Part 2 / Book 2 — CHAPTER II THE ANTINOMY OF PURE REASON[1495]

CHAPTER II THE ANTINOMY OF PURE REASON[1495]

This introduction summarises the preceding argument, and distinguishes the new problems of Antinomy from those of the Paralogisms. In rational psychology pure Reason attains, as it were, euthanasia; in the antinomies an entirely different situation is disclosed. For though rational cosmology is able to expound itself in a series of demonstrated theses, its teaching stands in irreconcilable conflict with the actual nature of appearances, as expressed through a series of antitheses which are demonstrable in an equally cogent manner.

SECTION I SYSTEM OF THE COSMOLOGICAL IDEAS[1496]

The first eight paragraphs of this section are of great textual interest. They must have been written at a time when Kant still intended to expound his entire criticism of metaphysical science in the form of a doctrine of antinomy. For they define the Ideas of Reason as exclusively cosmological,[1497] and give a very different explanation of their origin from that which has been expounded in the preceding chapters. Evidently, therefore, this part of the section must have been written prior to Kant’s formulation of the metaphysical deduction from the three species of syllogism. This is supported by the fact that the argument begins anew, just as if the matter had not previously been discussed; and that, though a new view of the nature of Reason is propounded, there is not the least mention of the more Idealist view which it displaces. Reason, Kant here teaches, is not a faculty separate from the understanding, and does not therefore produce any concept peculiar to itself. Reason is simply a name for the understanding in so far as it acts independently of sensibility, and seeks, by means of its pure forms, in abstraction from all empirical limitations, to grasp the unconditioned. “The transcendental Ideas are in reality nothing but categories extended to the unconditioned.” The intelligible, as thus conceived by the understanding, expresses itself, as he later shows, in a series of theses; while the sensuous expresses its opposite and conflicting character in a series of antitheses.

Yet not all categories yield a concept of the unconditioned. That is possible only to those which concern themselves with a series of members conditioning and conditioned, and in reference to which, therefore, the postulate of an unconditioned would seem to be legitimate, viz.: (1) unconditioned quantity in space and time; (2) unconditioned quality (indivisibility and simplicity) of reality in space (matter); (3) unconditioned causality of appearances; (4) unconditioned necessity of appearances. As this arrangement is determined by the needs of Kant’s architectonic, no detailed comment is here called for. Its consequences we shall have ample opportunity to consider later. As already noted, Kant’s statement in A 414 = B 441, that “the category of substance and accident does not lend itself to a transcendental Idea,” shows very clearly that, at the time when he composed this passage, he had not yet bethought himself of placing a separate and independent Idea at the basis of rational psychology. But as Kant here strives to follow the fourfold arrangement of the categories, the content of these paragraphs must either have been later recast or have been composed in the interval between his discovery of the metaphysical deduction of the categories and his formulation of the corresponding deduction of the Ideas from the three forms of syllogism. It may also be observed that the derivation of the cosmological Idea from the hypothetical syllogism, which embodies only the category of causality, clashes with the above specification of it in terms of all four rubrics of category.

The remaining paragraphs (ninth to thirteenth) of this section must be of later date, as they are developed in view of the independent treatment of the theological Ideal.[1498] (Adickes, in dating the ninth and tenth paragraphs with the preceding instead of with the concluding paragraphs, would seem to have overlooked this fact.) In order to justify the treatment of the Ideas of a first cause and of unconditioned necessity, as cosmological, Kant now asserts that the antinomies concern only appearances—“our [cosmical] Ideas being directed only to what is unconditioned among the appearances,”[1499] and not to noumena.[1500] His explanation of the nature of transcendental illusion, and of the antinomies in particular, as being due to a failure to distinguish between appearance and things in themselves, is thus ruthlessly sacrificed to considerations of architectonic. Kant could not, of course, consistently hold to the position here adopted; but it causes him from time to time, especially in dealing with the third and fourth antinomies, to make statements which tend seriously to obscure the argument and to bewilder the careful reader.

Kant is far from clear as to the relation in which the concepts of the totality of conditions and of the unconditioned stand to one another.[1501] In A 322 = B 379 they would seem to be taken as exactly equivalent concepts. In A 416-17 = B 443-5 they are apparently regarded as distinct, the former only leading up to the latter. But discussion of this important point must meantime be deferred.[1502]

SECTION II 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.

SECTION III THE INTEREST OF REASON IN THIS SELF-CONFLICT[1535]

This section, though extremely important, requires no lengthy comment. It is lucid and straightforward. It may be summarised as follows. The theses and the antitheses rest upon diverse and conflicting interests. The theses, though expressed in dry formulas, divested of the empirical features through which alone their true grandeur can be displayed, represent the proud pretensions of dogmatic Reason. The antitheses give expression to principles of pure empiricism. The former are supported by interests of a practical and popular character: upon them morals and religion are based. The latter, while conflicting with our spiritual interests, far exceed the theses in their intellectual advantages. This explains

“...the zelotic passion of the one party, and the calm assurance of the other, and why the world hails the one with eager approval, and is implacably prejudiced against the other.”

No legitimate objection could be raised against the principles of the empirical philosopher, if he sought only to rebuke the rashness and presumption of Reason when it boasts of knowledge, and when it represents as speculative insight that which is grounded only in faith.

