The following section, by showing their application, will place these observations in their proper light.
The Antinomy of Pure Reason
Section IX
Of the Empirical Use of the Regulative Principle of Reason with Regard to all Cosmological Ideas
No transcendental use, as we have shown on several occasions, can be made of the concepts either of the understanding or of reason; and the absolute totality of the series of conditions in the world of sense is due entirely to a transcendental use of reason, which demands this unconditioned completeness from what presupposes as a thing by itself. As no such thing is contained in the world of sense, we can never speak again of the absolute quantity of different series in it, whether they be limited or in themselves unlimited; but the question can only be, how far, in the empirical regressus, we may go back in tracing experience to its conditions, in order to stop, according to the rule of reason, at no other answer of its questions but such as is in accordance with the object.
What therefore remains to us is only the validity of the principle of reason, as a rule for the continuation and for the extent of a possible experience, after its invalidity, as a constitutive principle of things by themselves, has been sufficiently established. If we have clearly established that invalidity, the conflict of reason with itself will be entirely finished, because not only has the illusion which led to that conflict been removed through critical analysis, but in its place the sense in which reason agrees with itself, and the misapprehension of which was the only cause of conflict, has been clearly exhibited, and a principle formerly dialectical changed into a doctrinal one. In fact, if that principle, according to its subjective meaning, can be proved fit to determine the greatest possible use of the understanding in experience, as adequate to its objects, this would be the same as if it determined, as an axiom (which is impossible from pure reason), the objects themselves a priori: for this also could not, with reference to the objects of experience, exercise a greater influence on the extension and correction of our knowledge, than proving itself efficient in the most extensive use of our understanding, as applied to experience.
I
Solution of the Cosmological Idea of the Totality of the Composition of Phenomena in an Universe
Here, as well as in the other cosmological problems, the regulative principle of reason is founded on the proposition that, in the empirical regressus, no experience of an absolute limit, that is, of any condition as such, which empirically is absolutely unconditioned, can exist. The ground of this is that such an experience would contain a limitation of phenomena by nothing or by the void, on which the continued regressus by means of experience must abut; and this is impossible.
This proposition, which says that in an empirical regressus I can only arrive at the condition which itself must be considered empirically conditioned, contains the rule in terminis, that however far I may have reached in the ascending series, I must always enquire for a still higher member of that series, whether it be known to me by experience or not.
For the solution, therefore, of the first cosmological problem, nothing more is wanted than to determine whether, in the regressus to the unconditioned extension of the universe (in time and in space), this nowhere limited ascent is to be called a regressus in infinitum, or a regressus in indefinitum.
The mere general representation of the series of all past states of the world, and of the things which exist together in space, is itself nothing but a possible empirical regressus, which I represent to myself, though as yet as indefinite, and through which alone the concept of such a series of conditions of the perception given to me can arise.17 Now the universe exists for me as a concept only, and never (as a whole) as an intuition. Hence I cannot from its quantity conclude the quantity of the regressus, and determine the one by the other; but I must first frame to myself a concept of the quantity of the world through the quantity of the empirical regressus. Of this, however, I never know anything more than that, empirically, I must go on from every given member of the series of conditions to a higher and more distant member. Hence the quantity of the whole of phenomena is not absolutely determined, and we cannot say therefore that it is a regressus in infinitum, because this would anticipate the members which the regressus has not yet reached, and represent its number as so large that no empirical synthesis could ever reach it. It would therefore (though negatively only) determine the quantity of the world prior to the regressus, which is impossible, because it is not given to me by any intuition (in its totality), so that its quantity cannot be given prior to the regressus. Hence we cannot say anything of the quantity or extension of the world by itself, not even that there is in it a regressus in infinitum; but we must look for the concept of its quantity according to the rule that determines the empirical regressus in it. This rule, however, says no more than that, however far we may have got in the series of empirical conditions, we ought never to assume an absolute limit, but subordinate every phenomenon, as conditioned, to another, as its condition, and that we must proceed further to that condition. This is the regressus in indefinitum, which, as it fixes no quantity in the object, can clearly enough be distinguished from the regressus in infinitum.
I cannot say therefore that, as to time past or as to space, the world is infinite. For such a concept of quantity, as a given infinity, is empirical, and therefore, with reference to the world as an object of the senses, absolutely impossible. Nor shall I say that the regressus, beginning with a given perception, and going on to everything that limits it in a series, both in space and in time past, goes on in infinitum, because this would presuppose an infinite quantity of the world. Nor can I say again that it is finite, for the absolute limit is likewise empirically impossible. Hence it follows that I shall not be able to say anything of the whole object of experience (the world of sense), but only of the rule, according to which experience can take place and be continued in accordance with its object.
