanding in empirical concepts, but to the unity of reason in mere ideas. Since this unity of reason involves a synthesis according to rules, it must conform to the understanding; and yet as demanding absolute unity of synthesis it must at the same time harmonise with reason. But the conditions of this unity are such that when it is adequate to reason it is too great for the understanding; and when suited to the understanding, too small for reason. There thus arises a conflict which cannot be avoided, do what we will.

These pseudo-rational assertions thus disclose a dialectical battlefield in which the side permitted to open the attack is invariably victorious, and the side constrained to act on the defensive is always defeated. Accordingly, vigorous fighters, no matter whether they support a good or a bad cause, if only they contrive to secure the right to make the last attack, and are not required to withstand a new onslaught from their opponents, may always count upon carrying off the laurels. We can easily understand that while this arena should time and again be contested, and that numerous triumphs should be gained by both sides, the last decisive victory always leaves the champion of the good cause master of the field, simply because his rival is forbidden to resume the combat. As impartial umpires, we must leave aside the question whether it is for the good or the bad cause that the contestants are fighting. They must be left to decide the issue for themselves. After they have rather exhausted than injured one another, they will perhaps themselves perceive the futility of their quarrel, and part good friends.

This method of watching, or rather provoking, a conflict of assertions, not for the purpose of deciding in favour of one or other side, but of investigating whether the object of controversy is not perhaps a deceptive appearance which each vainly strives to grasp, and in regard to which, even if there were no opposition to be overcome, neither can arrive at any result,—this procedure, I say, may be entitled the sceptical method. It is altogether different from scepticism—a principle of technical and scientific ignorance, which undermines the foundations of all knowledge, and strives in all possible ways to destroy its reliability and steadfastness. For the sceptical method aims at certainty. It seeks to discover the point of misunderstanding in the case of disputes which are sincerely and competently conducted by both sides, just as from the embarrassment of judges in cases of litigation wise legislators contrive to obtain instruction regarding the defects and ambiguities of their laws. The antinomy which discloses itself in the application of laws is for our limited wisdom the best criterion of the legislation that has given rise to them. Reason, which does not in abstract speculation easily become aware of its errors, is hereby awakened to consciousness of the factors [that have to be reckoned with] in the determination of its principles.

But it is only for transcendental philosophy that this sceptical method is essential. Though in all other fields of enquiry it can, perhaps, be dispensed with, it is not so in this field. In mathematics its employment would, indeed, be absurd; for in mathematics no false assertions can be concealed and rendered invisible, inasmuch as the proofs must always proceed under the guidance of pure intuition and by means of a synthesis that is always evident. In experimental philosophy the delay caused by doubt may indeed be useful; no misunderstanding is, however, possible which cannot easily be removed; and the final means of deciding the dispute, whether found early or late, must in the end be supplied by experience. Moral philosophy can also present its principles, together with their practical consequences, one and all in concreto, in what are at least possible experiences; and the misunderstanding due to abstraction is thereby avoided. But it is quite otherwise with transcendental assertions which lay claim to insight into what is beyond the field of all possible experiences. Their abstract synthesis can never be given in any a priori intuition, and they are so constituted that what is erroneous in them can never be detected by means of any experience. Transcendental reason consequently admits of no other test than the endeavour to harmonise its various assertions. But for the successful application of this test the conflict into which they fall with one another must first be left to develop free and untrammelled. This we shall now set about arranging.

The world has a beginning in time, and is also limited as regards space.

If we assume that the world has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away in the world an infinite series of successive states of things. Now the infinity of a series consists in the fact that it can never be completed through successive synthesis. It thus follows that it is impossible for an infinite world-series to have passed away, and that a beginning of the world is therefore a necessary condition of the world’s existence. This was the first point that called for proof.

As regards the second point, let us again assume the opposite, namely, that the world is an infinite given whole of coexisting things. Now the magnitude of a quantum which is not given in intuition as within certain limits, can be thought only through the synthesis of its parts, and the totality of such a quantum only through a synthesis that is brought to completion through repeated addition of unit to unit.” In order, therefore, to think, as a whole, the world which fills all spaces, the successive synthesis of the parts of an infinite world must be viewed as completed, that is, an infinite time must be viewed as having elapsed in the enumeration of all coexisting things. This, however, is impossible. An infinite aggregate of actual things cannot therefore be viewed as a given whole, nor consequently as simultaneously given. The world is, therefore, as regards extension in space, not infinite, but is enclosed within limits. This was the second point in dispute.

