Critique of Pure Reason

by Immanuel Kant

  Hence we see that the major of the cosmological argument takes the conditioned in the transcendental sense of a pure category, while the minor takes it in the empirical sense of a concept of the understanding, referring to mere phenomena, so that it contains that dialectical deceit which is called Sophisma figurae dictionis. That deceit, however, is not artificial, but a perfectly natural illusion of our common reason. It is owing to it that, in the major, we presuppose the conditions and their series as it were on trust, if anything is given as conditioned, because this is no more than the logical postulate to assume complete premisses for any given conclusion. Nor does there exist in the connection of the conditioned with its condition any order of time, but they are presupposed in themselves as given together. It is equally natural also in the minor to look on phenomena as things by themselves, and as objects given to the understanding only in the same manner as in the major, as no account was taken of all the conditions of intuition under which alone objects can be given. But there is an important distinction between these concepts, which has been overlooked. The synthesis of the conditioned with its condition, and the whole series of conditions in the major, was in no way limited by time, and was free from any concept of succession. The empirical synthesis, on the contrary, and the series of conditions in phenomena, which was subsumed in the minor, is necessarily successive and given as such in time only. Therefore I had no right to assume the absolute totality of the synthesis and of the series represented by it in this case as well as in the former. For in the former all the members of the series are given by themselves (without determination in time), while here they are possible through the successive regressus only, which cannot exist unless it is actually carried out.

  After convicting them of such a mistake in the argument adopted by both parties as the foundation of their cosmological assertions, both might justly be dismissed as not being able to produce any good title in support of their claims. But even thus their quarrel is not yet ended, as if it had been proved that both parties, or one of them, were wrong in the matter contended for (in the conclusion), though they had failed to support it by valid proof. Nothing seems clearer than that, if one maintains that the world has a beginning, and the other that it has no beginning, but exists from all eternity, one or the other must be right. But if this were so, as the arguments on both sides are equally clear, it would still remain impossible ever to find out on which side the truth lies, and the suit continues, although both parties have been ordered to keep the peace before the tribunal of reason. Nothing remains therefore in order to settle the quarrel once for all, and to the satisfaction of both parties, but to convince them that, though they can refute each other so eloquently, they are really quarrelling about nothing, and that a certain transcendental illusion has mocked them with a reality where no reality exists. We shall now enter upon this way of adjusting a dispute, which cannot be adjudicated.

  The Eleatic philosopher Zeno, a subtle dialectician, was severely reprimanded by Plato as a heedless Sophist who, in order to display his skill, would prove a proposition by plausible arguments and subvert the same immediately afterwards by arguments equally strong. He maintained, for instance, that God (which to him was probably nothing more than the universe) is neither finite nor infinite, neither in motion nor at rest, neither similar nor dissimilar to any other thing. It seemed to his critics as if he had intended to deny completely both of the two self-contradictory proposition which would be absurd. But I do not think that he can be rightly charged with this. We shall presently consider the first of these propositions more carefully. With regard to the others, if by the word God he meant the universe, he could not but say that it is neither permanently present in its place (at rest) nor that it changes it (in motion), because all places exist in the universe only, while the universe exists in no place. If the universe comprehends in itself everything that exists, it follows that it cannot be similar or dissimilar to any other thing, because there is no other thing besides it with which it could be compared. If two opposite judgments presuppose an inadmissible condition, they both, in spite of their contradiction (which, however, is no real contradiction), fall to the ground, because the condition fails under which alone either of the propositions was meant to be valid.

  If somebody were to say that everybody has either a good or a bad smell, a third case is possible, namely, that it has no smell at all, in which case both contradictory propositions would be false. If I say that it is either good smelling or not good smelling (vel suaveolens vel non suaveolens), in that case the two judgments are contradictory, and the former only is wrong, while its contradictory opposite, namely, that some bodies are not good smelling, comprehends those bodies also which have no smell at all. In the former opposition (per disparata) the contingent condition of the concept of a body (smell) still remained in the contradictory judgment and was not eliminated by it, so that the latter could not be called the contradictory opposite of the former.

  If I say therefore that the world is either infinite in space or is not infinite (non est infinitus), then, if the former proposition is wrong, its contradictory opposite, that the world is not infinite, must be true. I should thus only eliminate an infinite world without affirming another, namely, the finite. But if I had said the world is either infinite or finite (not-infinite), both statements may be false. For I then look upon the world, as by itself, determined in regard to its extent, and I do not only eliminate in the opposite statement the infinity, and with it, it may be, its whole independent existence, but I add a determination to the world as a thing existing by itself, which may be false, because the world may not be a thing by itself, and therefore, with regard to extension, neither infinite nor finite. This kind of opposition I may be allowed to call dialectical, that the real contradiction, the analytical opposition. Thus then of two judgments opposed to each other dialectically both may be false, because the one does not only contradict the other, but says something more than is requisite for a contradiction.