“But when empiricism itself, as frequently happens, becomes dogmatic ..., and confidently denies whatever lies beyond the sphere of its intuitive knowledge, it betrays the same lack of modesty; and that is all the more reprehensible owing to the irreparable injury which is thereby caused to the practical interests of Reason.”

Each party asserts more than it knows. The one allows our practical interests to delude Reason as to its inherent powers; the other would so extend empirical knowledge as to destroy the validity of our moral principles. Kant regards the opposition as being historically typified by the contrasted systems of Platonism and Epicureanism. It befits us, as self-reflecting beings, to free ourselves, at least provisionally, from the partiality of those divergent interests, and by application of “the sceptical method,” unconcerned about consequences, to penetrate to the primary sources of this perennial conflict. As Kant states in the next section, the conflict is of such a character as to be genuinely resolvable.

This section must have been written, or at least first sketched, at the time when Kant still intended to bring his whole criticism of the metaphysical sciences within the scope of his doctrine of antinomy.[1536]

SECTION IV OF THE TRANSCENDENTAL PROBLEMS OF PURE REASON, IN SO FAR AS THEY ABSOLUTELY MUST BE CAPABLE OF SOLUTION[1537]

There are sciences the very nature of which requires that every question which can occur in them must be completely answerable from what can be presumed to be known. This is true of the science of ethics. When I ask to what course of action I am committed in moral duty, the question must be answerable in terms of the considerations which have led to its being propounded. For there can be no moral obligation in regard to that of which we cannot have knowledge. We must not plead that the problem is unanswerable; a solution must be found. Kant proceeds to argue that this is no less true of transcendental philosophy.

“...it is unique among speculative sciences in that no question which concerns an object given to pure Reason is insoluble for this same human Reason, and that no excuse of an unavoidable ignorance, or of the unfathomable depth of the problem, can release us from the obligation to answer it thoroughly and completely. That very concept which enables us to ask the question must also qualify us to answer it, since, as in the case of right and wrong, the object is not to be met with outside the concept.”

The third and fourth paragraphs would seem to be later interpolations. The section, like Section III., must have been written at the time when Kant still regarded the doctrine of antinomy as covering the entire field of metaphysics. Transcendental philosophy is identified with cosmology, as dealt with in the antinomies. But in the third paragraph the former is taken as a wider term. Also, in the first two paragraphs the problems of pure Reason are regarded as soluble because their objects are not to be met with outside the concepts of them; whereas in the third paragraph they are viewed as soluble because their object is given empirically. Again, in the second paragraph transcendental philosophy has been taken as unique among speculative [i.e. theoretical] sciences; in the fourth paragraph mathematics is placed alongside it.

Examination of this section as a whole (and the same is true of the immediately following section) justifies the conclusion that at the time when it was written Kant regarded the Ideas of Reason as having a purely and exclusively regulative function, and consequently as exhausting their inherent meaning in their empirical reference. He regards them as entirely lacking in metaphysical significance. They are invented by Reason for Reason’s own satisfaction, and must therefore yield in their internal content the explanation of their existence, and must also supply a complete and thorough answer to all problems which are traceable to them. A dogmatic (i.e. ontological) solution of the antinomies is, as we have already found, impossible; the Critical solution considers the question subjectively,

“...in accordance with the foundation of the knowledge upon which it is based.”[1538] “For your object is only in your brain, and cannot be given outside it; so that you have only to take care to be at one with yourself, and to avoid the amphiboly which transforms your Idea into a supposed representation of an object which is empirically given and therefore to be known according to the laws of experience.”[1539]

Kant’s argument in proof of this purely subjective interpretation of the Ideas consists in showing that they are not presented in any given appearances, and are not even necessary to explain appearances. The unconditioned, whether of quantity, of division, or of origination, has nothing to do with any experience, whether actual or possible.

“You would not, for instance, in any wise be able to explain the appearances of a body better, or even differently, if you assumed that it consists either of simple or of inexhaustibly composite parts; for neither a simple appearance nor an infinite composition can ever come before you. Appearances demand explanation only in so far as the conditions of their explanation are given in perception, [and the unconditioned can never be so given].”[1540]

This standpoint, at once sceptical and empirical, is further developed in the next section.

SECTION V SCEPTICAL REPRESENTATION OF THE COSMOLOGICAL QUESTIONS[1541]

Applying the “sceptical method,”[1542] Kant argues that even supposing one or other party could conclusively establish itself through final refutation of the other, no advantage of any kind would accrue. The victory would be a fruitless one, and the outcome “mere nonsense.”[1543] The sole validity of the Ideas lies in their empirical reference; and yet that reference is one which proves them to be, when objectively interpreted, entirely meaningless. The cosmological Idea is always either too large or too small for any concept of the understanding. No matter what view is taken, the only possible object (viz. that yielded by experience) will not fit into it. If the world has no beginning, or is infinitely divisible, or has no first cause, the regress transcends all empirical concepts; while if the world has a beginning, is composed of simple parts, and has a first cause, it is too small for the concepts through which alone it can be experienced. In other words, the cosmological Ideas are always either too large or too small for the empirical regress, and therefore stand condemned by sense-experience, which can alone impart relation to an object, i.e. truth and meaning to any concept. For, as Kant explicitly states, we must not reverse this relation and condemn empirical concepts, as being in the one case too small, and in the other case too large for the Idea. Experience, not Ideas, is the criterion alike of reality and of truth.