In stating these conflicting arguments I have not sought to elaborate sophisms. That is to say, I have not resorted to the method of the special pleader who attempts to take advantage of an opponent’s carelessness—freely allowing the appeal to a misunderstood law, in order that he may be in a position to establish his own unrighteous claims by the refutation of that law. Each of the above proofs arises naturally out of the matter in dispute, and no advantage has been taken of the openings afforded by erroneous conclusions arrived at by dogmatists in either party.

I might have made a pretence of establishing the thesis in the usual manner of the dogmatists, by starting from a defective concept of the infinitude of a given magnitude. I might have argued that a magnitude is infinite if a greater than itself, as determined by the multiplicity of given units which it contains, is not possible. Now no multiplicity is the greatest, since one or more units can always be added to it. Consequently an infinite given magnitude, and therefore an infinite world (infinite as regards the elapsed series or as regards extension) is impossible; it must be limited in both respects. Such is the line that my proof might have followed. But the above concept is not adequate to what we mean by an infinite whole. It does not represent how great it is, and consequently is not the concept of a maximum. Through it we think only its relation to any assignable unit in respect to which it is greater than all number. According as the unit chosen is greater or smaller, the infinite would be greater or smaller. Infinitude, however, as it consists solely in the relation to the given unit, would always remain the same. The absolute magnitude of the whole would not, therefore, be known in this way; indeed, the above concept does not really deal with it.

The true transcendental concept of infinitude is this, that the successive synthesis of units required for the enumeration of a quantum can never be completed. Hence it follows with complete certainty that an eternity of actual successive states leading up to a given (the present) moment cannot have elapsed, and that the world must therefore have a beginning.

In the second part of the thesis the difficulty involved in a series that is infinite and yet has elapsed does not arise, since the manifold of a world which is infinite in respect of extension is given as co-existing. But if we are to think the totality of such a multiplicity, and yet cannot appeal to limits that of themselves constitute it a totality in intuition, we have to account for a concept which in this case cannot proceed from the whole to the determinate multiplicity of the parts, but which must demonstrate the possibility of a whole by means of the successive synthesis of the parts. Now since this synthesis must constitute a never to be completed series, I cannot think a totality either prior to the synthesis or by means of the synthesis. For the concept of totality is in this case itself the representation of a completed synthesis of the parts. And since this completion is impossible, so likewise is the concept of it.

The world has no beginning, and no limits in space; it is infinite as regards both time and space.

For let us assume that it has a beginning. Since the beginning is an existence which is preceded by a time in which the thing is not, there must have been a preceding time in which the world was not, i.e. an empty time. Now no coming to be of a thing is possible in an empty time, because no part of such a time possesses, as compared with any other, a distinguishing condition of existence rather than of non-existence; and this applies whether the thing is supposed to arise of itself or through some other cause. In the world many series of things can, indeed, begin; but the world itself cannot have a beginning, and is therefore infinite in respect of past time.

As regards the second point, let us start by assuming the opposite, namely, that the world in space is finite and limited, and consequently exists in an empty space which is unlimited. Things will therefore not only be related in space but also related to space. Now since the world is an absolute whole beyond which there is no object of intuition, and therefore no correlate with which the world stands in relation, the relation of the world to empty space would be a relation of it to no object. But such a relation, and consequently the limitation of the world by empty space, is nothing. The world cannot, therefore, be limited in space; that is, it is infinite in respect of extension.