To the cosmological question, therefore, respecting the quantity of the world, the first and negative answer is, that the world has no first beginning in time, and no extreme limit in space.
For, in the contrary case, the world would be limited by empty time and empty space. As however, as a phenomenon, it cannot, by itself, be either,—a phenomenon not being a thing by itself,—we should have to admit the perception of a limitation by means of absolute empty time or empty space, by which these limits of the world could be given in a possible experience. Such an experience, however, would be perfectly void of contents, and therefore impossible. Consequently an absolute limit of the world is impossible empirically, and therefore absolutely also.18
From this follows at the same time the affirmative answer, that the regressus in the series of the phenomena of the world, intended as a determination of the quantity of the world, goes on in indefinitum, which is the same as if we say that the world of sense has no absolute quantity, but that the empirical regressus (through which alone it can be given on the side of its conditions) has its own rule, namely, to advance from every member of the series, as conditioned, to a more distant member, whether by our own experience, or by the guidance of history, or through the chain of causes and their effects; and never to dispense with the extension of the possible empirical use of the understanding, this being the proper and really only task of reason and its principles.
We do not prescribe by this a definite empirical regressus advancing without end in a certain class of phenomena; as, for instance, that from a living person one ought always to ascend in a series of ancestors, without ever expecting a first pair; or, in the series of cosmical bodies, without admitting in the end an extremest sun. All that is demanded is a progressus from phenomena to phenomena, even if they should not furnish us with a real perception (if it is too weak in degree to become experience in our consciousness), because even thus they belong to a possible experience.
Every beginning is in time, and every limit of extension in space. Space and time,
however, exist in the world of sense only. Hence phenomena only are limited in the world conditionally; the world itself, however, is limited neither conditionally nor unconditionally.
For the same reason, and because the world can never be given complete, and even the series of conditions of something given as conditioned cannot, as a cosmical series, be given as complete, the concept of the quantity of the world can be given through the regressus only, and not before it in any collective intuition. That regressus, however, consists only in the determining of the quantity, and does not give, therefore, any definite concept, nor the concept of any quantity which, with regard to a certain measure, could be called infinite. It does not therefore proceed to the infinite (as if given), but only into an indefinite distance, in order to give a quantity (of experience) which has first to be realized by that very regressus.
II
Solution of the Cosmological Idea of the Totality of the Division of a Whole given in Intuition
If I divide a whole, given in intuition, I proceed from the conditioned to the conditions of its possibility. The division of the parts (subdivisio or decompositio) is a regressus in the series of those conditions. The absolute totality of this series could only be given, if the regressus could reach the simple parts. But if all parts in a continuously progressing decomposition are always divisible again, then the division, that is, the regressus from the conditioned to its conditions, goes on in infinitum; because the conditions (the parts) are contained in the conditioned itself, and as that is given as complete in an intuition enclosed within limits, are all given with it. The regressus must therefore not be called a regressus in indefinitum, such as was alone allowed by the former cosmological idea, where from the conditioned we had to proceed to conditions outside it, and therefore not given at the same time through it, but first to be added in the empirical regressus. It is not allowed, however, even in the case of a whole that is divisible in infinitum, to say, that it consists of infinitely many parts. For although all parts are contained in the intuition of the whole, yet the whole division is not contained in it, because it consists in the continuous decomposition, or in the regressus itself, which first makes that series real. As this regressus is infinite, all members (parts) at which it arrives are contained, no doubt, in the given whole as aggregates; but not so the whole series of the division, which is successively infinite and never complete, and cannot, therefore, represent an infinite number, or any comprehension of it as a whole.
It is easy to apply this remark to space. Every space, perceived within its limits, is such a whole the parts of which, in spite of all decomposition, are always spaces again, and therefore divisible in infinitum.
From this follows, quite naturally, the second application to an external phenomenon, enclosed within its limits (body). The divisibility of this is founded on the divisibility of space, which constitutes the possibility of the body, as an extended whole. This is therefore divisible in infinitum, without consisting, however, of an infinite number of parts.