“The possible empirical concept is, therefore, the standard by which we must judge whether the Idea is mere Idea and thought-entity (Gedankending), or whether it finds its object in the world.”[1544]

When two things are compared, that for the sake of which the other exists is the sole proper standard. We do not say “that a man is too long for his coat, but that the coat is too short for the man.”[1545] We are thus confirmed in the view that the antinomies rest upon a false view of the manner in which the object of the cosmological Ideas can be given; and are set upon the track, followed out in the next section, of the illusion to which they are due.

This reduction of the Ideas to mere thought-entities is one of the two alternative views which, as we have already stated,[1546] compete with one another throughout the entire Dialectic. We may, for instance, compare the above explanation of the conflict between the Ideas and experience with that given in A 422 = B 450. In the latter passage the antinomies are traced to a conflict between Reason and understanding. If the unity is adequate to the demands of Reason, it is too great for the understanding; if it is adequate to the understanding, it is too small for Reason. Kant does not here allow that the claims of Reason are ipso facto condemned through the incapacity of experience to fulfil them. On the contrary, he implies that it is through the Ideas that we come to realise the merely phenomenal character of everything experienced.

Our task, in this Commentary, is only to distinguish the passages in which those two conflicting tendencies appear, and to trace the consequences which follow from Kant’s alternation between them. Discussion of their significance had best be deferred to the close of the Dialectic, where Kant dwells upon the regulative function of Reason. At present we need merely note that the main content of the above sections, in which the sceptical view is expounded, is of early date, prior to the working out of the Paralogisms and of the Ideal.

SECTION VI TRANSCENDENTAL IDEALISM AS THE KEY TO THE SOLUTION OF THE COSMOLOGICAL DIALECTIC[1547]

In this section subjectivism is dominant. The type of transcendental idealism expounded is that earlier and less developed form which connects with the doctrine of the transcendental object.[1548] It shows no trace of Kant’s maturer teaching. No distinction is drawn between representation and the objects represented. To the transcendental object, the “purely intelligible cause” of appearances in general, and to it alone, Kant ascribes “the whole extent and connection of our possible perceptions.”[1549] Appearances exist only in the degree to which they are constructed in experience. As they are mere representations, they cannot exist outside the mind. Independently of such construction, they may indeed be said to be given in the transcendental object, but they only become objects to us on the supposition that they can be reached through extension of the series of our actual perceptions. It is in this form alone, as conceived in a regressive series of possible perceptions, and not as having existed in itself, that even the immemorial past course of the world can be represented as real;

“...so that all events which have taken place in the immense periods that have preceded my own existence mean really nothing but the possibility of extending the chain of experience from the present perception back to the conditions which determine it in time.”[1550]

A similar interpretation has to be given to all propositions which assert the present reality of that which has never been actually experienced.

“In outcome it is a matter of indifference whether I say that in the empirical progress in space I can meet with stars a hundred times farther removed than the outermost now perceptible to me, or whether I say that they are perhaps to be met with in cosmical space even though no human being has ever perceived or ever will perceive them. For even if they were given as things in themselves, without relation to possible experience,[1551] they are still nothing for me, and therefore are not objects, save in so far as they are contained in the series of the empirical regress.”[1552]

The distinction between appearances and things in themselves must always, Kant observes, be borne in mind when we are interpreting the meaning of our empirical concepts; and this is especially necessary when those concepts are brought into connection with the cosmological Idea of an unconditioned. The antinomies are due to a failure to appreciate this fundamental distinction, and the key to their solution lies in its recognition.

“It would be an injustice to ascribe to us that long-decried empirical idealism which, while it admits the genuine actuality of space, denies the existence of the extended beings in it....”[1553]

This is in line with the passages from the Prolegomena commented upon above.[1554]

SECTION VII CRITICAL DECISION OF THE COSMOLOGICAL CONFLICT OF REASON WITH ITSELF[1555]

Kant’s argument is as follows. The antinomies rest upon the principle that if the conditioned be given, the entire series of all its conditions is likewise given. If the objects of the senses were independently real, there would be no escape from this assumption, and the dialectical conflict would consequently be irresolvable. Transcendental idealism, as above stated, reveals a way out of the dilemma. As appearances are merely representations, their antecedent conditions do not exist as appearances, save in the degree in which they are mentally constructed. Though the appearances are given, their empirical conditions are not thereby given. The most that we can say is that a regress to the conditions, i.e. a continued empirical synthesis in that direction, is commanded or required. The cosmological argument can thus be shown to be logically invalid. The syllogism, which it involves, is as follows:

If the conditioned be given, the entire series of all its conditions is likewise given.

The objects of the senses are given.

Therefore the entire series of all their conditions is likewise given.

