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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.

ON THE ANTITHESIS.

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)* may

therefore be limited by phenomena, but phenomena cannot be limited

by an empty space without them. This is true of time also. All this

being granted, it is nevertheless indisputable, that we must assume

these two nonentities, void space without and void time before the

world, if we assume the existence of cosmical limits, relatively to

space or time.

*It is evident that what is meant here is, that empty space, in so

far as it is limited by phenomena- space, that is, within the world-

does not at least contradict transcendental principles, and may

therefore, as regards them, be admitted, although its possibility

cannot on that account be affirmed.

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 a 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.

SECOND CONFLICT OF TRANSCENDENTAL IDEAS.

THESIS.

Every composite substance in the world consists of simple parts; and

there exists nothing that is not either itself simple, or composed

of simple parts.

PROOF.

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.

ANTITHESIS.

No composite thing in the world consists of simple parts; and

there does not exist in the world any simple substance.

PROOF.

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.

The second proposition of the antithesis- that there exists in the

world nothing that is simple- is here equivalent to the following: The

existence of the absolutely simple cannot be demonstrated from any

experience or perception either external or internal; and the

absolutely simple is a mere idea, the objective reality of which

cannot be demonstrated in any possible experience; it is consequently,

in the exposition of phenomena, without application and object. For,

let us take for granted that an object may be found in experience

for this transcendental idea; the empirical intuition of such an

object must then be recognized to contain absolutely no manifold

with its parts external to each other, and connected into unity.

Now, as we cannot reason from the non-consciousness of such a manifold

to the impossibility of its existence in the intuition of an object,

and as the proof of this impossibility is necessary for the

establishment and proof of absolute simplicity; it follows that this

simplicity cannot be inferred from any perception whatever. As,

therefore, an absolutely simple object cannot be given in any

experience, and the world of sense must be considered as the sum total

of all possible experiences: nothing simple exists in the world.

This second proposition in the antithesis has a more extended aim

than the first. The first merely banishes the simple from the

intuition of the composite; while the second drives it entirely out of

nature. Hence we were unable to demonstrate it from the conception

of a given object of external intuition (of the composite), but we

were obliged to prove it from the relation of a given object to a

possible experience in general.

OBSERVATIONS ON THE SECOND ANTINOMY.

THESIS.

When I speak of a whole, which necessarily consists of simple parts,

I understand thereby only a substantial whole, as the true

composite; that is to say, I understand that contingent unity of the

manifold which is given as perfectly isolated (at least in thought),

placed in reciprocal connection, and thus constituted a unity. Space

ought not to be called a compositum but a totum, for its parts are

possible in the whole, and not the whole by means of the parts. It

might perhaps be called a compositum ideale, but not a compositum

reale. But this is of no importance. As space is not a composite of

substances (and not even of real accidents), if I abstract all

composition therein- nothing, not even a point, remains; for a point

is possible only as the limit of a space- consequently of a composite.

Space and time, therefore, do not consist of simple parts. That

which belongs only to the condition or state of a substance, even

although it possesses a quantity (motion or change, for example),

likewise does not consist of simple parts. That is to say, a certain

degree of change does not originate from the addition of many simple

changes. Our inference of the simple from the composite is valid

only of self-subsisting things. But the accidents of a state are not

self-subsistent. The proof, then, for the necessity of the simple,

as the component part of all that is substantial and composite, may

prove a failure, and the whole case of this thesis be lost, if we

carry the proposition too far, and wish to make it valid of everything

that is composite without distinction- as indeed has really now and

then happened. Besides, I am here speaking only of the simple, in so

far as it is necessarily given in the composite- the latter being

capable of solution into the former as its component parts. The proper

signification of the word monas (as employed by Leibnitz) ought to

relate to the simple, given immediately as simple substance (for

example, in consciousness), and not as an element of the composite. As

an clement, the term atomus would be more appropriate. And as I wish

to prove the existence of simple substances, only in relation to,

and as the elements of, the composite, I might term the antithesis

of the second Antinomy, transcendental Atomistic. But as this word has

long been employed to designate a particular theory of corporeal

phenomena (moleculae), and thus presupposes a basis of empirical

conceptions, I prefer calling it the dialectical principle of

Monadology.

ANTITHESIS.

Against the assertion of the infinite subdivisibility of matter

whose ground of proof is purely mathematical, objections have been

alleged by the Monadists. These objections lay themselves open, at

first sight, to suspicion, from the fact that they do not recognize

the clearest mathematical proofs as propositions relating to the

constitution of space, in so far as it is really the formal

condition of the possibility of all matter, but regard them merely

as inferences from abstract but arbitrary conceptions, which cannot

have any application to real things. just as if it were possible to

imagine another mode of intuition than that given in the primitive

intuition of space; and just as if its a priori determinations did not

apply to everything, the existence of which is possible, from the fact

alone of its filling space. If we listen to them, we shall find

ourselves required to cogitate, in addition to the mathematical point,

which is simple- not, however, a part, but a mere limit of space-

physical points, which are indeed likewise simple, but possess the

peculiar property, as parts of space, of filling it merely by their

aggregation. I shall not repeat here the common and clear

refutations of this absurdity, which are to be found everywhere in

numbers: every one knows that it is impossible to undermine the

evidence of mathematics by mere discursive conceptions; I shall only

remark that, if in this case philosophy endeavours to gain an

advantage over mathematics by sophistical artifices, it is because

it forgets that the discussion relates solely to Phenomena and their

conditions. It is not sufficient to find the conception of the

simple for the pure conception of the composite, but we must

discover for the intuition of the composite (matter), the intuition of

the simple. Now this, according to the laws of sensibility, and

consequently in the case of objects of sense, is utterly impossible.

In the case of a whole composed of substances, which is cogitated

solely by the pure understanding, it may be necessary to be in

possession of the simple before composition is possible. But this does

not hold good of the Totum substantiale phaenomenon, which, as an

empirical intuition in space, possesses the necessary property of

containing no simple part, for the very reason that no part of space

is simple. Meanwhile, the Monadists have been subtle enough to

escape from this difficulty, by presupposing intuition and the

dynamical relation of substances as the condition of the possibility

of space, instead of regarding space as the condition of the

possibility of the objects of external intuition, that is, of

bodies. Now we have a conception of bodies only as phenomena, and,

as such, they necessarily presuppose space as the condition of all

external phenomena. The evasion is therefore in vain; as, indeed, we

have sufficiently shown in our Aesthetic. If bodies were things in