The proof of the infinitude of the given world-series and of the world-whole, rests upon the fact that, on the contrary assumption, an empty time and an empty space, must constitute the limit of the world. I am aware that attempts have been made to evade this conclusion by arguing that a limit of the world in time and space is quite possible without our having to make the impossible assumption of an absolute time prior to the beginning of the world, or of an absolute space extending beyond the real world. With the latter part of this doctrine, as held by the philosophers of the Leibnizian school, I am entirely satisfied. Space is merely the form of outer intuition; it is not a real object which can be outwardly intuited; it is not a correlate of the appearances, but the form of the appearances themselves. And since space is thus no object but only the form of possible objects, it cannot be regarded as something absolute in itself that determines the existence of things. Things, as appearances, determine space, that is, of all its possible predicates of magnitude and relation they determine this or that particular one to belong to the real. Space, on the other hand, viewed as a self-subsistent something, is nothing real in itself; and cannot, therefore, determine the magnitude or shape of real things. Space, it further follows, whether full or empty, may be limited by appearances, but appearances cannot be limited by an empty space outside them. This is likewise true of time. But while all this may be granted, it yet cannot be denied that these two non-entities, empty space outside the world and empty time prior to it, have to be assumed if we are to assume a limit to the world in space and in time.

The method of argument which professes to enable us to avoid the above consequence (that of having to assume that if the world has limits in time and space, the infinite void must determine the magnitude in which actual things are to exist) consists in surreptitiously substituting for the sensible world some intelligible world of which we know nothing; for the first beginning (an existence preceded by a time of non-existence) an existence in general which presupposes no other condition whatsoever; and for the limits of extension boundaries of the world-whole—thus getting rid of time and space. But we are here treating only of the mundus phaenomenon and its magnitude, and cannot therefore abstract from the aforesaid conditions of sensibility without destroying the very being of that world. If the sensible world is limited, it must necessarily lie in the infinite void. If that void, and consequently space in general as a priori condition of the possibility of appearances, be set aside, the entire sensible world vanishes. This world is all that is given us in our problem. The mundus intelligibilis is nothing but the general concept of a world in general, in which abstraction is made from all conditions of its intuition, and in reference to which, therefore, no synthetic proposition, either affirmative or negative, can possibly be asserted.

Every composite substance in the world is made up of simple parts, and nothing anywhere exists save the simple or what is composed of the simple.

Let us assume that composite substances are not made up of simple parts. If all composition be then removed in thought, no composite part, and (since we admit no simple parts) also no simple part, that is to say, nothing at all, will remain, and accordingly no substance will be given. Either, therefore, it is impossible to remove in thought all composition, or after its removal there must remain something which exists without composition, that is, the simple. In the former case the composite would not be made up of substances; composition, as applied to substances, is only an accidental relation in independence of which they must still persist as self-subsistent Since this contradicts our supposition, there remains only the original supposition, that a composite of substances in the world is made up of simple parts.

It follows, as an immediate consequence, that the things in the world are all, without exception, simple beings; that composition is merely an external state of these beings; and that although we can never so isolate these elementary substances as to take them out of this state of composition, reason must think them as the primary subjects of all composition, and therefore, as simple beings, prior to all composition.

When I speak of a whole as necessarily made up of simple parts, I am referring only to a substantial whole that is composite in the strict sense of the term ‘composite’, that is, to that accidental unity of the manifold which, given as separate (at least in thought), is brought into a mutual connection, and thereby constitutes a unity. Space should properly be called not compositum but totum, since its parts are possible only in the whole, not the whole through the parts. It might, indeed, be called a compositum ideale, but not reale. This, however, is a mere subtlety. Since space is not a composite made up of substances (nor even of real accidents), if I remove all compositeness from it, nothing remains, not even the point. For a point is possible only as the limit of a space, and so of a composite. Space and time do not, therefore, consist of simple parts. What belongs only to the state of a substance, even though it has a magnitude, e.g. alteration, does not consist of the simple; that is to say, a certain degree of alteration does not come about through the accretion of many simple alterations. Our inference from the composite to the simple applies only to self-subsisting things. Accidents of the state [of a thing] are not self-subsisting. Thus the proof of the necessity of the simple, as the constitutive parts of the substantially composite, can easily be upset (and therewith the thesis as a whole), if it be extended too far and in the absence of a limiting qualification be made to apply to everything composite—as has frequently happened.

Moreover I am here speaking only of the simple in so far as it is necessarily given in the composite—the latter being resolvable into the simple, as its constituent parts. The word monas, in the strict sense in which it is employed by Leibniz, should refer only to the simple which is immediately given as simple substance (e.g. in self-consciousness), and not to an element of the composite. This latter is better entitled atomus As I am seeking to prove the [existence of] simple substances only as elements in the composite, I might entitle the thesis of the second antinomy, transcendental atomistic. But as this word has long been appropriated to signify a particular mode of explaining bodily appearances (moleculae), and therefore presupposes empirical concepts, the thesis may more suitably be entitled the dialectical principle of monadology.

