ANTITHETIC OF PURE REASON[1503]
”[Antithetic] is the conflict between two apparently dogmatic
judgments [_Erkenntnisse_] to neither of which can we ascribe any
superior claim to acceptance over the other, _i.e._ by Antithetic I
mean a _thesis_, together with an _antithesis_.” “Transcendental
Antithetic is an investigation of the antinomy of pure Reason, its
causes and outcome.”
The very existence of such antinomy presupposes a twofold condition:
first, that it does not refer to a gratuitous but to an inevitable
problem of human Reason, “one which it must necessarily encounter in its
natural progress”; and secondly, that the thesis and the antithesis
together generate a “natural and inevitable illusion,” which continues
to persist even after its deceptive power has been clearly disclosed.
Such conflict is caused by the fact that Reason seeks a unity which
transcends the understanding, and which nevertheless is meant to
conform to the conditions of the understanding. If the unity is adequate
to the demands of Reason, it is too great for the understanding; if it
is commensurate with the understanding, it is too small for
Reason.[1504] The theses express the higher unity at which Reason aims;
the antitheses are the judgments to which the understanding is
constrained by the nature of the appearances with which both it and
Reason profess to deal. If we hold to Reason, we make assertions
contradictory of the appearances; while if we place reliance on the
understanding, Reason condemns our conclusions.
This conflict is limited to those few problems above enumerated in which
we are called upon to complete a given series.[1505] Since totality,
whether in the form of a first beginning of the series or as an actual
infinity of the whole series, can never itself be experienced, these are
problems in regard to which experience can be of no assistance to us. It
can neither confirm nor refute any particular solution. The only
possible method of deciding between the competing claims is to watch or
even to provoke the conflict, in the hope that we may finally be able to
detect some misunderstanding, and so to resolve the conflict to the
satisfaction of both the litigants. Such is Kant’s description of what
he entitles his “sceptical method.”[1506]
Without here attempting a full discussion of the subject, it seems
advisable to point out at the very start what Kant’s exposition
seriously obscures, namely, the real character of the evidence upon
which the theses and the antitheses respectively rest. The latter are
not correctly stated as transcending experience, and as therefore
incapable of confirmation by it. The proofs which Kant offers of them
are, indeed, of a non-empirical _a priori_ character. They are
formulated in terms of the dogmatic rationalism of the Leibnizian
position, with a constant appeal to abstract principles. But, as a
matter of fact, they can be much more adequately established--in so far
as they can be established at all--through analysis of the spatial and
temporal conditions of material existence. As space and time are
continuous and homogeneous, any assertion which is true of a space or
time however small is likewise true of a space or time however large.
Any space consists of spaces, and must be regarded as itself part of a
larger whole.[1507] Any time consists of parts which are themselves
times, and is apprehensible only as following upon preceding times. It
is by such considerations as these that we are led to regard the
material world as unlimited, as infinitely divisible, and as having no
first state.
Kant’s method of demonstrating the theses--that the world is limited, is
finitely divisible, and has a first state--is no less misleading. Here
again his rationalistic arguments conceal the basis upon which the
various theses really rest. Their true determining ground is the demand
of Reason for some more satisfactory form of unconditionedness than that
which is found in the actual infinite. It is this demand which has led
philosophers to look around for proofs in support of the theses, and to
elaborate those rationalistic arguments which Kant here reproduces. Thus
the grounds of the antitheses are altogether different from those of the
theses; and in neither case are they properly represented by the
arguments which Kant employs.[1508]
The reasons why Kant in his detailed statement of the antinomies has
omitted, or at least subordinated, the above considerations, are complex
and various. In the first place, this doctrine of antinomy was in
several of its main features already formulated prior to his development
of the Critical philosophy. It forms part of his _Dissertation_ of 1770;
and at that time Kant was still largely in fundamental sympathy with the
Leibnizian ontology. Secondly, Kant is here professing to criticise the
science of rational cosmology, and is therefore bound to expound it in
more or less current form. And in the third place, he teaches that _the
antinomies exist as antinomies only when viewed from the false
standpoint of dogmatic rationalism_. Had he eliminated the rationalistic
proofs, the conflict of the antinomies, in its strictly logical form,
as the conflict of direct contradictories, would at once have vanished.
