The Critique of Pure Reason; Part 17

Ft: Translated by J. M. D. Meiklejohn

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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.

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.

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.

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.



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.

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
themselves, the proof of the Monadists would be unexceptionable.

The second dialectical assertion possesses the peculiarity of
having opposed to it a dogmatical proposition, which, among all such
sophistical statements, is the only one that undertakes to prove in the
case of an object of experience, that which is properly a transcendental
idea--the absolute simplicity of substance. The proposition is that the
object of the internal sense, the thinking Ego, is an absolute simple
substance. Without at present entering upon this subject--as it has been
considered at length in a former chapter--I shall merely remark that, if
something is cogitated merely as an object, without the addition of any
synthetical determination of its intuition--as happens in the case
of the bare representation, I--it is certain that no manifold and no
composition can be perceived in such a representation. As, moreover, the
predicates whereby I cogitate this object are merely intuitions of the
internal sense, there cannot be discovered in them anything to prove
the existence of a manifold whose parts are external to each other,
and, consequently, nothing to prove the existence of real composition.
Consciousness, therefore, is so constituted that, inasmuch as the
thinking subject is at the same time its own object, it cannot divide
itself--although it can divide its inhering determinations. For every
object in relation to itself is absolute unity. Nevertheless, if the
subject is regarded externally, as an object of intuition, it must, in
its character of phenomenon, possess the property of composition. And it
must always be regarded in this manner, if we wish to know whether there
is or is not contained in it a manifold whose parts are external to each
other.



THIRD CONFLICT OF THE TRANSCENDENTAL IDEAS.

THESIS.

Causality according to the laws of nature, is not the only causality
operating to originate the phenomena of the world. A causality of
freedom is also necessary to account fully for these phenomena.


PROOF.

Let it be supposed, that there is no other kind of causality than that
according to the laws of nature. Consequently, everything that happens
presupposes a previous condition, which it follows with absolute
certainty, in conformity with a rule. But this previous condition must
itself be something that has happened (that has arisen in time, as it
did not exist before), for, if it has always been in existence, its
consequence or effect would not thus originate for the first time,
but would likewise have always existed. The causality, therefore, of a
cause, whereby something happens, is itself a thing that has happened.
Now this again presupposes, in conformity with the law of nature, a
previous condition and its causality, and this another anterior to the
former, and so on. If, then, everything happens solely in accordance
with the laws of nature, there cannot be any real first beginning of
things, but only a subaltern or comparative beginning. There cannot,
therefore, be a completeness of series on the side of the causes which
originate the one from the other. But the law of nature is that
nothing can happen without a sufficient a priori determined cause. The
proposition therefore--if all causality is possible only in accordance
with the laws of nature--is, when stated in this unlimited and general
manner, self-contradictory. It follows that this cannot be the only kind
of causality.

From what has been said, it follows that a causality must be admitted,
by means of which something happens, without its cause being determined
according to necessary laws by some other cause preceding. That is to
say, there must exist an absolute spontaneity of cause, which of itself
originates a series of phenomena which proceeds according to natural
laws--consequently transcendental freedom, without which even in the
course of nature the succession of phenomena on the side of causes is
never complete.


ANTITHESIS.

There is no such thing as freedom, but everything in the world happens
solely according to the laws of nature.


PROOF.

Granted, that there does exist freedom in the transcendental sense, as a
peculiar kind of causality, operating to produce events in the world--a
faculty, that is to say, of originating a state, and consequently a
series of consequences from that state. In this case, not only the
series originated by this spontaneity, but the determination of this
spontaneity itself to the production of the series, that is to say, the
causality itself must have an absolute commencement, such that nothing
can precede to determine this action according to unvarying laws. But
every beginning of action presupposes in the acting cause a state of
inaction; and a dynamically primal beginning of action presupposes a
state, which has no connection--as regards causality--with the preceding
state of the cause--which does not, that is, in any wise result from it.
Transcendental freedom is therefore opposed to the natural law of cause
and effect, and such a conjunction of successive states in effective
causes is destructive of the possibility of unity in experience and
for that reason not to be found in experience--is consequently a mere
fiction of thought.

We have, therefore, nothing but nature to which we must look for
connection and order in cosmical events. Freedom--independence of the
laws of nature--is certainly a deliverance from restraint, but it is
also a relinquishing of the guidance of law and rule. For it cannot
be alleged that, instead of the laws of nature, laws of freedom may be
introduced into the causality of the course of nature. For, if freedom
were determined according to laws, it would be no longer freedom,
but merely nature. Nature, therefore, and transcendental freedom are
distinguishable as conformity to law and lawlessness. The former imposes
upon understanding the difficulty of seeking the origin of events ever
higher and higher in the series of causes, inasmuch as causality is
always conditioned thereby; while it compensates this labour by the
guarantee of a unity complete and in conformity with law. The latter, on
the contrary, holds out to the understanding the promise of a point
of rest in the chain of causes, by conducting it to an unconditioned
causality, which professes to have the power of spontaneous origination,
but which, in its own utter blindness, deprives it of the guidance of
rules, by which alone a completely connected experience is possible.