No composite thing in the world is made up of simple parts, and there nowhere exists in the world anything simple.

Assume that a composite thing (as substance) is made up of simple parts. Since all external relation, and therefore all composition of substances, is possible only in space, a space must be made up of as many parts as are contained in the composite which occupies it. Space, however, is not made up of simple parts, but of spaces. Every part of the composite must therefore occupy a space. But the absolutely first parts of every composite are simple. The simple therefore occupies a space. Now since everything real, which occupies a space, contains in itself a manifold of constituents external to one another, and is therefore composite; and since a real composite is not made up of accidents (for accidents could not exist outside one another, in the absence of substance) but of substances, it follows that the simple would be a composite of substances—which is self-contradictory.

The second proposition of the antithesis, that nowhere in the world does there exist anything simple, is intended to mean only this, that the existence of the absolutely simple cannot be established by any experience or perception, either outer or inner; and that the absolutely simple is therefore a mere idea, the objective reality of which can never be shown in any possible experience, and which, as being without an object, has no application in the explanation of the appearances. For if we assumed that in experience an object might be found for this transcendental idea, the empirical intuition of such an object would have to be known as one that contains no manifold [factors] external to one another and combined into unity. But since from the non-consciousness of such a manifold we cannot conclude to its complete impossibility in every kind of intuition of an object; and since without such proof absolute simplicity can never be established, it follows that such simplicity cannot be inferred from any perception whatsoever. An absolutely simple object can never be given in any possible experience. And since by the world of sense we must mean the sum of all possible experiences, it follows that nothing simple is to be found anywhere in it.

This second proposition of the antithesis has a much wider application than the first. Whereas the first proposition banishes the simple only from the intuition of the composite, the second excludes it from the whole of nature. Accordingly it has not been possible to prove this second proposition by reference to the concept of a given object of outer intuition (of the composite), but only by reference to its relation to a possible experience in general.

Against the doctrine of the infinite divisibility of matter, the proof of which is purely mathematical, objections have been raised by the monadists. These objections, however, at once lay the monadists open to suspicion. For however evident mathematical proofs may be, they decline to recognise that the proofs are based upon insight into the constitution of space, in so far as space is in actual fact the formal condition of the possibility of all matter. They regard them merely as inferences from abstract but arbitrary concepts, and so as not being applicable to real things. How can it be possible to invent a different kind of intuition from that given in the original intuition of space, and how can the a priori determinations of space fail to be directly applicable to what is only possible in so far as it fills this space! Were we to give heed to them, then beside the mathematical point, which, while simple, is not a part but only the limit of a space, we should have to conceive physical points as being likewise simple, and yet as having the distinguishing characteristic of being able, as parts of space, to fill space through their mere aggregation. Without repeating the many familiar and conclusive refutations of this absurdity—it being quite futile to attempt to reason away by sophistical manipulation of purely discursive concepts the evident demonstrated truth of mathematics—I make only one observation, that when philosophy here plays tricks with mathematics, it does so because it forgets that in this discussion we are concerned only with appearances and their condition. Here it is not sufficient to find for the pure concept of the composite formed by the understanding the concept of the simple; what has to be found is an intuition of the simple for the intuition of the composite (matter). But by the laws of sensibility, and therefore in objects of the senses, this is quite impossible. Though it may be true that when a whole, made up of substances, is thought by the pure understanding alone, we must, prior to all composition of it, have the simple, this does not hold of the totum substantiale phaenomenon which, as empirical intuition in space, carries with it the necessary characteristic that no part of it is simple, because no part of space is simple. The monadists have, indeed, been sufficiently acute to seek escape from this difficulty by refusing to treat space as a condition of the possibility of the objects of outer intuition (bodies), and by taking instead these and the dynamical relation of substances as the condition of the possibility of space. But we have a concept of bodies only as appearances; and as such they necessarily presuppose space as the condition of the possibility of all outer appearance. This evasion of the issue is therefore futile, and has already been sufficiently disposed of in the Transcendental Aesthetic. The argument of the monadists would indeed be valid if bodies were things in themselves.