The general framework of this division of the _Dialectic_ demanded a
rationalistic treatment of both theses and antitheses, and Kant believed
that the rationalistic proofs which he propounds in their support are
unanswerable, so long as the dogmatic standpoint of ordinary
consciousness and of Leibnizian ontology is preserved. But even when
that important limitation is kept in view, Kant fails to justify this
interpretation of the conflict, and we must therefore be prepared to
find that his proofs, _whether of theses or of antitheses_, are in all
cases inconclusive. I shall append to each of his arguments a statement
of the reasons which constrain us to reject them as unsound. We shall
then be in a position to consider his whole doctrine of antinomy in its
broader aspects, and in its connection with the teaching of the other
main divisions of the _Dialectic_.
FIRST ANTINOMY
=Thesis.=--(_a_) The world has a beginning in time, and (_b_) is also
limited in regard to space.
=Thesis= _a._ =Proof.=--If we assume the opposite, namely, that the world
has no beginning in time, and if we define the infinite as that which
can never be completed by means of a successive synthesis, we must
conclude that the world-series can never complete itself. But the entire
series of past events _elapses_, _i.e._ completes itself at each moment.
It cannot therefore be infinite.
=Criticism.=--This argument gains its plausibility from the illegitimate
use of the term ‘elapse’ (_verfliessen_) as equivalent to ‘complete
itself.’ If it be really correct to define the infinite as that which
can never be completed, the conclusion to be drawn is that the temporal
series is always actually infinite, and that no point or event in it is
nearer to or further from either its beginning or its end.[1509] We may
select any point in the series as that from which we propose to begin a
regress to the earlier members of the series, but if the series is
actually infinite, it will be a regress without possibility of
completion, and one therefore which removes all justification for
asserting that at the point chosen a series has completed itself. It has
no beginning, and has no completion. What it has done at each moment of
the past it is still doing at each present moment, namely, coming out of
an inexhaustible past and passing into an equally inexhaustible future.
Time is by its given nature capable of being interpreted only as
actually infinite, alike in its past and in its future. It cannot
complete itself any more than it can begin itself. The one would be as
gross a violation of its nature as would the other. The present exists
only as a species of transition, unique in itself, but analogous in
nature to the innumerable other times that constitute time past. It is a
transition from the infinite through the infinite to the infinite. That
we cannot comprehend how, from an infinitude that has no beginning, the
present should ever have been reached, is no sufficient reason for
denying what by the very nature of time we are compelled to accept as a
correct description of the situation which is being analysed. The actual
nature of time is such as to rule out from among the possibilities the
thesis which Kant is here professing to be able to establish; time,
being such as it actually is, can have no beginning.
What thus holds of time may likewise hold of events in time. If time is
actually infinite, no proof can be derived from it in support of the
assumption that the world has had a beginning in time.
The phrase “by means of a successive synthesis” gives a needlessly
subjectivist colouring to Kant’s method of proof. The antinomy is
professedly being stated from the realist standpoint, and ought not
therefore to be complicated by any such reference. This objection
applies, as we shall find, still more strongly to Kant’s proof of the
second part of the thesis. The latter proof depends upon this
subjectivist reference; the present proof does not.
Kant limits his problem to the past infinitude of time. The reason for
this lies, of course, in the fact that he is concerned with the problem
of creation. The limitation is, however, misleading.
=Thesis= _b._--The world is limited in regard to space.
=Proof.=--Assume the opposite, namely, that the world is an infinite,
given whole of coexisting parts. A magnitude not given within the
determinate limits of an intuition can only be thought through the
synthesis of its parts, and its totality through their completed
synthesis. In order, therefore, that we may be able to think as a single
whole the world which fills all space, the successive synthesis of the
parts of an infinite world must be regarded as completed, _i.e._ an
infinite must be regarded as having elapsed in the enumeration of all
coexisting things. This, however, is impossible. An infinite aggregate
of actual things cannot therefore be viewed as a given whole, nor as
being given as coexistent. Consequently the world of spatial existences
must be regarded as finite.
