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determine how far we must proceed in the empirical regress from

condition to condition, in order to discover, in conformity with the

rule of reason, a full and correct answer to the questions proposed by

reason itself.

This principle of reason is hence valid only as a rule for the

extension of a possible experience- its invalidity as a principle

constitutive of phenomena in themselves having been sufficiently

demonstrated. And thus, too, the antinomial conflict of reason with

itself is completely put an end to; inasmuch as we have not only

presented a critical solution of the fallacy lurking in the opposite

statements of reason, but have shown the true meaning of the ideas

which gave rise to these statements. The dialectical principle of

reason has, therefore, been changed into a doctrinal principle. But in

fact, if this principle, in the subjective signification which we have

shown to be its only true sense, may be guaranteed as a principle of

the unceasing extension of the employment of our understanding, its

influence and value are just as great as if it were an axiom for the a

priori determination of objects. For such an axiom could not exert a

stronger influence on the extension and rectification of our

knowledge, otherwise than by procuring for the principles of the

understanding the most widely expanded employment in the field of

experience.

I. Solution of the Cosmological Idea of the Totality of the

Composition of Phenomena in the Universe.

Here, as well as in the case of the other cosmological problems, the

ground of the regulative principle of reason is the proposition that

in our empirical regress no experience of an absolute limit, and

consequently no experience of a condition, which is itself

absolutely unconditioned, is discoverable. And the truth of this

proposition itself rests upon the consideration that such an

experience must represent to us phenomena as limited by nothing or the

mere void, on which our continued regress by means of perception

must abut- which is impossible.

Now this proposition, which declares that every condition attained

in the empirical regress must itself be considered empirically

conditioned, contains the rule in terminis, which requires me, to

whatever extent I may have proceeded in the ascending series, always

to look for some higher member in the series- whether this member is

to become known to me through experience, or not.

Nothing further is necessary, then, for the solution of the first

cosmological problem, than to decide, whether, in the regress to the

unconditioned quantity of the universe (as regards space and time),

this never limited ascent ought to be called a regressus in

infinitum or indefinitum.

The general representation which we form in our minds of the

series of all past states or conditions of the world, or of all the

things which at present exist in it, is itself nothing more than a

possible empirical regress, which is cogitated- although in an

undetermined manner- in the mind, and which gives rise to the

conception of a series of conditions for a given object.* Now I have a

conception of the universe, but not an intuition- that is, not an

intuition of it as a whole. Thus I cannot infer the magnitude of the

regress from the quantity or magnitude of the world, and determine the

former by means of the latter; on the contrary, I must first of all

form a conception of the quantity or magnitude of the world from the

magnitude of the empirical regress. But of this regress I know nothing

more than that I ought to proceed from every given member of the

series of conditions to one still higher. But the quantity of the

universe is not thereby determined, and we cannot affirm that this

regress proceeds in infinitum. Such an affirmation would anticipate

the members of the series which have not yet been reached, and

represent the number of them as beyond the grasp of any empirical

synthesis; it would consequently determine the cosmical quantity prior

to the regress (although only in a negative manner)- which is

impossible. For the world is not given in its totality in any

intuition: consequently, its quantity cannot be given prior to the

regress. It follows that we are unable to make any declaration

respecting the cosmical quantity in itself- not even that the

regress in it is a regress in infinitum; we must only endeavour to

attain to a conception of the quantity of the universe, in

conformity with the rule which determines the empirical regress in it.

But this rule merely requires us never to admit an absolute limit to

our series- how far soever we may have proceeded in it, but always, on

the contrary, to subordinate every phenomenon to some other as its

condition, and consequently to proceed to this higher phenomenon. Such

a regress is, therefore, the regressus in indefinitum, which, as not

determining a quantity in the object, is clearly distinguishable

from the regressus in infinitum.

*The cosmical series can neither be greater nor smaller than the

possible empirical regress, upon which its conception is based. And as

this regress cannot be a determinate infinite regress, still less a

determinate finite (absolutely limited), it is evident that we

cannot regard the world as either finite or infinite, because the

regress, which gives us the representation of the world, is neither

finite nor infinite.

It follows from what we have said that we are not justified in

declaring the world to be infinite in space, or as regards past

time. For this conception of an infinite given quantity is

empirical; but we cannot apply the conception of an infinite

quantity to the world as an object of the senses. I cannot say, "The

regress from a given perception to everything limited either in

space or time, proceeds in infinitum," for this presupposes an

infinite cosmical quantity; neither can I say, "It is finite," for

an absolute limit is likewise impossible in experience. It follows

that I am not entitled to make any assertion at all respecting the

whole object of experience- the world of sense; I must limit my

declarations to the rule according to which experience or empirical

knowledge is to be attained.

To the question, therefore, respecting the cosmical quantity, the

first and negative answer is: "The world has no beginning in time, and

no absolute limit in space."

For, in the contrary case, it would be limited by a void time on the

one hand, and by a void space on the other. Now, since the world, as a

phenomenon, cannot be thus limited in itself for a phenomenon is not a

thing in itself; it must be possible for us to have a perception of

this limitation by a void time and a void space. But such a

perception- such an experience is impossible; because it has no

content. Consequently, an absolute cosmical limit is empirically,

and therefore absolutely, impossible.*

*The reader will remark that the proof presented above is very

different from the dogmatical demonstration given in the antithesis of

the first antinomy. In that demonstration, it was taken for granted

that the world is a thing in itself- given in its totality prior to

all regress, and a determined position in space and time was denied to

it- if it was not considered as occupying all time and all space.