The second dialectical assertion has this peculiarity, that over against it stands a dogmatic assertion which is the only one of all the pseudo-rational assertions that undertakes to afford manifest evidence, in an empirical object, of the reality of that which we have been ascribing only to transcendental ideas, namely, the absolute simplicity of substance—I refer to the assertion that the object of inner sense, the ‘I’ which there thinks, is an absolutely simple substance. Without entering upon this question (it has been fully considered above), I need only remark, that if (as happens in the quite bare representation, ‘I’) anything is thought as object only, without the addition of any synthetic determination of its intuition, nothing manifold and no compositeness can be perceived in such a representation. Besides, since the predicates through which I think this object are merely intuitions of inner sense, nothing can there be found which shows a manifold [of elements] external to one another, and therefore real compositeness. Self-consciousness is of such a nature that since the subject which thinks is at the same time its own object, it cannot divide itself, though it can divide the determinations which inhere in it for in regard to itself every object is absolute unity. Nevertheless, when this subject is viewed outwardly, as an object of intuition, it must exhibit [some sort of] compositeness in its appearance; and it must always be viewed in this way if we wish to know whether or not there be in it a manifold [of elements] external to one another.

Causality in accordance with laws of nature is not the only causality from which the appearances of the world can one and all be derived. To explain these appearances it is necessary to assume that there is also another causality, that of freedom.

Let us assume that there is no other causality than that in accordance with laws of nature. This being so, everything which takes place presupposes a preceding state upon which it inevitably follows according to a rule. But the preceding state must itself be something which has taken place (having come to be in a time in which it previously was not); for if it had always existed, its consequence also would have always existed, and would not have only just arisen. The causality of the cause through which something takes place is itself, therefore, something that has taken place, which again presupposes, in accordance with the law of nature, a preceding state and its causality, and this in similar manner a still earlier state, and so on. If, therefore, everything takes place solely in accordance with laws of nature, there will always be only a relative and never a first beginning, and consequently no completeness of the series on the side of the causes that arise the one from the other. But the law of nature is just this, that nothing takes place without a cause sufficiently determined a priori. The proposition that no causality is possible save in accordance with laws of nature, when taken in unlimited universality, is therefore self- contradictory; and this cannot, therefore, be regarded as the sole kind of causality.

We must, then, assume a causality through which something takes place, the cause of which is not itself determined, in accordance with necessary laws, by another cause antecedent to it, that is to say, an absolute spontaneity of the cause, whereby a series of appearances, which proceeds in accordance with laws of nature, begins of itself. This is transcendental freedom, without which, even in the [ordinary] course of nature, the series of appearances on the side of the causes can never be complete.

The transcendental idea of freedom does not by any means constitute the whole content of the psychological concept of that name, which is mainly empirical. The transcendental idea stands only for the absolute spontaneity of an action, as the proper ground of its imputability. This, however, is, for philosophy, the real stumbling-block; for there are insurmountable difficulties in the way of admitting any such type of unconditioned causality. What has always so greatly embarrassed speculative reason in dealing with the question of the freedom of the will, is its strictly transcendental aspect. The problem, properly viewed, is solely this: whether we must admit a power of spontaneously beginning a series of successive things or states. How such a power is possible is not a question which requires to be answered in this case, any more than in regard to causality in accordance with the laws of nature. For, [as we have found], we have to remain satisfied with the a priori knowledge that this latter type of causality must be presupposed; we are not in the least able to comprehend how it can be possible that through one existence the existence of another is determined, and for this reason must be guided by experience alone. The necessity of a first beginning, due to freedom, of a series of appearances we have demonstrated only in so far as it is required to make an origin of the world conceivable; for all the later following states can be taken as resulting according to purely natural laws. But since the power of spontaneously beginning a series in time is thereby proved (though not understood), it is now also permissible for us to admit within the course of the world different series as capable in their causality of beginning of themselves, and so to attribute to their substances a power of acting from freedom. And we must not allow ourselves to be prevented from drawing this conclusion by a misapprehension, namely that, as a series occurring in the world can have only a relatively first beginning, being always preceded in the world by some other state of things, no absolute first beginning of a series is possible during the course of the world. For the absolutely first beginning of which we are here speaking is not a beginning in time, but in causality. If, for instance, I at this moment arise from my chair, in complete freedom, without being necessarily determined thereto by the influence of natural causes, a new series, with all its natural consequences in infinitum, has its absolute beginning in this event, although as regards time this event is only the continuation of a preceding series. For this resolution and act of mine do not form part of the succession of purely natural effects, and are not a mere continuation of them. In respect of its happening, natural causes exercise over it no determining influence whatsoever. It does indeed follow upon them, but without arising out of them; and accordingly, in respect of causality though not of time, must be entitled an absolutely first beginning of a series of appearances.