=Criticism.=--From the impossibility of traversing infinite space in
thought by the successive addition of part to part, Kant here argues
that “an infinite aggregate of actual things cannot be viewed as a given
whole,” and consequently that the world cannot be infinitely extended in
space. That is, from a _subjective impossibility of apprehension_ he
infers an _objective impossibility of existence_. But Kant has himself
defined the infinite as involving this subjective impossibility; for in
the proof of thesis a he has stated that the infinitude of a series
consists in the very fact that it can never be completed through
successive synthesis. Kant is therefore propounding against the
_existence_ of the infinite the very feature which by definition
constitutes its infinitude. The implication would seem to be that the
concept of the infinite is the concept of that which _ex definitione_
cannot exist, and that there is therefore a contradiction in the very
idea of the actual infinite.
Deferring for a moment the further objections to which such procedure
lies open, we may observe that Kant, in arguing from a subjective to an
objective impossibility, commits the fallacy of _ignoratio elenchi_. For
when the conditions of objective existence are recognised in their
distinction from those of mental apprehension, the supposed
contradiction vanishes, and the argument ceases to have any cogency. The
use of the words ‘given’ and ‘whole’ is misleading. If space is
infinite, it is without bounds, and cannot therefore exist as a whole in
any usual meaning of that term. For the same reason it must be incapable
of being given as a whole. Its infinitude is a presupposition which
analysis of actually given portions of it constrains us to postulate,
and has to be conceived in terms of the definition employed in thesis
_a_. The given must always be conceived as involving what is not itself
given and what is not even capable of complete construction. In terms of
this presupposition an actual infinite, not given and not capable of
construction, can be represented with entire consistency.
But to return to the main assumption upon which Kant’s proof would seem
to rest: it is all-important to observe that Kant does not, either in
the _Critique_ or in any other of his writings, assert that the concept
of the actual infinite is inherently self-contradictory. This is a
matter in regard to which many of Kant’s critics have misrepresented his
teaching. Kant’s argument may, as we have just maintained, be found on
examination to involve the above assertion; but this, if clearly
established, so far from commending the argument to Kant, would have led
him to reject it as invalid. The passage in the _Dissertation_[1510] of
1770, which contains his most definite utterance on this point,
represents the view from which he never afterwards departed. It may be
quoted in full.
“Those who reject the actual mathematical infinite do so in a very
casual manner. For they so construct their definition of the
_infinite_ that they are able to extract a contradiction from it.
The infinite is described by them as _a quantity than which none
greater is possible_, and the mathematical infinite as a
multiplicity--of an assignable unit--than which none greater is
possible. Since they thus substitute _maximum_ for _infinitum_, and
a greatest multiplicity is impossible, they easily conclude against
this infinite which they have themselves invented. Or, it may be,
they entitle an infinite multiplicity an _infinite number_, and
point out that such a phrase is meaningless, as is, indeed,
perfectly evident. But again they have fought and overthrown only
the figments of their own minds. If, however, they had conceived
the mathematical infinite as a quantity which, when related to
measure, as its unity, is _a multiplicity greater than all number_;
and if furthermore, they had observed that _measurability_ here
denotes only the relation [of the infinite] to the standards of the
human intellect, which is not permitted to attain to a _definite
conception of multiplicity_ save by the successive addition of unit
to unit, nor to the _sum-total_ (which is called _number_) save by
completing this progress in a finite time; they would have
perceived clearly that what does not conform to the established law
of some subject need not on that account exceed all intellection.
An intellect may exist, though not indeed a human intellect, which
perceives a multiplicity distinctly in one intuition [_uno obtutu_]
without the successive application of a measure.”
The concluding sentences of this _Dissertation_ passage may be taken as
Kant’s own better and abiding judgment in regard to the question before
us. We must not argue from the impossibility of mentally traversing the
infinite to the impossibility of its existence. Indeed the essentials
of the above passage are restated in the ‘Observation’ on this
thesis.[1511] Thus the concept of the actual infinite is not only, as a
concept, perfectly self-consistent, it is also one which, in view of the
nature of time and of space, we are constrained to accept as a correct
representation of the actually given. The thesis of this first antinomy
runs directly counter to admitted facts. That Kant is here arguing in
respect to the world, and not merely in respect to space and time, does
not essentially alter the situation. For if space and time are
necessarily to be viewed as infinite, there can be no _a priori_
proof--none, at least, of the kind here attempted--that the world-series
may not be so likewise.
=Antithesis.=--(_a_) The world has no beginning in time; (_b_) has no
limits in space. In both these respects the world is infinite.
