The Antinomy of Pure Reason
Section II
Antithetic of Pure Reason
If every collection of dogmatical doctrines is called Thetic, I may denote by Antithetic, not indeed dogmatical assertions of the opposite, but the conflict between different kinds of apparently dogmatical knowledge (thesis cum antithesi), to none of which we can ascribe a superior claim to our assent. This antithetic, therefore, has nothing to do with one-sided assertions, but considers general knowledge of reason with reference to the conflict only that goes on in it, and its causes. The transcendental antithetic is in fact an investigation of the antinomy of pure reason, its causes and its results. If we apply our reason, not only to objects of experience, in order to make use of the principles of the understanding, but venture to extend it beyond the limit of experience, there arise rationalising or sophistical propositions, which can neither hope for confirmation nor need fear refutation from experience. Every one of them is not only in itself free from contradiction, but can point to conditions of its necessity in the nature of reason itself, only that, unfortunately, its opposite can produce equally valid and necessary grounds for its support.
The questions which naturally arise in such a Dialectic of pure reason are the following. 1. In what propositions is pure reason inevitably subject to an antinomy? 2. On what causes does this antinomy depend? 3. Whether, and in what way, reason may, in spite of this contradiction, find a way to certainty?
A dialectical proposition of pure reason must have this characteristic to distinguish it from all purely sophistical propositions, first, that it does not refer to a gratuitous question, but to one which human reason in its natural progress must necessarily encounter, and, secondly, that it, as well as its opposite, carries with itself not a merely artificial illusion, which when once seen through disappears, but a natural and inevitable illusion, which, even when it deceives us no longer, always remains, and though rendered harmless, cannot be annihilated.
This dialectical doctrine will not refer to the unity of the understanding in concepts of experience, but to the unity of reason in mere ideas, the condition of which, as it is meant to agree, as a synthesis according to rules, with the understanding, and yet at the same time, as the absolute unity of that synthesis, with reason, must either, if it is adequate to the unity of reason, be too great for the understanding, or, if adequate to the understanding, too small for reason. Hence a conflict must arise, which cannot be avoided, do what we will.
These apparently rational, but really sophistical assertions open a dialectical battle-field, where that side always obtains the victory which is allowed to make the attack, and where those must certainly succumb who are obliged to keep on the defensive. Hence doughty knights, whether fighting for the good or the bad cause, are sure to win their laurels, if only they take care that they have the right to make the last attack, and are not obliged to stand a new onslaught of the enemy. We can easily imagine that this arena has often been entered, and many victories have been won on both sides, the last decisive victory being always guarded by the defender of the good cause maintaining his place, his opponent being forbidden ever to carry arms again. As impartial judges we must take no account of whether it be the good or the bad cause which the two champions defend. It is best to let them fight it out between themselves in the hope that, after they have rather tired out than injured each other, they may themselves perceive the uselessness of their quarrel, and part as good friends.
This method of watching or even provoking such a conflict of assertions, not in order to decide in favour of one or the other side, but in order to find out whether the object of the struggle be not a mere illusion, which everybody tries to grasp in vain, and which never can be of any use to any one, even if no resistance were made to him, this method, I say, may be called the sceptical method. It is totally different from scepticism, or that artificial and scientific agnosticism which undermines the foundations of all knowledge, in order if possible to leave nothing trustworthy and certain anywhere. The sceptical method, on the contrary, aims at certainty, because, while watching a contest which on both sides is carried on honestly and intelligently, it tries to discover the point where the misunderstanding arises, in order to do what is done by wise legislators, namely, to derive from the embarrassments of judges in law-suits information as to what is imperfectly, or not quite accurately, determined in their laws. The antinomy which shows itself in the application of laws, is, considering our limited wisdom, the best criterion of the original legislation (nomothetic), and helps to attract the attention of reason, which in abstract speculations does not easily become aware of its errors, to the important points in the determination of its principles.
This sceptical method is essential in transcendental philosophy only, while it may be dispensed with in other fields of investigation. It would be absurd in mathematics, for no false assertions can there be hidden or rendered invisible, because the demonstrations must always be guided by pure intuition, and proceed by evident synthesis. In experimental philosophy a doubt, which causes delay, may be useful, but at least no misunderstanding is possible that could not be easily removed, and the final means for deciding a question, whether found sooner or later, must always be supplied by experience. Moral philosophy too can always produce its principles and their practical consequences in the concrete also, or at least in possible experience, and thus avoid the misunderstandings inherent in abstraction. Transcendental assertions, on the contrary, pretending to knowledge far beyond the field of possible experience, can never produce their abstract synthesis in any intuition a priori, nor can their flaws be discovered by means of any experience. Transcendental reason, therefore, admits of no other criterion but an attempt to combine its conflicting assertions, and therefore, previous to this, unrestrained conflict between them. This is what we shall now attempt to do.3
Thesis
The Antinomy
First Conflict Of The
Thesis
The world has a beginning in time, and is limited also with regard to space.
