The Critique of Pure Reason · Immanuel Kant
Section VII. Critical Solution of the Cosmological Problem
This principle of reason is hence valid only as a rule for the extension of a possible experience—its invalidity as a principle constitutive of phenomena in themselves having been sufficiently demonstrated. And thus, too, the antinomial conflict of reason with itself is completely put an end to; inasmuch as we have not only presented a critical solution of the fallacy lurking in the opposite statements of reason, but have shown the true meaning of the ideas which gave rise to these statements. The dialectical principle of reason has, therefore, been changed into a doctrinal principle. But in fact, if this principle, in the subjective signification which we have shown to be its only true sense, may be guaranteed as a principle of the unceasing extension of the employment of our understanding, its influence and value are just as great as if it were an axiom for the à priori determination of objects. For such an axiom could not exert a stronger influence on the extension and rectification of our knowledge, otherwise than by procuring for the principles of the understanding the most widely expanded employment in the field of experience. I. Solution of the Cosmological Idea of the Totality of the Composition of Phenomena in the Universe Here, as well as in the case of the other cosmological problems, the ground of the regulative principle of reason is the proposition that in our empirical regress no experience of an absolute limit, and consequently no experience of a condition, which is itself absolutely unconditioned, is discoverable. And the truth of this proposition itself rests upon the consideration that such an experience must represent to us phenomena as limited by nothing or the mere void, on which our continued regress by means of perception must abut—which is impossible.
Now this proposition, which declares that every condition attained in the empirical regress must itself be considered empirically conditioned, contains the rule in terminis, which requires me, to whatever extent I may have proceeded in the ascending series, always to look for some higher member in the series—whether this member is to become known to me through experience, or not. Nothing further is necessary, then, for the solution of the first cosmological problem, than to decide, whether, in the regress to the unconditioned quantity of the universe (as regards space and time), this never limited ascent ought to be called a regressus in infinitum or indefinitum. The general representation which we form in our minds of the series of all past states or conditions of the world, or of all the things which at present exist in it, is itself nothing more than a possible empirical regress, which is cogitated—although in an undetermined manner—in the mind, and which gives rise to the conception of a series of conditions for a given object.[60] Now I have a conception of the universe, but not an intuition—that is, not an intuition of it as a whole. Thus I cannot infer the magnitude of the regress from the quantity or magnitude of the world, and determine the former by means of the latter; on the contrary, I must first of all form a conception of the quantity or magnitude of the world from the magnitude of the empirical regress. But of this regress I know nothing more than that I ought to proceed from every given member of the series of conditions to one still higher. But the quantity of the universe is not thereby determined, and we cannot affirm that this regress proceeds in infinitum.
Such an affirmation would anticipate the members of the series which have not yet been reached, and represent the number of them as beyond the grasp of any empirical synthesis; it would consequently determine the cosmical quantity prior to the regress (although only in a negative manner)—which is impossible. For the world is not given in its totality in any intuition: consequently, its quantity cannot be given prior to the regress. It follows that we are unable to make any declaration respecting the cosmical quantity in itself—not even that the regress in it is a regress in infinitum; we must only endeavour to attain to a conception of the quantity of the universe, in conformity with the rule which determines the empirical regress in it. But this rule merely requires us never to admit an absolute limit to our series—how far soever we may have proceeded in it, but always, on the contrary, to subordinate every phenomenon to some other as its condition, and consequently to proceed to this higher phenomenon. Such a regress is, therefore, the regressus in indefinitum, which, as not determining a quantity in the object, is clearly distinguishable from the regressus in infinitum. [60] The cosmical series can neither be greater nor smaller than the possible empirical regress, upon which its conception is based. And as this regress cannot be a determinate infinite regress, still less a determinate finite (absolutely limited), it is evident that we cannot regard the world as either finite or infinite, because the regress, which gives us the representation of the world, is neither finite nor infinite.