In the major premiss the concept of the conditioned is employed transcendently (Kant says transcendentally), in the minor empirically. But though the inference thus commits the logical fallacy of sophisma figurae dictionis, the ground of its occurrence, and the reason why it is not at once detected, lie in a natural and inevitable illusion which leads us to accept the sensible world in space as being independently real. Only through Critical investigation can the deceptive power of this illusion be overcome. Owing to its influence, the above fallacy has been committed by dogmatists and empiricists alike. It can be shown that in refuting each other

... “they are really quarrelling about nothing, and that a certain transcendental illusion has caused them to see a reality where none is to be found.”[1556]

The existence of antinomy, Kant further argues, presupposes that theses and antitheses are contradictory opposites, i.e. that no third alternative is possible. When opposed assertions are not contradictories but contraries, the opposition, to use Kant’s terms, is not analytical but dialectical. Both may be false; for the one does not merely contradict the other, but makes, in addition, a further statement on its own account. Now examination of the illusion above described enables us to perceive that the opposites, in reference to which antinomy occurs, are of this dialectical character. Theses and antitheses are alike false. Since the world does not exist as a thing in itself, it exists neither as an infinite whole nor as a finite whole, but only in the degree in which it is constructed in an empirical regress. We must not apply “the Idea of absolute totality, which is valid only as a condition of things in themselves,”[1557] to appearances. (The words which I have italicised mark the emergence of Kant’s non-sceptical, non-empirical view of the nature and function of the Ideas of Reason.) Thus antinomy, rightly understood, does not favour scepticism, but only the “sceptical method,” and indeed yields an indirect proof of the correctness of Critical teaching. This proof may be presented in the form of a dilemma. If the world is a whole existing in itself, it is either finite or infinite. But the former alternative is refuted by the proofs given of the antitheses, and the latter alternative by the proofs of the theses. Therefore the world cannot be a whole existing in itself. From this it follows that appearances are nothing outside our representations; and that is what is asserted in the doctrine of transcendental idealism.

In A 499 = B 527 Kant uses ambiguous language,[1558] which can be interpreted as asserting that in the regress there can be no lack of given conditions. Such a statement would presuppose positive knowledge regarding the unknown transcendental object.[1559] The opposite, more correct, view is given in A 514-15 = B 542-3 and A 517 ff. = B 545 ff., though in the latter passage with a reversion to the above position.[1560]

The earlier manuscripts, which Kant has so far been employing, probably terminate either, as Adickes suggests,[1561] at the end of this section, or at the close of Section VIII., which is of doubtful date. Section IX. is certainly from a later period; it represents a more complex standpoint, in which Reason is no longer viewed as possessing a merely empirical function, and in which consequently the theses and antitheses are no longer indiscriminately denounced as being alike false. Under the influence of his later, more Idealistic preoccupations, Kant so far modifies the above solution as to assert that in the ease of the last two antinomies both theses and antitheses are true, when properly interpreted.

SECTION VIII THE REGULATIVE PRINCIPLE OF PURE REASON IN REGARD TO THE COSMOLOGICAL IDEAS[1562]

The principle of pure Reason, correctly formulated, is that when the conditioned is given a regress upon the totality of its conditions is set as a problem. As such it is valid,

“...not indeed as an axiom ... but as a problem for the understanding ..., leading it to undertake and to continue, according to the completeness in the Idea, the regress in the series of conditions of any given conditioned.”[1563]

It does not anticipate, prior to the regress, what actually exists as object, but only postulates, in the form of a rule, how the understanding ought to proceed. It does not tell us whether or how the unconditioned exists, but how the empirical regress is to be carried out under the guidance of a mere Idea. Such a rule can be regulative only, and the Idea of totality which it contains must never be invested with objective reality. As the absolutely unconditioned can never be met with in experience, we know, indeed, beforehand that in the process of the regress the unconditioned will never be reached. But the duty of seeking it by way of such regress is none the less prescribed.

Kant proceeds to give a somewhat bewildering account of the familiar distinction between progressus in infinitum and progressus in indefinitum, and to draw a very doubtful distinction between the series in division of a given whole and the series in extension of it.[1564] The illustration from the series of human generations is an unfortunate one; the discovery that it began at some one point in the past would not necessarily violate any demand of Reason. Such a series is not comparable with those of space, time, and causality.[1565] The only important result of this digression is the conclusion that whatever demand be made, whether of regress in infinitum or of regress in indefinitum, in neither case can the series of conditions be regarded as being given as infinite in the object.

“The question, therefore, is no longer how great this series of conditions may be in itself, whether finite or infinite, for it is nothing in itself; but how we are to carry out the empirical regress, and how far we should continue it.”[1566]

