The Critique of Pure Reason

Thetic is the term applied to every collection of dogmatical propositions. By antithetic I do not understand dogmatical assertions of the opposite, but the self-contradiction of seemingly dogmatical cognitions (thesis cum antithesis), in none of which we can discover any decided superiority. Antithetic is not, therefore, occupied with one-sided statements, but is engaged in considering the contradictory nature of the general cognitions of reason and its causes. Transcendental antithetic is an investigation into the antinomy of pure reason, its causes and result. If we employ our reason not merely in the application of the principles of the understanding to objects of experience, but venture with it beyond these boundaries, there arise certain sophistical propositions or theorems. These assertions have the following peculiarities: They can find neither confirmation nor confutation in experience; and each is in itself not only self-consistent, but possesses conditions of its necessity in the very nature of reason—only that, unluckily, there exist just as valid and necessary grounds for maintaining the contrary proposition.

The questions which naturally arise in the consideration of this dialectic of pure reason, are therefore: 1st. In what propositions is pure reason unavoidably subject to an antinomy? 2nd. What are the causes of this antinomy? 3rd. Whether and in what way can reason free itself from this self-contradiction?

A dialectical proposition or theorem of pure reason must, according to what has been said, be distinguishable from all sophistical propositions, by the fact that it is not an answer to an arbitrary question, which may be raised at the mere pleasure of any person, but to one which human reason must necessarily encounter in its progress. In the second place, a dialectical proposition, with its opposite, does not carry the appearance of a merely artificial illusion, which disappears as soon as it is investigated, but a natural and unavoidable illusion, which, even when we are no longer deceived by it, continues to mock us and, although rendered harmless, can never be completely removed.

This dialectical doctrine will not relate to the unity of understanding in empirical conceptions, but to the unity of reason in pure ideas. The conditions of this doctrine are—inasmuch as it must, as a synthesis according to rules, be conformable to the understanding, and at the same time as the absolute unity of the synthesis, to the reason—that, if it is adequate to the unity of reason, it is too great for the understanding, if according with the understanding, it is too small for the reason. Hence arises a mutual opposition, which cannot be avoided, do what we will.

These sophistical assertions of dialectic open, as it were, a battle-field, where that side obtains the victory which has been permitted to make the attack, and he is compelled to yield who has been unfortunately obliged to stand on the defensive. And hence, champions of ability, whether on the right or on the wrong side, are certain to carry away the crown of victory, if they only take care to have the right to make the last attack, and are not obliged to sustain another onset from their opponent. We can easily believe that this arena has been often trampled by the feet of combatants, that many victories have been obtained on both sides, but that the last victory, decisive of the affair between the contending parties, was won by him who fought for the right, only if his adversary was forbidden to continue the tourney. As impartial umpires, we must lay aside entirely the consideration whether the combatants are fighting for the right or for the wrong side, for the true or for the false, and allow the combat to be first decided. Perhaps, after they have wearied more than injured each other, they will discover the nothingness of their cause of quarrel and part good friends.

This method of watching, or rather of originating, a conflict of assertions, not for the purpose of finally deciding in favour of either side, but to discover whether the object of the struggle is not a mere illusion, which each strives in vain to reach, but which would be no gain even when reached—this procedure, I say, may be termed the sceptical method. It is thoroughly distinct from scepticism—the principle of a technical and scientific ignorance, which undermines the foundations of all knowledge, in order, if possible, to destroy our belief and confidence therein. For the sceptical method aims at certainty, by endeavouring to discover in a conflict of this kind, conducted honestly and intelligently on both sides, the point of misunderstanding; just as wise legislators derive, from the embarrassment of judges in lawsuits, information in regard to the defective and ill-defined parts of their statutes. The antinomy which reveals itself in the application of laws, is for our limited wisdom the best criterion of legislation. For the attention of reason, which in abstract speculation does not easily become conscious of its errors, is thus roused to the momenta in the determination of its principles.