  If we regard the two statements that the world is infinite in extension, and that the world is finite in extension, as contradictory opposites, we assume that the world (the whole series of phenomena) is a thing by itself; for it remains, whether I remove the infinite or the finite regressus in the series of its phenomena. But if we remove this supposition, or this transcendental illusion, and deny that it is a thing by itself, then the contradictory opposition of the two statements becomes purely dialectical, and as the world does not exist by itself (independently of the regressive series of my representations), it exists neither as a whole by itself infinite, nor as a whole by itself finite. It exists only in the empirical regressus in the series of phenomena, and nowhere by itself. Hence, if that series is always conditioned, it can never exist as complete, and the world is therefore not an inconditioned whole, and does not exist as such, either with infinite or finite extension.

  What has here been said of the first cosmological idea, namely, that of the absolute totality of extension in phenomena, applies to the others also. The series of conditions is to be found only in the regressive synthesis, never by itself, as complete, in phenomenon as an independent thing, existing prior to every regressus. Hence I shall have to say that the number of parts in any given phenomenon is by itself neither finite nor infinite, because a phenomenon does not exist by itself, and its parts are only found through the regressus of the decomposing synthesis through and in the regressus, and that regressus can never be given as absolutely complete, whether as finite or as infinite. The same applies to the series of causes, one being prior to the other, and to the series leading from conditioned to unconditioned necessary existence, which can never be regarded either by itself finite in its totality or infinite, because, as a series of subordinated representations, it forms a dynamical regressus only, and cannot exist prior to it, by itself, as a self-subsistent series of things.

  The antinomy of pure reason with regard to its cosmological ideas is therefore removed by showing
that it is dialectical only, and a conflict of an illusion produced by our applying the idea of absolute totality, which exists only as a condition of things by themselves, to phenomena, which exist in our representation only, and if they form a series, in the successive regressus, but nowhere else. We may, however, on the other side, derive from that antinomy a true, if not dogmatical, at least critical and doctrinal advantage, namely, by proving through it indirectly the transcendental ideality of phenomena, in case anybody should not have been satisfied by the direct proof given in the transcendental Æsthetic. The proof would consist in the following dilemma. If the world is a whole existing by itself, it is either finite or infinite. Now the former as well as the latter proposition is false, as has been shown by the proofs given in the antithesis on one and in the thesis on the other side. It is false, therefore, that the world (the sum total of all phenomena) is a whole existing by itself. Hence it follows that phenomena in general are nothing outside our representations, which was what we meant by their transcendental ideality.

  This remark is of some importance, because it shows that our proofs of the fourfold antinomy were not mere sophistry, but honest and correct, always under the (wrong) supposition that phenomena, or a world of sense which comprehends them all, are things by themselves. The conflict of the conclusions drawn from this shows, however, that there is a flaw in the supposition, and thus leads us to the discovery of the true nature of things, as objects of the senses. This transcendental Dialectic therefore does not favour scepticism, but only the sceptical method, which can point to it as an example of its great utility, if we allow the arguments of reason to fight against each other with perfect freedom, from which something useful and serviceable for the correction of our judgments will always result, though it may not be always that which we were looking for.

  The Antinomy of Pure Reason

  Section VIII

  The Regulative Principle of Pure Reason with Regard to the Cosmological Ideas

  As through the cosmological principle of totality no real maximum is given of the series of conditions in the world of sense, as a thing by itself, but can only be required in the regressus of that series, that principle of pure reason, if thus amended, still retains its validity, not indeed as an axiom, requiring us to think the totality in the object as real, but as a problem for the understanding, and therefore for the subject, encouraging us to undertake and to continue, according to the completeness in the idea, the regressus in the series of conditions of anything given as conditioned. In our sensibility, that is, in space and time, every condition which we can reach in examining given phenomena is again conditioned, because these phenomena are not objects by themselves, in which something absolutely unconditioned might possibly exist, but empirical representations only, which always must have their condition in intuition, whereby they are determined in space and time. The principle of reason is therefore properly a rule only, which in the series of conditions of given phenomena postulates a regressus which is never allowed to stop at anything absolutely unconditioned. It is therefore no principle of the possibility of experience and of the empirical knowledge of the objects of the senses, and not therefore a principle of the understanding, because every experience is (according to a given intuition) within its limits; nor is it a constitutive principle of reason, enabling us to extend the concept of the world of sense beyond all possible experience, but it is merely a principle of the greatest possible continuation and extension of our experience, allowing no empirical limit to be taken as an absolute limit. It is therefore a principle of reason, which, as a rule, postulates what we ought to do in the regressus, but does not anticipate what may be given in the object, before such regressus. I therefore call it a regulative principle of reason, while, on the contrary, the principle of the absolute totality of the series of conditions, as given in the object (the phenomena) by itself, would be a constitutive cosmological principle, the hollowness of which I have tried to indicate by this very distinction, thus preventing what otherwise would have inevitably happened (through a transcendental surreptitious proceeding), namely, an idea, which is to serve as a rule only, being invested with objective reality.