It might seem indeed, as a body must be represented as a substance in space, that, with regard to the law of the divisibility of space, it might differ from it, for we might possibly concede, that in the latter case decomposition could never do away with all composition, because in that case all space, which besides has nothing independent of its own, would cease to be (which is impossible), while, even if all composition of matter should be done away with in thought, it would not seem compatible with the concept of a substance that nothing should remain of it, because substance is meant to be the subject of all composition, and ought to remain in its elements, although their connection in space, by which they become a body, should have been removed. But, what applies to a thing by itself, represented by a pure concept of the understanding, does not apply to what is called substance, as a phenomenon. This is not an absolute subject, but only a permanent image of sensibility, nothing in fact but intuition, in which nothing unconditioned can ever be met with.
But although this rule of the progress in infinitum applies without any doubt to the subdivision of a phenomenon, as a mere occupant of space, it 'does not apply to the number of the parts, separated already in a certain way in a given whole, which thus constitute a quantum discretum. To suppose that in every organised whole every part is again organised, and that by thus dissecting the parts in infinitum we should meet again and again with new organised parts, in fact that the whole is organised in infinitum, is a thought difficult to think, though it is possible to think that the parts of matter decomposed in infinitum might become organised. For the infinity of the division of a given phenomenon in space is founded simply on this, that by it divisibility only, that is, an entirely indefinite number of parts, is given, while the parts themselves can only be given and determined through the subdivision, in short, that the whole is not itself already divided. Thus the division can determine a number in it, which goes so far as we like to go, in the regressus of a division. In an organic body, on the contrary, organised in infinitum the whole is by that very concept represented as divided, and a number of parts, definite in itself, and yet infinite, is found in it, before every regressus of division. This would be self-contradictory, because we should have to consider this infinite convolute as a never-to-be-completed series (infinite), and yet as complete in its (organised) comprehension. Infinite division takes the phenomenon only as a quantum continuum, and is inseparable from the occupation of space, because in this very occupation lies the ground of endless divisibility. But as soon as anything is taken as a quantum discretum, the number of units in it is determined, and therefore at all times equal to a certain number. How far the organisation in an organised body may go, experience alone can show us; but though it never arrived with certainty at any unorganised part, they would still have to be admitted as lying within possible experience. It is different with the transcendental division of a phenomenon. How far that may extend is not a matter of experience, but a principle of reason, which never allows us to consider the empirical regressus in the decomposition of extended bodies, according to the nature of these phenomena, as at any time absolutely completed.
Concluding Remarks on the Solution of the Transcendental-mathematical Ideas, and Preliminary Remark for the Solution of the Transcendental-dynamical Ideas
When exhibiting in a tabular form the antinomy of pure reason, through all the transcendental ideas, and indicating the ground of the conflict and the only means of removing it, by declaring both contradictory statements as false, we always represented the conditions as belonging to that which they conditioned, according to relations of space and time, this being the ordinary supposition of the common understanding, and in fact the source from which that conflict arose. In that respect all dialectical representations of the totality in a series of conditions of something given as conditioned were always of the same character. It was always a series in which the condition was connected with the conditioned, as members of the same series, both being thus homogeneous. In such a series the regressus was never conceived as completed, or, if that had to be done, one of the members, being in itself conditioned, had wrongly to be accepted as the first, and therefore as unconditioned. If not always the object, that is, the conditioned, yet the series of its conditions was always considered according to quantity only, and then the difficulty arose (which could not be removed by any compromise, but only by cutting the knot), that reason made it either too long or too short for the understanding, which could in neither case come up to the idea.
But in this we have overlooked an essential distinction between the objects, that is, the concepts of the understanding, which reason tries to raise into ideas. Two of them, according to the above table of the categories, imply a mathematical, the remaining two a dynamical synthesis of phenomena. Hitherto this overlooking was of no great importance, because, in the general representation of all transcendental ideas, we always remained under phenomenal conditions, and with regard to the two transcendental-mathema
tical ideas also, we had to do with no object but the phenomenal only. Now, however, as we have come to consider the dynamical concepts of the understanding, so far as they should be rendered adequate to the idea of reason, that distinction becomes important, and opens to us an entirely new insight into the character of the suit in which reason is implicated. That suit had before been dismissed, as resting on both sides on wrong presuppositions. Now, however, as there seems to be in the dynamical antinomy such a presupposition as may be compatible with the pretensions of reason, and as the judge himself supplies perhaps the deficiency of legal grounds, which had been misunderstood on both sides, the suit may possibly be adjusted, from this point of view, to the satisfaction of both parties, which was impossible in the conflict of the mathematical antinomy.
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