This requirement of reason, that we appeal in the series of natural causes to a first beginning, due to freedom, is amply confirmed when we observe that all the philosophers of antiquity, with the sole exception of the Epicurean School, felt themselves obliged, when explaining cosmical movements, to assume a prime mover, that is, a freely acting cause, which first and of itself began this series of states. They made no attempt to render a first beginning conceivable through nature’s own resources.

There is no freedom; everything in the world takes place solely in accordance with laws of nature.

Assume that there is freedom in the transcendental sense, as a special kind of causality in accordance with which the events in the world can have come about, namely, a power of absolutely beginning a state, and therefore also of absolutely beginning a series of consequences of that state; it then follows that not only will a series have its absolute beginning in this spontaneity, but that the very determination of this spontaneity to originate the series, that is to say, the causality itself, will have an absolute beginning; there will be no antecedent through which this act, in taking place, is determined in accordance with fixed laws. But every beginning of action presupposes a state of the not yet acting cause; and a dynamical beginning of the action, if it is also a first beginning, presupposes a state which has no causal connection with the preceding state of the cause, that is to say, in nowise follows from it. Transcendental freedom thus stands opposed to the law of causality; and the kind of connection which it assumes as holding between the successive states of the active causes renders all unity of experience impossible. It is not to be met with in any experience, and is therefore an empty thought-entity.

In nature alone, therefore, [not in freedom], must we seek for the connection and order of cosmical events. Freedom (independence) from the laws of nature is no doubt a liberation from compulsion, but also from the guidance of all rules. For it is not permissible to say that the laws of freedom enter into the causality exhibited in the course of nature, and so take the place of natural laws. If freedom were determined in accordance with laws, it would not be freedom; it would simply be nature under another name. Nature and transcendental freedom differ as do conformity to law and lawlessness. Nature does indeed impose upon the understanding the exacting task of always seeking the origin of events ever higher in the series of causes, their causality being always conditioned. But in compensation it holds out the promise of thoroughgoing unity of experience in accordance with laws. The illusion of freedom, on the other hand, offers a point of rest to the enquiring understanding in the chain of causes, conducting it to an unconditioned causality which begins to act of itself. This causality is, however, blind, and abrogates those rules through which alone a completely coherent experience is possible.

The defender of an omnipotent nature (transcendental physiocracy), in maintaining his position against the pseudo-rational arguments offered in support of the counter-doctrine of freedom, would argue as follows. If you do not, as regards time, admit anything as being mathematically first in the world, there is no necessity, as regards causality, for seeking something that is dynamically first. What authority have you for inventing an absolutely first state of the world, and therefore an absolute beginning of the everflowing series of appearances, and so of procuring a resting-place for your imagination by setting bounds to limitless nature? Since the substances in the world have always existed—at least the unity of experience renders necessary such a supposition—there is no difficulty in assuming that change of their states, that is, a series of their alterations, has likewise always existed, and therefore that a first beginning, whether mathematical or dynamical, is not to be looked for. The possibility of such an infinite derivation, without a first member to which all the rest is merely a sequel, cannot indeed, in respect of its possibility, be rendered comprehensible. But if for this reason you refuse to recognise this enigma in nature, you will find yourself compelled to reject many fundamental synthetic properties and forces, which as little admit of comprehension. The possibility even of alteration itself would have to be denied. For were you not assured by experience that alteration actually occurs, you would never be able to excogitate a priori the possibility of such a ceaseless sequence of being and not-being.

