SECTION II. Antithetic of Pure Reason[1503]

ANTITHETIC OF PURE REASON

”[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. 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. 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.”

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. 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.

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. 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 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. 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. 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, 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.”

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.

“...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.”

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, 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.”

Russell, 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 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, 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. 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, 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.

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. 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 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. 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. 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. 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 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 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, 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 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 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.