第 49 页

particular importance, but we shall afterwards find it to be of some

value.

SECTION II. Antithetic 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 a 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.*

*The antinomies stand in the order of the four transcendental

ideas above detailed.

FIRST CONFLICT OF THE TRANSCENDENTAL IDEAS.

THESIS.

The world has a beginning in time, and is also limited in

regard to space.

PROOF.

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,* 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.

*We may consider an undetermined quantity as a whole, when it is

enclosed within limits, although we cannot construct or ascertain

its totality by measurement, that is, by the successive synthesis of

its parts. For its limits of themselves determine its completeness

as a whole.

ANTITHESIS.

The world has no beginning, and no limits in space, but is, in

relation both to time and space, infinite.

PROOF.

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.*

*Space is merely the form of external intuition (formal

intuition), and not a real object which can be externally perceived.

Space, prior to all things which determine it (fill or limit it),

or, rather, which present an empirical intuition conformable to it,

is, under the title of absolute space, nothing but the mere

possibility of external phenomena, in so far as they either exist in

themselves, or can annex themselves to given intuitions. Empirical

intuition is therefore not a composition of phenomena and space (of

perception and empty intuition). The one is not the correlate of the

other in a synthesis, but they are vitally connected in the same

empirical intuition, as matter and form. If we wish to set one of

these two apart from the other- space from phenomena- there arise

all sorts of empty determinations of external intuition, which are

very far from being possible perceptions. For example, motion or

rest of the world in an infinite empty space, or a determination of

the mutual relation of both, cannot possibly be perceived, and is

therefore merely the predicate of a notional entity.

OBSERVATIONS ON THE FIRST ANTINOMY.

ON THE THESIS.

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.* 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.

*The quantum in this sense contains a congeries of given units,

which is greater than any number- and this is the mathematical

conception of the infinite.

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