OBSERVATIONS ON THE THIRD ANTINOMY.

ON THE THESIS.

The transcendental idea of freedom is far from constituting the entire
content of the psychological conception so termed, which is for the most
part empirical. It merely presents us with the conception of spontaneity
of action, as the proper ground for imputing freedom to the cause of a
certain class of objects. It is, however, the true stumbling-stone to
philosophy, which meets with unconquerable difficulties in the way of
its admitting this kind of unconditioned causality. That element in the
question of the freedom of the will, which has for so long a time placed
speculative reason in such perplexity, is properly only transcendental,
and concerns the question, whether there must be held to exist a faculty
of spontaneous origination of a series of successive things or states.
How such a faculty is possible is not a necessary inquiry; for in the
case of natural causality itself, we are obliged to content ourselves
with the a priori knowledge that such a causality must be presupposed,
although we are quite incapable of comprehending how the being of
one thing is possible through the being of another, but must for this
information look entirely to experience. Now we have demonstrated this
necessity of a free first beginning of a series of phenomena, only in so
far as it is required for the comprehension of an origin of the world,
all following states being regarded as a succession according to laws
of nature alone. But, as there has thus been proved the existence of a
faculty which can of itself originate a series in time--although we
are unable to explain how it can exist--we feel ourselves authorized to
admit, even in the midst of the natural course of events, a beginning,
as regards causality, of different successions of phenomena, and at the
same time to attribute to all substances a faculty of free action.
But we ought in this case not to allow ourselves to fall into a common
misunderstanding, and to suppose that, because a successive series in
the world can only have a comparatively first beginning--another state
or condition of things always preceding--an absolutely first beginning
of a series in the course of nature is impossible. For we are not
speaking here of an absolutely first beginning in relation to time, but
as regards causality alone. When, for example, I, completely of my own
free will, and independently of the necessarily determinative influence
of natural causes, rise from my chair, there commences with this event,
including its material consequences in infinitum, an absolutely
new series; although, in relation to time, this event is merely the
continuation of a preceding series. For this resolution and act of mine
do not form part of the succession of effects in nature, and are not
mere continuations of it; on the contrary, the determining causes of
nature cease to operate in reference to this event, which certainly
succeeds the acts of nature, but does not proceed from them. For
these reasons, the action of a free agent must be termed, in regard to
causality, if not in relation to time, an absolutely primal beginning of
a series of phenomena.

The justification of this need of reason to rest upon a free act as
the first beginning of the series of natural causes is evident from
the fact, that all philosophers of antiquity (with the exception of the
Epicurean school) felt themselves obliged, when constructing a theory of
the motions of the universe, to accept a prime mover, that is, a freely
acting cause, which spontaneously and prior to all other causes evolved
this series of states. They always felt the need of going beyond mere
nature, for the purpose of making a first beginning comprehensible.



ON THE ANTITHESIS.

The assertor of the all-sufficiency of nature in regard to causality
(transcendental Physiocracy), in opposition to the doctrine of freedom,
would defend his view of the question somewhat in the following manner.
He would say, in answer to the sophistical arguments of the opposite
party: If you do not accept a mathematical first, in relation to time,
you have no need to seek a dynamical first, in regard to causality. Who
compelled you to imagine an absolutely primal condition of the world,
and therewith an absolute beginning of the gradually progressing
successions of phenomena--and, as some foundation for this fancy of
yours, to set bounds to unlimited nature? Inasmuch as the substances in
the world have always existed--at least the unity of experience renders
such a supposition quite necessary--there is no difficulty in believing
also, that the changes in the conditions of these substances have always
existed; and, consequently, that a first beginning, mathematical or
dynamical, is by no means required. The possibility of such an infinite
derivation, without any initial member from which all the others result,
is certainly quite incomprehensible. But, if you are rash enough to
deny the enigmatical secrets of nature for this reason, you will find
yourselves obliged to deny also the existence of many fundamental
properties of natural objects (such as fundamental forces), which you
can just as little comprehend; and even the possibility of so simple
a conception as that of change must present to you insuperable
difficulties. For if experience did not teach you that it was real, you
never could conceive a priori the possibility of this ceaseless sequence
of being and non-being.

But if the existence of a transcendental faculty of freedom is
granted--a faculty of originating changes in the world--this faculty
must at least exist out of and apart from the world; although it is
certainly a bold assumption, that, over and above the complete content
of all possible intuitions, there still exists an object which cannot be
presented in any possible perception. But, to attribute to substances
in the world itself such a faculty, is quite inadmissible; for, in
this case; the connection of phenomena reciprocally determining and
determined according to general laws, which is termed nature, and along
with it the criteria of empirical truth, which enable us to distinguish
experience from mere visionary dreaming, would almost entirely
disappear. In proximity with such a lawless faculty of freedom, a system
of nature is hardly cogitable; for the laws of the latter would be
continually subject to the intrusive influences of the former, and
the course of phenomena, which would otherwise proceed regularly and
uniformly, would become thereby confused and disconnected.

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