In these antitheses Kant assumes that space and time are actually
infinite, and from that assumption advances to the proof that this is
likewise true of the world in its spatial and temporal aspects. This, by
itself, ought to be sufficient evidence that Kant does not regard the
actual infinite as an inherently impossible conception. As the
antinomies are avowedly formulated from the realist, dogmatic standpoint
of ordinary consciousness, Kant is also enabled to assume that if the
world begins to be, it must have an antecedent cause determining it to
exist at that moment rather than at another.
=Antithesis= _a._ =Proof.=--Let us assume the opposite, namely, that the
world has a beginning. It will then be preceded by an empty time in
which it was not. But in an empty time no becoming is possible, since in
such a time no part possesses over any other any distinguishing
condition of existence rather than of non-existence. The world must
therefore be infinite as regards past time.
=Criticism.=--In this argument everything depends upon what is to be meant
by the term ‘world.’ If Kant means by it merely the material world, the
assumption of its non-existence does not leave only empty time and
space. Other kinds of existence may be possible, and in these a
sufficient cause of its first beginning may be found. The nature of
creative action will remain mysterious and incomprehensible, but that is
no sufficient reason for denying its possibility. If, on the other hand,
Kant means by the world ‘all that is,’ the assumption of its
non-existence is likewise the assumption of the non-existence of all
its possible causes. That, however, is for ordinary consciousness a
quite impossible assumption, since it runs counter to the causal
principle which is taken as universally valid. From this point of view
the argument consists in making an impossible assumption, and in then
pointing out the impossible consequence which must follow. By such a
mode of argument no conclusion can be reached. Kant’s decision ought
rather to have been that, as time is actually infinite, the world may be
so likewise, but that though _reality_ must in some form be eternally
existent, the _material world_ cannot be proved to be so by any _a
priori_ proof of the kind here given.
=Antithesis= _b._ =Proof.=--Let us assume the opposite, namely, that the
world is finite, existing in an empty limitless space. There will then
be not only a relation of things _in space_, but also of things _to
space_. But as the world is a totality outside of which no object of
intuition can be found, the relation of the world to empty space is a
relation to _no object_. Such a relation is nothing. Consequently the
opposite holds; the world must be infinitely extended.
=Criticism.=--That Kant himself felt the inadequacy of this argument, when
taken from the dogmatic standpoint, is indicated by the lengthy note
which he has appended to it, and which develops his own Critical view of
space as not a real independent object, but merely the form of external
intuition. From the standpoint of ordinary consciousness space is a
self-existent entity, and there is no insuperable difficulty in
conceiving a relation as holding between it and its contents. The
introduction of the opposed standpoint of the _Aesthetic_ therefore runs
directly counter to Kant’s own intention of expounding the antinomies
from the dogmatic standpoint which involves this realist view of space,
and of showing that they afford, in independence of the arguments of the
_Aesthetic_, an indirect proof of the untenableness of that
belief.[1512] The conclusion which ought to have been drawn is analogous
to that above suggested for thesis _a._ As space is actually infinite,
the material world may be so likewise; but that it actually is so,
cannot be established by an _a priori_ argument of the kind here
attempted.
SECOND ANTINOMY
=Thesis.=--Every composite substance in the world consists of simple
parts, and nothing anywhere exists save the simple or what is composed
of it.
=Proof.=--Let us assume the opposite, namely, that substances do not
consist of simple parts. If all composition be then removed in thought,
no composite part, and (as there are no simple parts) also no simple
part, and therefore nothing whatsoever, will remain. Consequently no
substance will be given. Either, therefore, it is impossible to remove
in thought all composition, or after its removal something that exists
without composition, _i.e._ the simple, must remain. In the former case
the composite would not itself consist of substances (with them
composition is a merely accidental relation, and they must, as
self-persisting beings, be able to exist independently of it). As this
contradicts our assumption, only the latter alternative remains, namely,
that the substantial compounds in the world consist of simple parts.