We have already noted[1567] Kant’s ambiguous suggestion in A 499 = B 527, that in the empirical regress there can be no lack of given conditions. The statement, thus interpreted, is illegitimate. The most that he can claim is that, were further sensations not forthcoming, we should still have to conceive those last obtained as being preceded by empty space and time, and as lacking in any experienced cause. Under such circumstances we should experience neither finitude nor unconditionedness, but only incapacity to find a content suitable to the inexhaustible character of the spatial and temporal conditions of experience, or in satisfaction of our demand for causal antecedents. In A 514-15 = B 542-3 Kant shows consciousness of this difficulty, but in dealing with it adopts a half-way position which still lies open to objection. He recognises that, since no member of a series can be empirically given as absolutely unconditioned, a higher member is always possible, and that the search for it is therefore prescribed; none the less he asserts that in regard to given wholes we are justified in taking up a very different position, namely, that the regress in the series of their internal conditions does not proceed, as in the above case, in indefinitum, but in infinitum, i.e. that in this case more members exist and are empirically given than we can reach through the regress. In given wholes we are commanded to find more members; in serial extension we are justified only in inquiring for more. This half-way position is a makeshift, and is in no respect tenable. The evidence for the infinite extensibility of space and time is as conclusive as for their infinite divisibility. And when we consider sensuous existence under these forms, it is just as possible that the transcendental object may, beyond a certain point, fail to supply material for further division, as that it may fail to yield data for further expansion. What Kant asserts of the latter, that further advance must always remain as a possibility, and for that Reason must always call for the open mind of further inquiry, without any attempted anticipatory assertion either pro or contra, alone represents the true Critical standpoint. The cessation of data may really, however, be due to an increase in the subtlety of the conditioning processes that incapacitates them from acting upon our senses;[1568] by indirect means this disability may be overcome. Reason, in its conception of an unconditioned, prescribes to us a task that is inexhaustible in its demands. We have no right to lay down our intellectual arms before any barrier however baffling, or to despair before any chasm however empty and abrupt.

SECTION IX THE EMPIRICAL EMPLOYMENT OF THE REGULATIVE PRINCIPLE OF REASON IN REGARD TO ALL COSMOLOGICAL IDEAS[1569]

SOLUTION OF THE FIRST AND SECOND ANTINOMIES

Statement.—The fundamental fact upon which, as Kant has already stated, the regulative principle of Reason is based, is that it is impossible to experience an absolute limit. It is always possible that a still higher member of the series may be found; and that being so, it is our duty to search for it. But as we are here dealing with possibilities only, the regress is in indefinitum, not in infinitum.

“...we must seek the concept of the quantity of the world only according to the rule which determines the empirical regress in it. This rule says no more than that however far we may have attained in the series of empirical conditions, we should never assume an absolute limit, but should subordinate every appearance, as conditioned, to another as its condition, and that we must then advance to this condition. This is the regressus in indefinitum, which, as it determines no quantity in the object, is clearly enough distinguishable from the regressus in infinitum.”[1570]

We are acquainted only with the rule, and not with the whole object. Any assertion, therefore, which we can make, must be dictated solely by the rule, and be an expression of it. Neither the thesis nor the antithesis of the first antinomy is valid; there is a third alternative. The sensible world is neither finite nor infinite in extent; it is infinitely extensible, in terms of the rule.

Unfortunately Kant is not content to leave his conclusion in this form. He complicates his argument, and bewilders the reader, by maintaining that this is a virtual acceptance of the antithesis, in that we assert negatively, that an absolute limit in either time or space is empirically impossible;[1571] and affirmatively, that the regress goes on in indefinitum, and consequently has no absolute quantity.

Kant also repeats the argument of the preceding section in regard to given wholes.[1572] When the problem is that of subdivision, the regress starts from a given whole, and therefore from a whole whose conditions (the parts) are given with it. The division is, therefore, in infinitum, and not merely in indefinitum. This does not, however, he argues, mean that the given whole consists of infinitely many parts. For though the parts are contained in the intuition of the whole, yet the whole division arises only through the regress that generates it. It is a quantum continuum, not a quantum discretum.[1573] This argument has been criticised above.[1574] Kant here ignores the possibility that the parts of matter, though extended, may be physically indivisible, or that they may be centres of force which control, but do not occupy, a determinate space.

REMARKS ON THE DISTINCTION BETWEEN THE MATHEMATICAL-TRANSCENDENTAL AND THE DYNAMICAL-TRANSCENDENTAL IDEAS[1575]

Statement.—Kant again[1576] introduces the distinction between the mathematical and the dynamical. The mathematical Ideas synthesise the homogeneous, the dynamical may connect the heterogeneous. In employing the former we must therefore remain within the phenomenal; through the latter we may be able to transcend it. The way is thus opened for propounding, in regard to the third and fourth antinomies, a solution in which the pretensions of Reason no less than those of understanding may find satisfaction. Whereas both the theses and the antitheses of the first and second antinomies have to be declared false, those of the third and fourth antinomies may both be true—the theses applying to the intelligible realm, and the antitheses to the world of sense.

Comment.—When the distinction between the mathematical and the dynamical is thus extended from the categories to the Ideas, its validity becomes highly doubtful. Space and time are certainly themselves homogeneous, and the categories of quality and quantity, in so far as they are mathematically employed, may perhaps be similarly described. But when the term is still further extended, to cover the pairs of correlative opposites with which the first two antinomies deal, those, namely, between the limited and the unlimited, the simple and the infinitely divisible, Kant would seem to be making a highly artificial distinction. The first two antinomies deal not with space and time as such, but with the sensible world in space and time; and within this sensible world, even in its quantitative aspects, qualitative differences have to be reckoned with. Common sense does, indeed, tend to assume that the unlimited and the simple must, like that which they condition, be in space and time, and so form with the conditioned a homogeneous series. But this assumption ordinary consciousness is equally disposed to make in regard to a first cause and to the unconditionally necessary.