Hence our conclusion differed from that given above; for we inferred

in the antithesis the actual infinity of the world.

From this follows the affirmative answer: "The regress in the series

of phenomena- as a determination of the cosmical quantity, proceeds in

indefinitum." This is equivalent to saying: "The world of sense has no

absolute quantity, but the empirical regress (through which alone

the world of sense is presented to us on the side of its conditions)

rests upon a rule, which requires it to proceed from every member of

the series, as conditioned, to one still more remote (whether

through personal experience, or by means of history, or the chain of

cause and effect), and not to cease at any point in this extension

of the possible empirical employment of the understanding." And this

is the proper and only use which reason can make of its principles.

The above rule does not prescribe an unceasing regress in one kind

of phenomena. It does not, for example, forbid us, in our ascent

from an individual human being through the line of his ancestors, to

expect that we shall discover at some point of the regress a

primeval pair, or to admit, in the series of heavenly bodies, a sun at

the farthest possible distance from some centre. All that it demands

is a perpetual progress from phenomena to phenomena, even although

an actual perception is not presented by them (as in the case of our

perceptions being so weak as that we are unable to become conscious of

them), since they, nevertheless, belong to possible experience.

Every beginning is in time, and all limits to extension are in

space. But space and time are in the world of sense. Consequently

phenomena in the world are conditionally limited, but the world itself

is not limited, either conditionally or unconditionally.

For this reason, and because neither the world nor the cosmical

series of conditions to a given conditioned can be completely given,

our conception of the cosmical quantity is given only in and through

the regress and not prior to it- in a collective intuition. But the

regress itself is really nothing more than the determining of the

cosmical quantity, and cannot therefore give us any determined

conception of it- still less a conception of a quantity which is, in

relation to a certain standard, infinite. The regress does not,

therefore, proceed to infinity (an infinity given), but only to an

indefinite extent, for or the of presenting to us a quantity- realized

only in and through the regress itself.

II. Solution of the Cosmological Idea of the Totality of

the Division of a Whole given in Intuition.

When I divide a whole which is given in intuition, I proceed from

a conditioned to its conditions. The division of the parts of the

whole (subdivisio or decompositio) is a regress in the series of these

conditions. The absolute totality of this series would be actually

attained and given to the mind, if the regress could arrive at

simple parts. But if all the parts in a continuous decomposition are

themselves divisible, the division, that is to say, the regress,

proceeds from the conditioned to its conditions in infinitum;

because the conditions (the parts) are themselves contained in the

conditioned, and, as the latter is given in a limited intuition, the

former are all given along with it. This regress cannot, therefore, be

called a regressus in indefinitum, as happened in the case of the

preceding cosmological idea, the regress in which proceeded from the

conditioned to the conditions not given contemporaneously and along

with it, but discoverable only through the empirical regress. We are

not, however, entitled to affirm of a whole of this kind, which is

divisible in infinitum, that it consists of an infinite number of

parts. For, although all the parts are contained in the intuition of

the whole, the whole division is not contained therein. The division

is contained only in the progressing decomposition- in the regress

itself, which is the condition of the possibility and actuality of the

series. Now, as this regress is infinite, all the members (parts) to

which it attains must be contained in the given whole as an aggregate.

But the complete series of division is not contained therein. For this

series, being infinite in succession and always incomplete, cannot

represent an infinite number of members, and still less a

composition of these members into a whole.

To apply this remark to space. Every limited part of space presented

to intuition is a whole, the parts of which are always spaces- to

whatever extent subdivided. Every limited space is hence divisible

to infinity.

Let us again apply the remark to an external phenomenon enclosed

in limits, that is, a body. The divisibility of a body rests upon

the divisibility of space, which is the condition of the possibility

of the body as an extended whole. A body is consequently divisible

to infinity, though it does not, for that reason, consist of an

infinite number of parts.

It certainly seems that, as a body must be cogitated as substance in

space, the law of divisibility would not be applicable to it as

substance. For we may and ought to grant, in the case of space, that

division or decomposition, to any extent, never can utterly annihilate

composition (that is to say, the smallest part of space must still

consist of spaces); otherwise space would entirely cease to exist-

which is impossible. But, the assertion on the other band that when

all composition in matter is annihilated in thought, nothing

remains, does not seem to harmonize with the conception of

substance, which must be properly the subject of all composition and

must remain, even after the conjunction of its attributes in space-

which constituted a body- is annihilated in thought. But this is not

the case with substance in the phenomenal world, which is not a

thing in itself cogitated by the pure category. Phenomenal substance

is not an absolute subject; it is merely a permanent sensuous image,

and nothing more than an intuition, in which the unconditioned is

not to be found.

But, although this rule of progress to infinity is legitimate and

applicable to the subdivision of a phenomenon, as a mere occupation or

filling of space, it is not applicable to a whole consisting of a

number of distinct parts and constituting a quantum discretum- that is

to say, an organized body. It cannot be admitted that every part in an

organized whole is itself organized, and that, in analysing it to

infinity, we must always meet with organized parts; although we may

allow that the parts of the matter which we decompose in infinitum,

may be organized. For the infinity of the division of a phenomenon

in space rests altogether on the fact that the divisibility of a