Proof
For if we assumed that the world had no beginning in time, then an eternity must have elapsed up to every given point of time, and therefore an infinite series of successive states of things must have passed in the world. The infinity of a series, however, consists in this, that it never can be completed by means of a successive synthesis. Hence an infinite past series of worlds is impossible, and the beginning of the world a necessary condition of its existence. This was what had to be proved first.
With regard to the second, let us assume again the opposite. In that case the world would be given as an infinite whole of co-existing things. Now we cannot conceive in any way the extension of a quantum, which is not given within certain limits to every intuition,4 except through the synthesis of its parts, nor the totality of such a quantum in any way, except through
Antithesis
Of Pure Reason
Transcendental Ideas
Antithesis
The world has no beginning and no limits in space, but is infinite, in respect both to time and space.
Proof
For let us assume that it has a beginning. Then, as beginning is an existence which is preceded by a time in which the thing is not, it would follow that antecedently there was a time in which the world was not, that is, an empty time. In an empty time, however, it is impossible that anything should take its beginning, because of such a time no part possesses any condition as to existence rather than non-existence, which condition could distinguish that part from any other (whether produced by itself or through another cause). Hence, though many a series of things may take its beginning in the world, the world itself can have no beginning, and in reference to time past is infinite.
With regard to the second, let us assume again the opposite, namely, that the world is finite and limited in space. In that case the world would exist in an empty space without limits. We should therefore have not only a r
elation of things in space, but also of things to space. As however the world is an absolute whole, outside of which no object of intuition, and therefore no correlate of the world can be found, the relation of the world to empty
Thesis
a completed synthesis, or by the repeated addition of unity to itself.5 In order therefore to conceive the world, which fills all space, as a whole, the successive synthesis of the parts of an infinite world would have to be looked upon as completed; that is, an infinite time would have to be looked upon as elapsed, during the enumeration of all co-existing things. This is impossible. Hence an infinite aggregate of real things cannot be regarded as a given whole, nor, therefore, as given at the same time. Hence it follows that the world is not infinite, as regards extension in space, but enclosed in limits. This was the second that had to be proved.
Observations on The
I
On the Thesis
In exhibiting these conflicting arguments I have not tried to avail myself of mere sophisms for the sake of what is called special pleading, which takes advantage of the want of caution of the opponent, and gladly allows his appeal to a misunderstood law, in order to establish his own illegitimate claims on its refutation. Every one of our proofs has been deduced from the nature of the case, and no advantage has been taken of the wrong conclusions of dogmatists on either side.
Antithesis
space would be a relation to no object. Such a relation, and with it the limitation of the world by empty space, is nothing, and therefore the world is not limited with regard to space, that is, it is infinite in extension.6
First Antinomy
II
On the Antithesis
The proof of the infinity of the given series of world, and of the totality of the world, rests on this, that in the
Thesis
I might have apparently proved my thesis too by putting forward, as is the habit of dogmatists, a wrong definition of the infinity of a given quantity. I might have said that the quantity is infinite, if no greater quantity (that is, greater than the number of given units contained in it) is possible. As no number is the greatest, because one or more units can always be added to it, I might have argued that an infinite given quantity, and therefore also an infinite world (infinite as regards both the past series of time and extension in space) is impossible, and therefore the world limited in space and time. I might have done this, but, in that case, my definition would not have agreed with the true concept of an infinite whole. We do not represent by it how large it is, and the concept of it is not therefore the concept of a maximum, but we conceive by it its relation only to any possible unit, in regard to which it is greater than any number. According as this unit is either greater or smaller, the infinite would be greater or smaller, while infinity, consisting in the relation only to this given unit, would always remain the same, although the absolute quantity of the whole would not be known by it. This, however, does not concern us at present.
The true transcendental concept of infinity is, that the successive synthesis of units in measuring a quantum, can never be completed.7 Hence it follows with perfect certainty, that an eternity of real and successive states cannot have elapsed up to any given (the present) moment, and that the world therefore must have a beginning.