Kant further attempts[1577] to distinguish between the mathematical and the dynamical by asserting that the dynamical antinomies are not concerned with the quantity of their object, but only with its existence. He admits, however, that in all four cases a series arises which is either too large or too small for the understanding; and that being so, in each case the problem arises as to the existence of an unconditioned.

The artificiality of Kant’s distinction becomes clear when we recognise that the opposed solutions, which he gives of the two sets of antinomies, can be mutually interchanged. As the sensible world rests upon intelligible grounds, both the theses and the antitheses of the first two antinomies may be true, the former in the intelligible realm and the latter in the sensuous. Similarly, both the theses and antitheses of the third and fourth antinomies may be false. In the sensible world, about which alone anything can be determined, the series of dynamical conditions forms neither a finite nor an infinite series. There is a third alternative, akin to that of the antitheses, but distinct in character from it, namely, that the series is infinitely extensible. Kant’s differential treatment of the two sets of antinomies is arbitrary, and would seem to be due to his having attempted to superimpose, with the least possible modification, a later solution of the antinomies upon one previously developed. In the earlier view, as we have already had occasion to observe, Reason has a merely empirical application. Its Ideas are taken as existing “only in the brain.” Only their empirical reference can substantiate them, or indeed give them the least significance. And as they are by their very nature incapable of empirical embodiment, all assertions which involve them must necessarily be false. Later, Kant came to regard Reason as having its own independent rights. Encouraged by his successful establishment of the objective validity of the categories, progressively more and more convinced of the importance of the distinction, which that proof reinforced, between appearances and things in themselves, and preoccupied with the problems of the spiritual life, his old-time faith in the absolute claims of pure thought reasserted itself. Through Reason we realise our kinship with noumenal realities, and through its demands the nature of the unconditioned is foreshadowed to the mind. The theses and antitheses, which throughout the entire history of philosophy have competed with one another, may both be true. Their perennial conflict demonstrates the need for some more catholic standpoint from which the two great authorities by which human life is controlled and directed, the intellectual and the moral, may be reconciled. Neither can be made to yield to the other; each is supreme in its own field. The distinction between appearances and things in themselves, recognition of which is the first step towards an adequate theory of knowledge, and without which the nature of the intellectual life remains self-contradictory and incomprehensible, itself affords the means of such a reconciliation. The understanding is the sole key to the world of appearance, the moral imperative to the realm of things in themselves. Reason with its demand for the unconditioned mediates between them, and enables us to realise our dual vocation.

This radical alteration of standpoint was bound to make the employment of manuscript representing the earlier and more sceptical attitude altogether unsatisfactory; and only Kant’s constitutional unwillingness to sacrifice what he had once committed to paper can account for his retention of the older expositions. He allows his previous treatment of the first two antinomies to remain in its sceptical form, and, by means of the distinction between the mathematical and the dynamical, develops his newer, more Idealist view exclusively in reference to the third and fourth antinomies. That it is no less applicable to the others, we have already seen.

Though the Idealist view, as here expounded, may be thus described, relatively to the sceptical view of Reason, as later, that is not to be taken as meaning that it represents the latest stage in the development of Kant’s Critical teaching. It seems to belong to the period prior to that in which the central sections of the Analytic were composed. The evidence[1578] for this consists chiefly in its subjectivist references to the nature of appearances. It would seem to be contemporary with Kant’s doctrine of the transcendental object.

SOLUTION OF THE THIRD ANTINOMY[1579]

Statement.—As appearances are representations only, they must have a ground which is not itself an appearance;[1580] and though the effects of such an intelligible cause appear, and accordingly are determined through other appearances, its causality is not itself similarly conditioned. Both it and its causality lie outside the empirical series; only the effects fall within the realm of experience. And that causality, not being subject to time, does not require to stand under another cause as its effect. In this way Kant derives from his transcendental idealism an explanation of the possibility of an action being at once free and causally determined. This explanation he takes as applying either to a first cause of the whole realm of natural phenomena or to a finite being regarded as a free agent. The proof of the possibility of this metaphysical, or, as Kant entitles it, “transcendental freedom,” removes what has always been the real difficulty that lay in the way of “practical freedom.” The conception of freedom is a transcendental Idea which can neither be derived from experience nor verified by it. It is created by Reason for itself;[1581] and reveals the possibility that in this third antinomy both thesis and antithesis may be true. The alternatives—“every effect must arise from nature,” and “every effect must arise from freedom”—are not exclusive of one another. They may be true of one and the same event in different relations.[1582] The event may be free in reference to its intelligible cause, determined as an existence in space and time. Were appearances things in themselves, freedom and causality would necessarily conflict: by means of the above ontological distinction freedom can be asserted without any diminution in the scope allowed to the causal principle. All events, without a single possible exception, are subject to the law of natural determination; and yet every event may at the same time proceed from a free cause.