=Criticism.=--Kant here assumes, by his definition of terms, the point
which he professes to establish by argument. The substance referred to,
though never itself mentioned by name, is extended matter. Kant
identifies it with ‘composite substance.’ Substance, he further
dogmatically decides, is that which is capable of independent existence,
and to which all relations of composition are therefore merely
accidental. If these assumptions be granted, it at once follows that
composition cannot be essential to matter, and that when all composition
is thought away, its reality will be disclosed as consisting in simple
parts. Kant, however, makes no attempt to prove that extended matter can
be defined in any such terms. From the dogmatic point of view of
ordinary consciousness, though not from the sophisticated standpoint of
Leibniz, extension is of the very essence of matter; and, as Kant
himself believed,[1513] the continuity of extension is such as to
exclude all possibility of elimination of the composite. For he
maintains that, however far division be carried, the parts remain no
less composite than the whole from which the regress has started. On any
such view the extended and the composite are not equivalent terms. The
opposite of the composite is the simple; the opposite of the extended is
the non-extended. Kant is here surreptitiously substituting a Leibnizian
metaphysics in place of the empirical reality which is supposed to
necessitate the argument.
In the _Observation_ on this thesis Kant shows consciousness of the
defects of his argument. It does not apply to space, time, or change.
“We ought not to call space a _compositum_ but a _totum_, because
its parts are possible only in the whole, not the whole through the
parts.”[1514]
As Kant further states, he is speaking only of the simples of the
Leibnizian system. This thesis is “the dialectical principle of
monadology.” Again in the _Observation_ on the antithesis, in commenting
on the mathematical proof of the infinite divisibility of matter, Kant
even goes so far as to declare that the argument of the thesis is based
on an illegitimate substitution of things in themselves, conceived by
the pure understanding, for the appearances with which alone the
antinomy is concerned.[1515]
“...it is quite futile to attempt to overthrow, by sophistical
manipulation of purely discursive concepts, the manifest,
demonstrated truth of mathematics.”
=Antithesis.=--No composite thing in the world consists of simple parts,
and there nowhere exists in the world anything simple.
=Proof.=--Let us assume the opposite, namely, that a composite thing (as
substance) consists of simple parts. As all external relation, and
therefore all composition of substances, is only possible in space,
space must consist of as many parts as there are parts of the composite
that occupies it. Space, however, does not consist of simple parts, but
of spaces. The simple must therefore occupy a space. Now as everything
real which occupies a space contains in itself a manifold of
constituents external to one another, and therefore is composite, and as
a real composite is not composed of accidents (for without substance
accidents could not be outside one another), but of substances, the
simple would be a substantial composite, which is self-contradictory.
=Criticism.=--The Leibnizian standpoint is here completely deserted.
Instead of proceeding to demonstrate the direct opposite of the thesis,
Kant in this argument deals with the extended bodies of empirical
intuition. The proof given ultimately reduces to an argument from the
continuous nature of space to the continuous nature of the matter which
occupies it. But as the thesis and the antithesis thus refer to
different realities, the former to things in themselves conceived by
pure understanding, and the latter to the sensuous, no antinomy has
been shown to subsist. Antinomy presupposes that both the opposing
assertions have the same reference. Kant, as already noted, argues in
the _Observation_ to this antithesis that all attempts “made by the
monadists” to refute the mathematical proof of the infinite divisibility
of matter are quite futile, and are due to their forgetting that in this
discussion we are concerned only with appearances.
“The monadists have, indeed, been sufficiently acute to seek to
avoid this difficulty by not treating space as a condition of the
possibility of the objects of outer intuition (bodies), but by
taking these and the dynamical relation of substances as the
condition of the possibility of space. But we have a concept of
bodies only as appearances, and as such they necessarily presuppose
space as the condition of the possibility of all outer
appearance.”[1516]
How Kant, after writing these words, should still have left standing the
proof which he has given of the thesis may be partially explained as due
to the continuing influence of his earlier view,[1517] according to
which antinomy represents not a conflict between opposing views of the
world of ordinary consciousness, but between the demands of pure thought
and the forms of sensuous existence. That older view of antinomy here
gains the upper hand, notwithstanding its lack of agreement with the
general scheme of the _Dialectic_.
There is a further inconsistency in Kant’s procedure which may perhaps
be taken as indicating the early origin of this portion of the
_Critique_. He presents the mathematical proof of the continuity of
matter as conclusive. Yet in the _Metaphysical First Principles of
Natural Science_ (1786) he most emphatically states that “the infinite
divisibility of matter is very far from being proved through proof of
the infinite divisibility of space.”[1518]
Russell,[1519] in discussing the thesis and antithesis on their merits,
from the point of view of certain present-day mathematical theories,
makes the following criticism of Kant’s procedure.