But this sceptical method is essentially peculiar to transcendental philosophy, and can perhaps be dispensed with in every other field of investigation. In mathematics its use would be absurd; because in it no false assertions can long remain hidden, inasmuch as its demonstrations must always proceed under the guidance of pure intuition, and by means of an always evident synthesis. In experimental philosophy, doubt and delay may be very useful; but no misunderstanding is possible, which cannot be easily removed; and in experience means of solving the difficulty and putting an end to the dissension must at last be found, whether sooner or later. Moral philosophy can always exhibit its principles, with their practical consequences, in concreto—at least in possible experiences, and thus escape the mistakes and ambiguities of abstraction. But transcendental propositions, which lay claim to insight beyond the region of possible experience, cannot, on the one hand, exhibit their abstract synthesis in any à priori intuition, nor, on the other, expose a lurking error by the help of experience. Transcendental reason, therefore, presents us with no other criterion than that of an attempt to reconcile such assertions, and for this purpose to permit a free and unrestrained conflict between them. And this we now proceed to arrange.[50]

Granted that the world has no beginning in time; up to every given moment of time, an eternity must have elapsed, and therewith passed away an infinite series of successive conditions or states of things in the world. Now the infinity of a series consists in the fact that it never can be completed by means of a successive synthesis. It follows that an infinite series already elapsed is impossible and that, consequently, a beginning of the world is a necessary condition of its existence. And this was the first thing to be proved.

As regards the second, let us take the opposite for granted. In this case, the world must be an infinite given total of coexistent things. Now we cannot cogitate the dimensions of a quantity, which is not given within certain limits of an intuition,[51] in any other way than by means of the synthesis of its parts, and the total of such a quantity only by means of a completed synthesis, or the repeated addition of unity to itself. Accordingly, to cogitate the world, which fills all spaces, as a whole, the successive synthesis of the parts of an infinite world must be looked upon as completed, that is to say, an infinite time must be regarded as having elapsed in the enumeration of all co-existing things; which is impossible. For this reason an infinite aggregate of actual things cannot be considered as a given whole, consequently, not as a contemporaneously given whole. The world is consequently, as regards extension in space, not infinite, but enclosed in limits. And this was the second thing to be proved.

For let it be granted that it has a beginning. A beginning is an existence which is preceded by a time in which the thing does not exist. On the above supposition, it follows that there must have been a time in which the world did not exist, that is, a void time. But in a void time the origination of a thing is impossible; because no part of any such time contains a distinctive condition of being, in preference to that of non-being (whether the supposed thing originate of itself, or by means of some other cause). Consequently, many series of things may have a beginning in the world, but the world itself cannot have a beginning, and is, therefore, in relation to past time, infinite.

As regards the second statement, let us first take the opposite for granted—that the world is finite and limited in space; it follows that it must exist in a void space, which is not limited. We should therefore meet not only with a relation of things in space, but also a relation of things to space. Now, as the world is an absolute whole, out of and beyond which no object of intuition, and consequently no correlate to which can be discovered, this relation of the world to a void space is merely a relation to no object. But such a relation, and consequently the limitation of the world by void space, is nothing. Consequently, the world, as regards space, is not limited, that is, it is infinite in regard to extension.[52]

In bringing forward these conflicting arguments, I have not been on the search for sophisms, for the purpose of availing myself of special pleading, which takes advantage of the carelessness of the opposite party, appeals to a misunderstood statute, and erects its unrighteous claims upon an unfair interpretation. Both proofs originate fairly from the nature of the case, and the advantage presented by the mistakes of the dogmatists of both parties has been completely set aside.

The thesis might also have been unfairly demonstrated, by the introduction of an erroneous conception of the infinity of a given quantity. A quantity is infinite, if a greater than itself cannot possibly exist. The quantity is measured by the number of given units—which are taken as a standard—contained in it. Now no number can be the greatest, because one or more units can always be added. It follows that an infinite given quantity, consequently an infinite world (both as regards time and extension) is impossible. It is, therefore, limited in both respects. In this manner I might have conducted my proof; but the conception given in it does not agree with the true conception of an infinite whole. In this there is no representation of its quantity, it is not said how large it is; consequently its conception is not the conception of a maximum. We cogitate in it merely its relation to an arbitrarily assumed unit, in relation to which it is greater than any number. Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller; but the infinity, which consists merely in the relation to this given unit, must remain always the same, although the absolute quantity of the whole is not thereby cognized.

The true (transcendental) conception of infinity is: that the successive synthesis of unity in the measurement of a given quantum can never be completed.[53] Hence it follows, without possibility of mistake, that an eternity of actual successive states up to a given (the present) moment cannot have elapsed, and that the world must therefore have a beginning.