It follows from what we have said that we are not justified in declaring the world to be infinite in space, or as regards past time. For this conception of an infinite given quantity is empirical; but we cannot apply the conception of an infinite quantity to the world as an object of the senses. I cannot say, “The regress from a given perception to everything limited either in space or time, proceeds in infinitum,” for this presupposes an infinite cosmical quantity; neither can I say, “It is finite,” for an absolute limit is likewise impossible in experience. It follows that I am not entitled to make any assertion at all respecting the whole object of experience—the world of sense; I must limit my declarations to the rule according to which experience or empirical knowledge is to be attained. To the question, therefore, respecting the cosmical quantity, the first and negative answer is: “The world has no beginning in time, and no absolute limit in space.” For, in the contrary case, it would be limited by a void time on the one hand, and by a void space on the other. Now, since the world, as a phenomenon, cannot be thus limited in itself for a phenomenon is not a thing in itself; it must be possible for us to have a perception of this limitation by a void time and a void space. But such a perception—such an experience is impossible; because it has no content. Consequently, an absolute cosmical limit is empirically, and therefore absolutely, impossible.[61]
The above rule does not prescribe an unceasing regress in one kind of phenomena. It does not, for example, forbid us, in our ascent from an individual human being through the line of his ancestors, to expect that we shall discover at some point of the regress a primeval pair, or to admit, in the series of heavenly bodies, a sun at the farthest possible distance from some centre. All that it demands is a perpetual progress from phenomena to phenomena, even although an actual perception is not presented by them (as in the case of our perceptions being so weak as that we are unable to become conscious of them), since they, nevertheless, belong to possible experience. Every beginning is in time, and all limits to extension are in space. But space and time are in the world of sense. Consequently phenomena in the world are conditionally limited, but the world itself is not limited, either conditionally or unconditionally. For this reason, and because neither the world nor the cosmical series of conditions to a given conditioned can be completely given, our conception of the cosmical quantity is given only in and through the regress and not prior to it—in a collective intuition. But the regress itself is really nothing more than the determining of the cosmical quantity, and cannot therefore give us any determined conception of it—still less a conception of a quantity which is, in relation to a certain standard, infinite. The regress does not, therefore, proceed to infinity (an infinity given), but only to an indefinite extent, for or the of presenting to us a quantity—realized only in and through the regress itself.
II. Solution of the Cosmological Idea of the Totality of the Division of a Whole given in Intuition When I divide a whole which is given in intuition, I proceed from a conditioned to its conditions. The division of the parts of the whole (subdivisio or decompositio) is a regress in the series of these conditions. The absolute totality of this series would be actually attained and given to the mind, if the regress could arrive at simple parts. But if all the parts in a continuous decomposition are themselves divisible, the division, that is to say, the regress, proceeds from the conditioned to its conditions in infinitum; because the conditions (the parts) are themselves contained in the conditioned, and, as the latter is given in a limited intuition, the former are all given along with it. This regress cannot, therefore, be called a regressus in indefinitum, as happened in the case of the preceding cosmological idea, the regress in which proceeded from the conditioned to the conditions not given contemporaneously and along with it, but discoverable only through the empirical regress. We are not, however, entitled to affirm of a whole of this kind, which is divisible in infinitum, that it consists of an infinite number of parts. For, although all the parts are contained in the intuition of the whole, the whole division is not contained therein. The division is contained only in the progressing decomposition—in the regress itself, which is the condition of the possibility and actuality of the series. Now, as this regress is infinite, all the members (parts) to which it attains must be contained in the given whole as an aggregate. But the complete series of division is not contained therein. For this series, being infinite in succession and always incomplete, cannot represent an infinite number of members, and still less a composition of these members into a whole.
To apply this remark to space. Every limited part of space presented to intuition is a whole, the parts of which are always spaces—to whatever extent subdivided. Every limited space is hence divisible to infinity. Let us again apply the remark to an external phenomenon enclosed in limits, that is, a body. The divisibility of a body rests upon the divisibility of space, which is the condition of the possibility of the body as an extended whole. A body is consequently divisible to infinity, though it does not, for that reason, consist of an infinite number of parts. It certainly seems that, as a body must be cogitated as substance in space, the law of divisibility would not be applicable to it as substance. For we may and ought to grant, in the case of space, that division or decomposition, to any extent, never can utterly annihilate composition (that is to say, the smallest part of space must still consist of spaces); otherwise space would entirely cease to exist—which is impossible. But, the assertion on the other hand that when all composition in matter is annihilated in thought, nothing remains, does not seem to harmonize with the conception of substance, which must be properly the subject of all composition and must remain, even after the conjunction of its attributes in space—which constituted a body—is annihilated in thought. But this is not the case with substance in the phenomenal world, which is not a thing in itself cogitated by the pure category. Phenomenal substance is not an absolute subject; it is merely a permanent sensuous image, and nothing more than an intuition, in which the unconditioned is not to be found.
But, although this rule of progress to infinity is legitimate and applicable to the subdivision of a phenomenon, as a mere occupation or filling of space, it is not applicable to a whole consisting of a number of distinct parts and constituting a quantum discretum—that is to say, an organized body. It cannot be admitted that every part in an organized whole is itself organized, and that, in analysing it to infinity, we must always meet with organized parts; although we may allow that the parts of the matter which we decompose in infinitum, may be organized. For the infinity of the division of a phenomenon in space rests altogether on the fact that the divisibility of a phenomenon is given only in and through this infinity, that is, an undetermined number of parts is given, while the parts themselves are given and determined only in and through the subdivision; in a word, the infinity of the division necessarily presupposes that the whole is not already divided in se. Hence our division determines a number of parts in the whole—a number which extends just as far as the actual regress in the division; while, on the other hand, the very notion of a body organized to infinity represents the whole as already and in itself divided.