Even if a transcendental power of freedom be allowed, as supplying a beginning of happenings in the world, this power would in any case have to be outside the world (though any such assumption that over and above the sum of all possible intuitions there exists an object which cannot be given in any possible perception, is still a very bold one). But to ascribe to substances in the world itself such a power, can never be permissible; for, should this be done, that connection of appearances determining one another with necessity according to universal laws, which we entitle nature, and with it the criterion of empirical truth, whereby experience is distinguished from dreaming, would almost entirely disappear. Side by side with such a lawless faculty of freedom, nature [as an ordered system] is hardly thinkable; the influences of the former would so unceasingly alter the laws of the latter that the appearances which in their natural course are regular and uniform would be reduced to disorder and incoherence.

There belongs to the world, either as its part or as its cause, a being that is absolutely necessary.

The sensible world, as the sum-total of all appearances, contains a series of alterations. For without such a series even the representation of serial time, as a condition of the possibility of the sensible world, would not be given us. But every alteration stands under its condition, which precedes it in time and renders it necessary. Now every conditioned that is given presupposes, in respect of its existence, a complete series of conditions up to the unconditioned, which alone is absolutely necessary. Alteration thus existing as a consequence of the absolutely necessary, the existence of something absolutely necessary must be granted. But this necessary existence itself belongs to the sensible world. For if it existed outside that world, the series of alterations in the world would derive its beginning from a necessary cause which would not itself belong to the sensible world. This, however, is impossible. For since the beginning of a series in time can be determined only by that which precedes it in time, the highest condition of the beginning of a series of changes must exist in the time when the series as yet was not (for a beginning is an existence preceded by a time in which the thing that begins did not yet exist). Accordingly the causality of the necessary cause of alterations, and therefore the cause itself, must belong to time and so to appearance—time being possible only as the form of appearance. Such causality cannot, therefore, be thought apart from that sum of all appearances which constitutes the world of sense. Something absolutely necessary is therefore contained in the world itself, whether this something be the whole series of alterations in the world or a part of the series.

In proving the existence of a necessary being I ought not, in this connection, to employ any but the cosmological argument, that, namely, which ascends from the conditioned in the [field of] appearance to the unconditioned in concept, this latter being regarded as the necessary condition of the absolute totality of the series. To seek proof of this from the mere idea of a supreme being belongs to another principle of reason, and will have to be treated separately.

The pure cosmological proof, in demonstrating the existence of a necessary being, has to leave unsettled whether this being is the world itself or a thing distinct from it. To establish the latter view, we should require principles which are no longer cosmological and do not continue in the series of appearances. For we should have to employ concepts of contingent beings in general (viewed as objects of the understanding alone) and a principle which will enable us to connect these, by means of mere concepts, with a necessary being. But all this belongs to a transcendent philosophy; and that we are not yet in a position to discuss.

If we begin our proof cosmologically, resting it upon the series of appearances and the regress therein according to empirical laws of causality, we must not afterwards suddenly deviate from this mode of argument, passing over to something that is not a member of the series Anything taken as condition must be viewed precisely in the same manner in which we viewed the relation of the conditioned to its condition in the series which is supposed to carry us by continuous advance to the supreme condition. If, then, this relation is \€in sensible and falls within the province of the possible empirical employment of understanding, the highest condition or cause can bring the regress to a close only in accordance with the laws of sensibility, and therefore only in so far as it itself belongs to the temporal series. The necessary being must therefore be regarded as the highest member of the cosmical series.

Nevertheless certain thinkers have allowed themselves the liberty of making such a saltus (μετάβασις εἰς ἄλλο γένος). From the alterations in the world they have inferred their empirical contingency, that is, their dependence on empirically determining causes, and so have obtained an ascending series of empirical conditions. And so far they were entirely in the right. But since they could not find in such a series any first beginning, or any highest member, they passed suddenly from the empirical concept of contingency, and laid hold upon the pure category, which then gave rise to a strictly intelligible series the completeness of which rested on the existence of an absolutely necessary cause. Since this cause was not bound down to any sensible conditions, it was freed from the temporal condition which would require that its causality should itself have a beginning. But such procedure is entirely illegitimate, as may be gathered from what follows.