POSSIBILITY OF HARMONISING CAUSALITY THROUGH FREEDOM WITH THE UNIVERSAL LAW OF NATURAL NECESSITY[1583]

Statement.—The above conclusion is so seemingly paradoxical that Kant devotes this and the following section to its further elucidation. How can events be both free and determined? The answer lies in recognition of the two-sided character of every natural existence. It is, in one aspect, mere appearance; in another, it has at its foundation a transcendental object. It is an appearance of the latter, and for its complete comprehension this latter must be taken into account. Now there is nothing to prevent us from attributing to the transcendental object a causality which is not phenomenal. Such causality may make the appearance just that appearance which it is. In the world of sense every efficient cause must have a specific empirical character, since only so can it determine one effect rather than another according to the universal and invariable law expressive of its nature. We must similarly allow to the transcendental object an intelligible character, and trace to it all those appearances which as members of the empirical series stand to one another in unbroken causal connection. This transcendental object, owing to its intelligible character, is not in time. Its act does not either arise or perish, and is not, therefore, subject to the law of empirical determination which applies only to the changeable, i.e. to events subsequent upon previous states. Such supersensuous causality can find no place in the series of empirical conditions, and though it can be conceived only in terms of the empirical character which is its outcome, the difference between it and natural causality may be as complete as that which subsists between the transcendental and the empirical objects of knowledge. In its empirical character the action is a part of nature, and enters into a causal nexus which conforms to universal laws.[1584] All its effects are inevitably determined by antecedent natural conditions. In its intelligible character, however, this same active subject must be considered free from all influence of sensibility and from all determination through natural events. In so far as it is a noumenon, there can be no change in it, and therefore nothing which is capable of explanation in terms of natural causes. Even its empirical effects are not traceable to it as events in time. For as events these effects are always the results of antecedent empirical causes. What is alone due to noumenal causality is that empirical character in virtue of which appearances are what they are, and owing to which they stand in specific and necessary causal relations to one another.

“...the empirical character is permanent, while its effects, according to variation in the concomitant, and in part limiting conditions, appear in changeable forms.”[1585]

Empirical causality is itself in its specific nature conditioned by an intelligible cause.[1586]

EXPLANATION OF THE RELATION OF FREEDOM TO NECESSITY OF NATURE[1587]

Statement.—No single appearance can be exempted from the law of natural causality. For it would then be placed outside all possible experience, and would be for us a fiction of the brain, or rather could not be conceived at all. Nothing, therefore, in nature can act freely or spontaneously. But while thus recognising that all events without exception are empirically conditioned, we may, as already pointed out, regard empirical causality as itself an effect of a non-empirical and intelligible power.[1588] In events there may be nothing but nature, and yet nature itself, or perhaps even some of the existences composing it, may rest upon powers of a noumenal order. Kant proceeds to show that such an hypothesis is not only allowable, but is indispensable for understanding the distinguishing features of human life in its practical aspect.

Man is a natural existence, and his activities are subject to empirical laws. Like all other objects of nature, he has an empirical character, and in virtue of it takes his place as an integral part of the system of nature. But man is unique among all natural existences in that he not only knows himself as a sensible existence, but also, through pure apperception, becomes aware of himself as possessing faculties of a strictly intelligible character.[1589] Such are the faculties of understanding and Reason, especially the latter in its practical employment. The “ought” of the moral imperative expresses a kind of necessity and a form of causation which we nowhere find in the world of nature. The understanding can know in nature only what actually is, has been, or will be. Nothing natural can be other than it is in the particular relations in which it is found. Moral action transcends the natural in that it finds its cause, not in an appearance or set of appearances, but in an Ideal of pure Reason. Such action must indeed be possible under natural conditions, but such conditions do not determine its rightness, and consequently cannot determine its causality.

“Reason ... does not here follow the order of things as they present themselves in appearance, but frames to itself with perfect spontaneity an order of its own according to Ideas, to which it adapts the empirical conditions, and according to which it declares actions to be necessary even although they have never yet taken place, and perhaps never will take place. And at the same time it also presupposes that Reason can have causality in regard to all these actions, since otherwise no empirical effects could be expected from its Ideas.”[1590]

If such action of pure Reason be admitted to be possible, it will have to be viewed, purely intelligible though it be, as also possessing an empirical character, i.e. as conforming to the system of nature. Its empirical consequences will be the effects of antecedent appearances, and will empirically determine by natural necessity all subsequent acts. In this empirical character, therefore, there can be no freedom. Were our knowledge of the circumstances sufficiently extensive, every human action, so far as it is appearance, could be predicted and shown to be necessary. How, then, can we talk of actions as free, when from the point of view of appearances they must in all cases be regarded as inevitable? The solution is that which has already been given of the broader issue. The entire empirical character, the whole system of nature, is determined by the intelligible character. And the former results from the latter, not empirically, and therefore not according to any temporal, causal law. It does not arise or begin at a certain time. The intelligible character conditions the empirical series as a series, and not as if it were a first member of it.

“Thus what we have missed in all empirical series is disclosed as possible, namely, that the condition of a successive series of events may itself be empirically unconditioned.”[1591]

The intelligible character lies outside the series of appearances. “Reason is the abiding (beharrliche) condition of all free actions....”[1592] Freedom ought not, therefore, to be conceived only negatively as independence of empirical conditions, but also positively as the power of originating a series of events. The empirical series is in time. Reason, which is its unconditioned condition, admits of nothing antecedent to itself; it knows neither before nor after. The series is the immediate effect of a non-temporal reality.