In regard to the second part of the thesis, the difficulty as to an infinite and yet elapsed series disappears; for the manifold of a world infinite in extension is contemporaneously given. But, in order to cogitate the total of this manifold, as we cannot have the aid of limits constituting by themselves this total in intuition, we are obliged to give some account of our conception, which in this case cannot proceed from the whole to the determined quantity of the parts, but must demonstrate the possibility of a whole by means of a successive synthesis of the parts. But as this synthesis must constitute a series that cannot be completed, it is impossible for us to cogitate prior to it, and consequently not by means of it, a totality. For the conception of totality itself is in the present case the representation of a completed synthesis of the parts; and this completion, and consequently its conception, is impossible.

The proof in favour of the infinity of the cosmical succession and the cosmical content is based upon the consideration that, in the opposite case, a void time and a void space must constitute the limits of the world. Now I am not unaware, that there are some ways of escaping this conclusion. It may, for example, be alleged, that a limit to the world, as regards both space and time, is quite possible, without at the same time holding the existence of an absolute time before the beginning of the world, or an absolute space extending beyond the actual world—which is impossible. I am quite well satisfied with the latter part of this opinion of the philosophers of the Leibnitzian school. Space is merely the form of external intuition, but not a real object which can itself be externally intuited; it is not a correlate of phenomena, it is the form of phenomena itself. Space, therefore, cannot be regarded as absolutely and in itself something determinative of the existence of things, because it is not itself an object, but only the form of possible objects. Consequently, things, as phenomena, determine space; that is to say, they render it possible that, of all the possible predicates of space (size and relation), certain may belong to reality. But we cannot affirm the converse, that space, as something self-subsistent, can determine real things in regard to size or shape, for it is in itself not a real thing. Space (filled or void)[54] may therefore be limited by phenomena, but phenomena cannot be limited by an empty space without them. This is true of time also.

For, as regards the subterfuge adopted by those who endeavour to evade the consequence—that, if the world is limited as to space and time, the infinite void must determine the existence of actual things in regard to their dimensions—it arises solely from the fact that instead of a sensuous world, an intelligible world—of which nothing is known—is cogitated; instead of a real beginning (an existence, which is preceded by a period in which nothing exists), an existence which presupposes no other condition than that of time; and, instead of limits of extension, boundaries of the universe. But the question relates to the mundus phaenomenon, and its quantity; and in this case we cannot make abstraction of the conditions of sensibility, without doing away with the essential reality of this world itself. The world of sense, if it is limited, must necessarily lie in the infinite void. If this, and with it space as the à priori condition of the possibility of phenomena, is left out of view, the whole world of sense disappears. In our problem is this alone considered as given. The mundus intelligibilis is nothing but the general conception of a world, in which abstraction has been made of all conditions of intuition, and in relation to which no synthetical proposition—either affirmative or negative—is possible.

For, grant that composite substances do not consist of simple parts; in this case, if all combination or composition were annihilated in thought, no composite part, and (as, by the supposition, there do not exist simple parts) no simple part would exist. Consequently, no substance; consequently, nothing would exist. Either, then, it is impossible to annihilate composition in thought; or, after such annihilation, there must remain something that subsists without composition, that is, something that is simple. But in the former case the composite could not itself consist of substances, because with substances composition is merely a contingent relation, apart from which they must still exist as self-subsistent beings. Now, as this case contradicts the supposition, the second must contain the truth—that the substantial composite in the world consists of simple parts.

It follows, as an immediate inference, that the things in the world are all, without exception, simple beings—that composition is merely an external condition pertaining to them—and that, although we never can separate and isolate the elementary substances from the state of composition, reason must cogitate these as the primary subjects of all composition, and consequently, as prior thereto—and as simple substances.

Let it be supposed that a composite thing (as substance) consists of simple parts. Inasmuch as all external relation, consequently all composition of substances, is possible only in space; the space, occupied by that which is composite, must consist of the same number of parts as is contained in the composite. But space does not consist of simple parts, but of spaces. Therefore, every part of the composite must occupy a space. But the absolutely primary parts of what is composite are simple. It follows that what is simple occupies a space. Now, as everything real that occupies a space, contains a manifold the parts of which are external to each other, and is consequently composite—and a real composite, not of accidents (for these cannot exist external to each other apart from substance), but of substances—it follows that the simple must be a substantial composite, which is self-contradictory.