In the strict meaning of the category, the contingent is so named because its contradictory opposite is possible. Now we cannot argue from empirical contingency to intelligible contingency. When anything is altered, the opposite of its state is actual at another time, and is therefore possible. This present state is not, however, the contradictory opposite of the preceding state. To obtain such a contradictory opposite we require to conceive, that in the same time in which the preceding state was, its opposite could have existed in its place, and this can never be inferred from [the fact of] the alteration. A body which was in motion (= A) comes to rest (= non-A). Now from the fact that a state opposite to the state A follows upon the state A, we cannot argue that the contradictory opposite of A is possible, and that A is therefore contingent. To prove such a conclusion, it would have to be shown that in place of the motion, and at the time at which it occurred, there could have been rest. All that we know is that rest was real in the time that followed upon the motion, and was therefore likewise possible. Motion at one time and rest at another time are not related as contradictory opposites. Accordingly the succession of opposite determinations, that is, alteration, in no way establishes contingency of the type represented in the concepts of pure understanding; and cannot therefore carry us to the existence of a necessary being, similarly conceived in purely intelligible terms. Alteration proves only empirical contingency; that is, that the new state, in the absence of a cause which belongs to the preceding time, could never of itself have taken place. Such is the condition prescribed by the law of causality. This cause, even if it be viewed as absolutely necessary, must be such as can be thus met with in time, and must belong to the series of appearances.

An absolutely necessary being nowhere exists in the world, nor does it exist outside the world as its cause.

If we assume that the world itself is necessary, or that a necessary being exists in it, there are then two alternatives. Either there is a beginning in the series of alterations which is absolutely necessary, and therefore without a cause, or the series itself is without any beginning, and although contingent and conditioned in all its parts, none the less, as a whole, is absolutely necessary and unconditioned. The former alternative, however, conflicts with the dynamical law of the determination of all appearances in time; and the latter alternative contradicts itself, since the existence of a series cannot be necessary if no single member of it is necessary.

If, on the other hand, we assume that an absolutely necessary cause of the world exists outside the world, then this cause, as the highest member in the series of the causes of changes in the world, must begin the existence of the latter and their series. Now this cause must itself begin to act, and its causality would therefore be in time, and so would belong to the sum of appearances, that is, to the world. It follows that it itself, the cause, would not be outside the world—which contradicts our hypothesis. Therefore neither in the world, nor outside the world (though in causal connection with it), does there exist any absolutely necessary being.

The difficulties in the way of asserting the existence of an absolutely necessary highest cause, which we suppose ourselves to meet as we ascend in the series of appearances, cannot be such as arise in connection with mere concepts of the necessary existence of a thing in general. The difficulties are not, therefore, ontological, but must concern the causal connection of a series of appearances for which a condition has to be assumed that is itself unconditioned, and so must be cosmological, and relate to empirical laws. It must be shown that regress in the series of causes (in the sensible world) can never terminate in an empirically unconditioned condition, and that the cosmological argument from the contingency of states of the world, as evidenced by their alterations, does not support the assumption of a first and absolutely originative cause of the series.

A strange situation is disclosed in this antinomy. From the same ground on which, in the thesis, the existence of an original being was inferred, its non-existence is inferred in the antithesis, and this with equal stringency. We were first assured that a necessary being exists because the whole of past time comprehends the series of all conditions and therefore also the unconditioned (that is, the necessary); we are now assured that there is no necessary being, and precisely for the reason that the whole of past time comprehends the series of all conditions (which therefore are one and all themselves conditioned). The explanation is this. The former argument takes account only of the absolute totality of the series of conditions determining each other in time, and so reaches what is unconditioned and necessary. The latter argument, on the other hand, takes into consideration the contingency of everything which is determined in the temporal series (everything being preceded by a time in which the condition must itself again be determined as conditioned), and from this point of view everything unconditioned and all absolute necessity completely vanish. Nevertheless, the method of argument in both cases is entirely in conformity even with ordinary human reason, which frequently falls into conflict with itself through considering its object from two different points of view. M. de Mairan regarded the controversy between two famous astronomers, which arose from a similar difficulty in regard to choice of standpoint, as a sufficiently remarkable phenomenon to justify his writing a special treatise upon it. The one had argued that the moon revolves on its own axis, because it always turns the same side towards the earth. The other drew the opposite conclusion that the moon does not revolve on its own axis, because it always turns the same side towards the earth. Both inferences were correct, according to the point of view which each chose in observing the moon’s motion