Antithesis
opposite case an empty time, and likewise an empty space, would form the limits of the world. Now I am quite aware that people have tried to escape from this conclusion by saying that a limit of the world, both in time and space, is quite possible, without our having to admit an absolute time before the beginning of the world or an absolute space outside the real world, which is impossible. I have nothing to say against the latter part of this opinion, held by the philosophers of the school of Leibniz. Space is only the form of external intuition, and not a real object that could be perceived externally, nor is it a correlate of phenomena, but the form of phenomena themselves. Space, therefore, cannot exist absolutely (by itself) as something determining the existence of things, because it is no object, but only the form of possible objects. Things, therefore, as phenomenal, may indeed determine space, that is, impart reality to one or other of its predicates (quantity and relation); but space, on the other side, as something existing by itself, cannot determine the reality of things in regard to quantity or form, because it is nothing real in itself. Space therefore (whether full or empty8) may be limited by phenomena, but phenomena cannot be limited by empty space outside them. The same applies to time. But, granting all this, it cannot be denied that we should be driven to admit these two monsters, empty space outside, and empty time before the world, if we assumed the limit of the world, whether in space or time.
Thesis
With regard to the second part of the thesis, the difficulty of an endless and yet past series does not exist; for the manifold of a world, infinite in extension, is given at one and the same time. But, in order to conceive the totality of such a multitude of things, as we cannot appeal to those limits which in intuition produce that totality by themselves, we must render an account of our concept, which in our case cannot proceed from the whole to the determined multitude of the parts, but has to demonstrate the possibility of a whole by the successive synthesis of the parts. As such a synthesis would constitute a series that would never be completed, it is impossible to conceive a totality either before it, or through it. For the concept of totality itself is in this case the representation of a completed synthesis of parts, and such a completion, and therefore its concept also, is impossible.
Antithesis
For as to the plea by which people try to escape from the conclusion, that if the world has limits in time or space, the infinite void would determine the existence of real things, so far as their dimensions are concerned, it is really no more than a covered attempt at putting some unknown intelligible world in the place of our sensuous world, and an existence in general, which presupposes no other condition in the world, in the place of a first beginning (an existence preceded by a time of non-existence), and boundaries of the universe in place of the limits of extension,—thus getting rid of time and space. But we have to deal here with the mundus phænomenon and its quantity, and we could not ignore the conditions of sensibility, without destroying its very essence. The world of sense, if it is limited, lies necessarily within the infinite void. If we ignore this, and with it, space in general, as an a priori condition of the possibility of phenomena, the whole world of sense vanishes, which alone forms the object of our enquiry. The mundus intelligibilis is nothing but the general concept of any world, which takes no account of any of the conditions of intuition, and which therefore admits of no synthetical proposition, whether affirmative or negative.
Thesis
The Antinomy
Second Conflict of the
Thesis
Every compound substance in the world consists of simple parts, and nothing exists anywhere but the simple, or what is composed of it.
Proof
For let us assume that compound substances did not consist of simple parts, then, if all composition is removed in thought, there would be no compound part, and (as no simple parts are admitted) no simple part either, that is, there would remain nothing, and there would therefore be no substance at all. Either, therefore, it is impossible to remove all composition in thought, or, after its removal, there must remain something that exists without composition, that is the simple. In the former case the compound could not itself consist of substances (because with them composition is only an accidental relation of substances, which substances, as permanent beings, must subsist without it). As this contradicts the supposition, there remains only the second view, namely, that the substantial compounds in the world consist of simple parts.
It follows as an immediate consequence that all the things in the world are simple beings, that their composi-
Antithesis
Of Pure Reason
Transcendental Ideas
Antithe
sis
No compound thing in the world consists of simple parts, and there exists nowhere in the world anything simple.
Proof
Assume that a compound thing, a substance, consists of simple parts. Then as all external relation, and therefore all composition of substances also, is possible in space only, it follows that space must consist of as many parts as the parts of the compound that occupies the space. Space, however, does not consist of simple parts, but of spaces. Every part of a compound, therefore, must occupy a space. Now the absolutely primary parts of every compound are simple. It follows therefore that the simple occupies a space. But as everything real, which occupies a space, contains a manifold, the parts of which are by the side of each other, and which therefore is compounded, and, as a real compound, compounded not of accidents (for these could not exist by the side of each other, without a substance), but of substances, it would follow that the simple is a substantial compound, which is self-contradictory.
The second proposition of the antithesis, that there
Thesis
tion is only an external condition, and that, though we are unable to remove these elementary substances from their state of composition and isolate them, reason must conceive them as the first subjects of all composition, and therefore, antecedently to it, as simple beings.
Critique of Pure Reason Page 36