We expect, therefore, to find in it a determinate, but at the same time, infinite, number of parts—which is self-contradictory. For we should thus have a whole containing a series of members which could not be completed in any regress—which is infinite, and at the same time complete in an organized composite. Infinite divisibility is applicable only to a quantum continuum, and is based entirely on the infinite divisibility of space, But in a quantum discretum the multitude of parts or units is always determined, and hence always equal to some number. To what extent a body may be organized, experience alone can inform us; and although, so far as our experience of this or that body has extended, we may not have discovered any inorganic part, such parts must exist in possible experience. But how far the transcendental division of a phenomenon must extend, we cannot know from experience—it is a question which experience cannot answer; it is answered only by the principle of reason which forbids us to consider the empirical regress, in the analysis of extended body, as ever absolutely complete. Concluding Remark on the Solution of the Transcendental Mathematical Ideas—and Introductory to the Solution of the Dynamical Ideas.
We presented the antinomy of pure reason in a tabular form, and we endeavoured to show the ground of this self-contradiction on the part of reason, and the only means of bringing it to a conclusion—namely, by declaring both contradictory statements to be false. We represented in these antinomies the conditions of phenomena as belonging to the conditioned according to relations of space and time—which is the usual supposition of the common understanding. In this respect, all dialectical representations of totality, in the series of conditions to a given conditioned, were perfectly homogeneous. The condition was always a member of the series along with the conditioned, and thus the homogeneity of the whole series was assured. In this case the regress could never be cogitated as complete; or, if this was the case, a member really conditioned was falsely regarded as a primal member, consequently as unconditioned. In such an antinomy, therefore, we did not consider the object, that is, the conditioned, but the series of conditions belonging to the object, and the magnitude of that series. And thus arose the difficulty—a difficulty not to be settled by any decision regarding the claims of the two parties, but simply by cutting the knot—by declaring the series proposed by reason to be either too long or too short for the understanding, which could in neither case make its conceptions adequate with the ideas.
But we have overlooked, up to this point, an essential difference existing between the conceptions of the understanding which reason endeavours to raise to the rank of ideas—two of these indicating a mathematical, and two a dynamical synthesis of phenomena. Hitherto, it was necessary to signalize this distinction; for, just as in our general representation of all transcendental ideas, we considered them under phenomenal conditions, so, in the two mathematical ideas, our discussion is concerned solely with an object in the world of phenomena. But as we are now about to proceed to the consideration of the dynamical conceptions of the understanding, and their adequateness with ideas, we must not lose sight of this distinction. We shall find that it opens up to us an entirely new view of the conflict in which reason is involved. For, while in the first two antinomies, both parties were dismissed, on the ground of having advanced statements based upon false hypothesis; in the present case the hope appears of discovering a hypothesis which may be consistent with the demands of reason, and, the judge completing the statement of the grounds of claim, which both parties had left in an unsatisfactory state, the question may be settled on its own merits, not by dismissing the claimants, but by a comparison of the arguments on both sides. If we consider merely their extension, and whether they are adequate with ideas, the series of conditions may be regarded as all homogeneous. But the conception of the understanding which lies at the basis of these ideas, contains either a synthesis of the homogeneous (presupposed in every quantity—in its composition as well as in its division) or of the heterogeneous, which is the case in the dynamical synthesis of cause and effect, as well as of the necessary and the contingent.
Thus it happens that in the mathematical series of phenomena no other than a sensuous condition is admissible—a condition which is itself a member of the series; while the dynamical series of sensuous conditions admits a heterogeneous condition, which is not a member of the series, but, as purely intelligible, lies out of and beyond it. And thus reason is satisfied, and an unconditioned placed at the head of the series of phenomena, without introducing confusion into or discontinuing it, contrary to the principles of the understanding. Now, from the fact that the dynamical ideas admit a condition of phenomena which does not form a part of the series of phenomena, arises a result which we should not have expected from an antinomy. In former cases, the result was that both contradictory dialectical statements were declared to be false. In the present case, we find the conditioned in the dynamical series connected with an empirically unconditioned, but non-sensuous condition; and thus satisfaction is done to the understanding on the one hand and to the reason on the other.[62] While, moreover, the dialectical arguments for unconditioned totality in mere phenomena fall to the ground, both propositions of reason may be shown to be true in their proper signification. This could not happen in the case of the cosmological ideas which demanded a mathematically unconditioned unity; for no condition could be placed at the head of the series of phenomena, except one which was itself a phenomenon and consequently a member of the series.