“Here, again, the argument applies to things in space and time, and
to all collections, whether existent or not.... And with this
extension[1520] the proof of the proposition must, I think, be
admitted; only that _terms_ or _concepts_ should be substituted for
_substances_, and that, instead of the argument that relations
between substances are accidental (_zufällig_), we should content
ourselves with saying that relations imply terms and complexity
implies relations.”
Russell further argues that Kant’s assumption in the antithesis, that
“space does not consist of simple parts, but of spaces,” cannot be
granted. It
“...involves a covert use of the axiom of finitude, _i.e._ the
axiom that, if a space does consist of points, it must consist of
some finite number of points. When once this is denied, we may
admit that no finite number of divisions of a space will lead to
points, while yet holding every space to be composed of points. A
finite space is a whole consisting of simple parts, but not of any
finite number of simple parts. Exactly the same thing is true of
the stretch between 1 and 2. Thus the antinomy is not specially
spatial, and any answer which is applicable in Arithmetic is
applicable here also. The thesis, which is an essential postulate
of Logic, should be accepted, while the antithesis should be
rejected.”
But, as above observed,[1521] those mathematicians who adopt this view
so alter the meaning of the term point that it would perhaps be equally
true to say that the thesis, as thus interpreted by Russell, coincides
with what Kant believes himself to be asserting in the antithesis.
THIRD ANTINOMY
=Thesis.=--Causality according to the laws of nature is not the only
causality from which the appearances of the world can be deduced. There
is also required for their explanation another, that of freedom.
=Proof.=--Let us assume the opposite. In that case everything that happens
presupposes a previous state upon which it follows according to a rule.
That previous state is itself caused in similar fashion, and so on _in
infinitum_. But if everything thus happens according to the mere laws of
nature, there can never be a first beginning, and therefore no
completeness of the series on the side of the derivative causes. But the
law of nature is that nothing happens without a cause _sufficiently_
determined _a priori_. If, therefore, all causality is possible only
according to the laws of nature, the principle contradicts itself when
taken in unlimited universality. Such causality cannot therefore be the
sole causality possible. We must admit an absolute spontaneity, whereby
a series of appearances, that proceed according to laws of nature,
begins by itself.
=Criticism.=--The vital point of this argument lies in the assertion that
the principle of causality calls for a _sufficient_ cause for each
event, and that such sufficiency is not to be found in natural causes
which are themselves derivative or conditioned. As the antecedent series
of causes for an event can never be traced back to a first cause, it can
never be completed, and can never, therefore, be sufficient to account
for the event under consideration. Either, therefore, the principle of
causality contradicts itself, or some form of free self-originative
causality must be postulated. This argument cannot be accepted as valid.
Each natural cause is sufficient to account for its effect. That is to
say, the causation is sufficient _at each stage_. That the series of
antecedent causes cannot be completed is due to its actual infinitude,
not to any insufficiency in the causality which it embodies.[1522] To
prove his point, Kant would have to show that the conception of the
actual infinite is inherently self-contradictory; and that, as we have
already noted, he does not mean to assert. His argument here lies open
to the same criticism as we have already passed upon his argument in
proof of the thesis of the first antinomy.
=Antithesis.=--There is no freedom; everything in the world proceeds
solely in accordance with laws of nature.
=Proof.=--Let us assume the opposite. Free causality, _i.e._ the power of
absolute origination, presupposes the possibility of a state of the
cause which has no causal connection with its preceding state, and which
does not follow from it. But this is opposed to the law of causality,
and would render unity of experience impossible. Freedom is therefore an
empty thought-entity (_Gedankending_), and is not to be met with in any
experience.