  In order properly to determine the meaning of this rule of pure reason it should be remarked, first of all, that it cannot tell us what the object is, but only how the empirical regressus is to be carried out, in order to arrive at the complete concept of the object. If we attempted the first, it would become a constitutive principle, such as pure reason can never supply. It cannot therefore be our intention to say through this principle, that a series of conditions of something, given as conditioned, is by itself either finite or infinite; for in that case a mere idea of absolute totality, produced in itself only, would represent in thought an object such as can never be given in experience, and an objective reality, independent of empirical synthesis, would have been attributed to a series of phenomena. This idea of reason can therefore do no more than prescribe a rule to the regressive synthesis in the series of conditions, according to which that synthesis is to advance from the conditioned, through all subordinate conditions, towards the unconditioned, though it can never reach it, for the absolutely unconditioned can never be met with in experience.

  To this end it is necessary, first of all, to define accurately the synthesis of a series, so far as it never is complete. People are in the habit of using for this purpose two expressions which are meant to establish a difference, though they are unable clearly to define the ground of the distinction. Mathematicians speak only of a progressus in infinitum. Those who enquire into concepts (philosophers) will admit instead the expression of a progressus in indefinitum only. Without losing any time in the examination of the reasons which may have suggested such a distinction, and of its useful or useless application, I shall at once endeavour to define these concepts accurately for my own purpose.

  Of a straight line it can be said correctly that it may be produced to infinity; and here the distinction between an infinite and an indefinite progress (progressus in indefinitum) would be mere subtilty. No doubt, if we are told to carry on a line, it would be more correct to add in indefinitum, than in infinitum, because the former means no more than, produce it as far as you wish, but the second, you shall never cease producing it (which can never be intended). Nevertheless, if we speak only of what is possible, the former expression is quite correct, because we can always make it longer, if we like, without end. The same applies in all cases where we speak only of the progressus, that is, of our proceeding from the condition to the conditioned, for such progress proceeds in the series of phenomena without end. From a given pair of parents we may, in the descending line of generation, proceed without end, and conceive quite well that that line should so continue in the world. For here reason never requires an absolute totality of the series, because it is not presupposed as a condition, and as it were given (datum), but only as something conditioned, that is, capable only of being given (dabile), and can be added to without end.

  The case is totally different with the problem, how far the regressus from something given as conditioned may ascend in a series to its conditions; whether I may call it a regressus into the infinite, or only into the indefinite (in indefinitum; and whether I may ascend, for instance, from the men now living, through the series of their ancestors, in infinitum; or whether I may only say that, so far as I have gone back, I have never met with an empirical ground for considering the series limited anywhere, so that I feel justified, and at the same time obliged to search for an ancestor of every one of these ancestors, though not to presuppose them.

  I say, therefore, that where the whole is given in empirical intuition, the regressus in the series of its internal conditions proceeds in infinitum, while if a member only of a series is given, from which the regressus to the absolute totality has first to be carried out, the regressus is only in indefinitum. Thus we must say that the division of matter, as given between its limits (a body), goes on in infinitum, because th
at matter is complete and therefore, with all its possible parts, given in empirical intuition. As the condition of that whole consists in its part, and the condition of that part in the part of that part, and so on, and as in this regressus of decomposition we never meet with an unconditioned (indivisible) member of that series of conditions, there is nowhere an empirical ground for stopping the division; nay, the further members of that continued division are themselves empirically given before the continuation of the division, and therefore the division goes on in infinitum. The series of ancestors, on the contrary, of any given man, exists nowhere in its absolute totality, in any possible experience, while the regressus goes on from every link in the generation to a higher one, so that no empirical limit can be found which should represent a link as absolutely unconditioned. As, however, the links too, which might supply the condition, do not exist in the empirical intuition of the whole, prior to the regressus, that regressus does not proceed in infinitum (by a division of what is given), but to an indefinite distance, in its search for more links in addition to those which are given, and which themselves are again always conditioned only.

  In neither case—the regressus in infinitum nor the regressus in indefinitum—is the series of conditions to be considered as given as infinite in the object. They are not things by themselves, but phenomena only, which, as conditions of each other, are given only in the regressus itself. Therefore the question is no longer how great this series of conditions may be by itself, whether finite or infinite, for it is nothing by itself, but only how we are to carry out the empirical regressus, and how far we may continue it. And here we see a very important difference with regard to the rule of that progress. If the whole is given empirically, it is possible to go back in the series of its conditions in infinitum. But if the whole is not given, but has first to be given through an empirical regressus, I can only say that it is possible to proceed to still higher conditions of the series. In the former case I could say that more members exist and are empirically given than I can reach through the regressus (of decomposition); in the latter I can only say that I may advance still further in the regressus, because no member is empirically given as absolutely unconditioned, and a higher member therefore always possible, and therefore the enquiry for it necessary. In the former case it was necessary to find more members of the series, in the latter it is necessary to enquire for more, because no experience is absolutely limiting. For either you have no perception which absolutely limits your empirical regressus, and in that case you cannot consider that regressus as complete, or you have a perception which limits your series, and in that case it cannot be a part of your finished series (because what limits must be different from that which is limited by it), and you must therefore continue your regressus to that condition also, and so on for ever.