We must understand, on the contrary, by the term freedom, in the cosmological sense, a faculty of the spontaneous origination of a state; the causality of which, therefore, is not subordinated to another cause determining it in time. Freedom is in this sense a pure transcendental idea, which, in the first place, contains no empirical element; the object of which, in the second place, cannot be given or determined in any experience, because it is a universal law of the very possibility of experience, that everything which happens must have a cause, that consequently the causality of a cause, being itself something that has happened, must also have a cause. In this view of the case, the whole field of experience, how far soever it may extend, contains nothing that is not subject to the laws of nature. But, as we cannot by this means attain to an absolute totality of conditions in reference to the series of causes and effects, reason creates the idea of a spontaneity, which can begin to act of itself, and without any external cause determining it to action, according to the natural law of causality. It is especially remarkable that the practical conception of freedom is based upon the transcendental idea, and that the question of the possibility of the former is difficult only as it involves the consideration of the truth of the latter. Freedom, in the practical sense, is the independence of the will of coercion by sensuous impulses. A will is sensuous, in so far as it is pathologically affected (by sensuous impulses); it is termed animal (arbitrium brutum), when it is pathologically necessitated. The human will is certainly an arbitrium sensitivum, not brutum, but liberum; because sensuousness does not necessitate its action, a faculty existing in man of self-determination, independently of all sensuous coercion.
It is plain that, if all causality in the world of sense were natural—and natural only—every event would be determined by another according to necessary laws, and that, consequently, phenomena, in so far as they determine the will, must necessitate every action as a natural effect from themselves; and thus all practical freedom would fall to the ground with the transcendental idea. For the latter presupposes that although a certain thing has not happened, it ought to have happened, and that, consequently, its phenomenal cause was not so powerful and determinative as to exclude the causality of our will—a causality capable of producing effects independently of and even in opposition to the power of natural causes, and capable, consequently, of spontaneously originating a series of events. Here, too, we find it to be the case, as we generally found in the self-contradictions and perplexities of a reason which strives to pass the bounds of possible experience, that the problem is properly not physiological, but transcendental. The question of the possibility of freedom does indeed concern psychology; but, as it rests upon dialectical arguments of pure reason, its solution must engage the attention of transcendental philosophy. Before attempting this solution, a task which transcendental philosophy cannot decline, it will be advisable to make a remark with regard to its procedure in the settlement of the question.
If phenomena were things in themselves, and time and space forms of the existence of things, condition and conditioned would always be members of the same series; and thus would arise in the present case the antinomy common to all transcendental ideas—that their series is either too great or too small for the understanding. The dynamical ideas, which we are about to discuss in this and the following section, possess the peculiarity of relating to an object, not considered as a quantity, but as an existence; and thus, in the discussion of the present question, we may make abstraction of the quantity of the series of conditions, and consider merely the dynamical relation of the condition to the conditioned. The question, then, suggests itself, whether freedom is possible; and, if it is, whether it can consist with the universality of the natural law of causality; and, consequently, whether we enounce a proper disjunctive proposition when we say: “Every effect must have its origin either in nature or in freedom,” or whether both cannot exist together in the same event in different relations. The principle of an unbroken connection between all events in the phenomenal world, in accordance with the unchangeable laws of nature, is a well-established principle of transcendental analytic which admits of no exception.
The question, therefore, is: “Whether an effect, determined according to the laws of nature, can at the same time be produced by a free agent, or whether freedom and nature mutually exclude each other?” And here, the common but fallacious hypothesis of the absolute reality of phenomena manifests its injurious influence in embarrassing the procedure of reason. For if phenomena are things in themselves, freedom is impossible. In this case, nature is the complete and all-sufficient cause of every event; and condition and conditioned, cause and effect are contained in the same series, and necessitated by the same law. If, on the contrary, phenomena are held to be, as they are in fact, nothing more than mere representations, connected with each other in accordance with empirical laws, they must have a ground which is not phenomenal. But the causality of such an intelligible cause is not determined or determinable by phenomena; although its effects, as phenomena, must be determined by other phenomenal existences. This cause and its causality exist therefore out of and apart from the series of phenomena; while its effects do exist and are discoverable in the series of empirical conditions. Such an effect may therefore be considered to be free in relation to its intelligible cause, and necessary in relation to the phenomena from which it is a necessary consequence—a distinction which, stated in this perfectly general and abstract manner, must appear in the highest degree subtle and obscure. The sequel will explain. It is sufficient, at present, to remark that, as the complete and unbroken connection of phenomena is an unalterable law of nature, freedom is impossible—on the supposition that phenomena are absolutely real. Hence those philosophers who adhere to the common opinion on this subject can never succeed in reconciling the ideas of nature and freedom.
Ideas discussed in this chapter
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