=Criticism.=--We may first observe the strange relation in which the proof
of the thesis stands to that of the antithesis. According to the former,
freedom must be postulated because otherwise the principle of causality
would contradict itself. According to the latter, freedom is impossible,
and for the same reason. Now, as Erhardt has pointed out,[1523] a
principle cannot be reconciled with itself through the making of an
assumption which contradicts it. That would only be the institution of a
second contradiction, not the removal of the previous conflict. If the
proof of the thesis be correct, that of the antithesis must be false; if
the proof of the antithesis be correct, that of the thesis must be
invalid. For though the thesis and the antithesis may themselves
contradict one another, such conflict must not exist between the grounds
upon which they establish themselves. If the reasons cited in their
support are contradictory of one another, the total argument is rendered
null and void. The supporting proofs being contradictory of one another,
nothing whatsoever has been established. There will remain as a pressing
and immediate problem the task of distinguishing the truth from among
the competing alternatives; and until this has been done, the argument
cannot proceed. The assumption of freedom either does or does not
contradict the principle of causality. Antinomy is not the simple
assertion that both A and not-A are true, but that A and not-A, though
contradictory of one another, can both be established by arguments in
which such contradiction does not occur.[1524]
The proof given of the thesis would seem, as already noted, to be
untenable. The principle of natural causality is not self-contradictory.
What now is to be said regarding the proof of the antithesis? If the
principle of natural causality be formulated as asserting that every
event has an _antecedent_ cause determining it to exist, then certainly
free, spontaneous, or self-originating causality is excluded. Here, as
in Kant’s proof of the antithesis of the first antinomy, everything
depends upon definition of the terms employed. It must be borne in mind
that the antinomies are asserted to exist only on the dogmatic level.
Critical considerations must not, therefore, be allowed to intervene.
Now for ordinary consciousness the concept of causality has a very
indefinite meaning, and a very wide application. Causation may be
spontaneous as well as mechanical, spiritual as well as material. All
possibilities lie open, and no mere reference to the concept of causal
dependence suffices to decide between them. Free causality, so far as
_dogmatic_ analysis of the causal postulate can show to the contrary,
may or may not be possible.[1525] Kant has failed to establish the
antithesis save by the surreptitious introduction of conclusions which
presuppose the truth of his Critical teaching. This is especially shown
in the emphasis laid upon ‘unity of experience.’ The further
statement[1526] that freedom means lawlessness is only true if Kant’s
teaching is mutilated by reduction merely to its assertion of the
objective validity of the mechanistic principles of natural science.
Kant is both running with the hare and hunting with the hounds.
Though this antinomy is chiefly concerned with the problem of freedom,
_i.e._ of spontaneous origination _within_ the world, the proof of the
thesis refers only to the cosmological problem of a first cause.[1527]
The reasons of this oscillation we shall have occasion to consider in
dealing with the fourth antinomy. The terms world and nature play the
same ambiguous part as in the antithesis of the first antinomy; they
tend to be employed in the narrower, mechanistic sense of Kant’s own
Critical teaching.
FOURTH ANTINOMY
As the proofs of the thesis and antithesis proceed on lines identical
with those of the third antinomy, I shall omit detailed statement of
them.[1528] Kant again argues from the fact that every change has a
condition which precedes it in time. There is no difference in the
proofs themselves, but only in the nature of the inference which they
are made to support. In the third antinomy they lead to the assertion
and denial of free causality; in the fourth antinomy they lead to the
assertion and denial of an absolutely necessary being. The assertion is
required in order to save the principle of causality from
self-contradiction; the denial is also necessary, and for the same
reason. The illegitimacy of this procedure has already been pointed
out.[1529] Though the thesis and the antithesis will, if antinomy be
assumed to represent an actual conflict, contradict one another, no
such conflict is allowable in the grounds which profess to establish
them. We must not assert, as _argument_, that both A and not-A are true.
In the _Observation_ on the antithesis[1530] Kant has himself taken
notice of this “strange” situation.
“From the same ground on which, in the thesis, the existence of an
original being was inferred, its non-existence is inferred, and
that with equal stringency.”
A necessary being is inferred to exist, because the past series of
events cannot contain all the conditions of an event, unless the
unconditioned is to be found among them. A necessary being is denied to
exist, because the series of merely conditioned events contains all the
conditions that there are. Kant’s defence of this procedure is as
follows:
“Nevertheless, the method of argument in both cases is entirely in
conformity even with ordinary human reason, which frequently falls
into conflict with itself from considering its object from two
different points of view. M. de Mairan[1531] regarded the
controversy between two famous astronomers, which arose from a
similar difficulty in regard to choice of standpoint, as a
sufficiently remarkable phenomenon to justify his writing a special
treatise upon it. The one had argued that _the moon revolves on its
own axis_, because it always turns the same side towards the earth.
The other drew the opposite conclusion that _the moon does not
revolve on its own axis_, because it always turns the same side
towards the earth. Both inferences were correct, according to the
point of view which each chose in observing the moon’s motion.”
This example is not really relevant. In spite of Kant’s assertion to the
contrary, the point of view is one and the same in thesis and in
antithesis. In both cases the absolutely necessary being is viewed as
the first of the changes in the world of sense. To maintain that when
thus viewed it both is and is not demanded by the law of causality, is
as impossible as to assert that in one and the same meaning of our terms
the moon both does and does not revolve on its own axis.
That the proofs of the fourth antinomy are identical with those of the
third is due to the fact that Kant, under the stress of his
architectonic,[1532] is striving to construct four antinomies while only
three are really distinguishable. The third and fourth antinomies
coincide as formulations of the problem whether or not the conditioned
implies, and originates in, the unconditioned. The precise
determination of this unconditioned, whether as free causality or as a
necessary being, or in any other way, is a further problem, and does not
properly fall within the scope of the _cosmological_ inquiries, which
are alone in place in this division of the _Critique_.
The manner in which Kant, in treating of freedom, makes the
transition[1533] from the cosmological (or theological) unconditioned to
the psychological is significant. The cosmological unconditioned is
proved to exist by the argument of the thesis, and its existence is at
once interpreted as establishing at least in this one case the actuality
of free spontaneous causality. Kant remarks that this
“...transcendental Idea of freedom does not by any means constitute
the entire content of the psychological concept of that name, which
is mainly empirical, but only that of absolute spontaneity of
action.... The necessity of a first beginning, due to freedom, of a
series of appearances we have demonstrated only in so far as it is
required for the conceivability of an origin of the world.... But
as, after all, the power of spontaneously originating a series in
time has thus been proved (though not understood), it is now
permissible for us to admit within the course of the world
different series as capable in their causality of beginning of
themselves, and so to attribute to their substances a power of
acting from freedom.”
That each such successive series in the world can only have a relatively
primary beginning, and must always be preceded by some other state of
things, is no sufficient objection to such causality.
“For we are here speaking of an absolutely first beginning not in
time, but in causality. If, for instance, I at this moment arise
from my chair in complete freedom, without being necessarily
determined thereto by the influence of natural causes, a new
series, with all its natural consequences _in infinitum_, has its
absolute beginning in this event, although the event itself is
only, with regard to time, the continuation of a preceding series.”
Thus Kant’s proof of freedom in the thesis of the third antinomy is
merely a corollary from his proof of the existence of a cosmological or
theological unconditioned; and further, this freedom is not, like the
cosmological unconditioned, proved to exist, but only to be “admissible”
as a possibility. Similarly in the antithesis, the only disproof of
freedom is the disproof of unconditioned causality _in general_. The
antinomy deals with the general opposition and relation between the
contingent and the unconditioned.
It is this same opposition exactly which constitutes the subject-matter
of the fourth antinomy. The terms used are different, but their meanings
are one and the same. For though Kant substitutes ‘absolutely necessary
being’ for ‘unconditioned causality,’ the former is still conceived as
belonging to the world of sense, as the unconditioned origin of its
changes. And as Kant is careful to add, only the causal, cosmological
argument can be employed to establish the existence of an absolutely
necessary being; nothing can legitimately be inferred from the mere
Idea. The verbal change is consequently verbal only; the argument of the
fourth antinomy coincides in result no less than in method of proof with
the argument of the third. It is impossible to define the unconditioned
in any more specific fashion save by an enquiry which entirely
transcends the scope of the argument that Kant is here presenting.
Kant’s procedure also lies open to the further objection that the
conception of an absolutely necessary being, which he here introduces
without preliminary analysis or explanation, is later shown by him[1534]
to be devoid of significance. He employs it, but precludes himself from
either investigating it or from drawing any serviceable consequences
from it. The situation is not without the elements of comedy. In order
to seem to mark a real distinction between the fourth and the third
antinomies, Kant has perforce to trespass upon the domain of theology;
but as he is aware that the trespass is forbidden, he seeks to mitigate
the offence by returning from the foray empty-handed. To such unhappy
straits is he again reduced by his over-fond devotion to architectonic.