In illustration of his meaning, not, as he is careful to add, with the profession of thereby confirming its truth, Kant points out that moral judgment upon a vicious action is not determined in view of the inheritance, circumstances and past life of the offender, but is passed just as if he might in each action be supposed to begin, quite by himself, a new series of effects. This, in Kant’s view, shows that practical Reason is regarded as a cause completely capable, independently of all empirical conditions, of determining the act, and that it is present in all the actions of men under all conditions, and is always the same. To explain why the intelligible character should in any specific case produce just this particular empirical character, good or bad,

“...transcends all the powers of our Reason, indeed all its rights of questioning, just as if we were to ask why the transcendental object of our outer sense-intuition yields intuition in space only and no other.”[1593]

In conclusion Kant states that his intention has not been to establish the reality of freedom, not even to prove its possibility. Freedom has been dealt with only as a transcendental Idea; and the only point established is that freedom is, so to speak, a possible possibility, in that it is not contradicted either by experience or by anything that can be proved to be a presupposition of experience.

Comment.—Adequate comment upon this section is difficult for many reasons. The section is full of archaic expressions from the earlier stages of Kant’s Critical teaching. Secondly, the section anticipates a problem which is first adequately dealt with in the second Critique. And lastly, but not least, the discussion of freedom in connection with a cosmological antinomy leads Kant to treat it in the same manner as the general antinomy, and in so doing to ignore the chief difficulty to which human freedom, as an independent problem with its own peculiar difficulties, lies open. For it is comparatively easy to reconcile the universality of the causal principle with the unconditionedness of the transcendental ground upon which nature as a whole is made to rest. It is a very different matter to reconcile the spontaneous origination of particular causal series, or the freedom of particular existences, such as human beings, with the singleness and uniformity of a natural system in which every part is determined by every other. Self-consciousness, with the capacity which it confers of constructing rational ideals, certainly, as Kant rightly contends, creates a situation to which mechanical categories are by no means adequate. But the mere reference to the conceivability of distinct causal series, having each a pure conception as their intelligible ground, does not suffice to meet the fundamental difficulty that, on Kant’s own admission, each such separate series must form an integral part of the unitary system of natural law. In only one passage does Kant even touch upon this difficulty. Speaking[1594] of Reason’s power of originating a series of events, he adds that while nothing begins in Reason itself (as it admits of no conditions antecedent to itself in time), the new series must none the less have a beginning in the natural world. But the proviso, which he at once makes, indicates that he is aware that this statement is untenable. For he adds the qualification that though a beginning of the series, it is never an absolutely first beginning. In other words, it is not a beginning in any real sense of the term. As the argument of his next paragraph shows, it is the entire system of nature, and not any one series within it, which can alone account, in empirical terms, for any one action.

It is open to Kant to argue, as he has already done,[1595] that the transcendental object conditions each separate appearance as well as all appearances in their totality, and that the specific empirical character of each causal series is therefore no less noumenally conditioned than is nature as a whole. But this does not suffice to meet the difficulty—how, if all natural phenomena constitute a single closed system in which everything is determined by everything else, a moral agent, acting spontaneously, can be free to originate a genuinely new series of natural events. We seem constrained to conclude that Kant has failed to sustain his position. A solution is rendered impossible by the very terms in which he formulates the problem. If the spiritual and the natural be opposed to one another as the timeless and the temporal, and if the natural be further viewed as a unitary system, individual moral freedom is no longer defensible. Only the “transcendental freedom” of the cosmological argument can be reckoned as among the open possibilities.

As regards the character of the Critical doctrine which underlies this section, we need only note that the statement in A 546-7 = B 574-5, that man knows himself through pure apperception as “a purely intelligible object,”[1596] does not conform to Kant’s final teaching. The section can be dated through its unwavering adherence to the subjectivist doctrine of the transcendental object.[1597]

SOLUTION OF THE FOURTH ANTINOMY[1598]

Statement.—The above solution is adopted. Both thesis and antithesis may be true, the latter of the world of sense and the former of its non-empirical ground. All things sensible are contingent, but the contingent series in its entirety may nevertheless rest upon an unconditionally necessary being. The unconditioned, since it is outside the series, does not require that any one link in the series should be itself unconditioned. “Reason follows its own course in the empirical, and again a peculiar course in its transcendental use,” i.e. it limits itself by the law of causality in dealing with appearances, lest in losing the thread of the empirical conditions it should fall into idle and empty speculations; while, on the other hand, it limits that law to appearances, lest it should wrongly declare that what is useless for the explanation of appearances is therefore impossible in itself. This does not prove that an absolutely necessary being is really possible, but only that its impossibility must not be concluded from the necessary contingency of all things sensuous.

Comment.—Kant’s method of distinguishing[1599] this conclusion from that of the preceding antinomy is again artificial. “Necessary being” is not in conception more extramundanum than “unconditioned cause.” If Kant’s distinction were valid, the argument of the fourth antinomy would no longer be cosmological; it would coincide with the problem of the Ideal of Pure Reason.

CONCLUDING NOTE ON THE WHOLE ANTINOMY OF PURE REASON[1600]

Statement.—When we seek the unconditioned entirely beyond experience, our Ideas cease to be cosmological; they become transcendent. They separate themselves off from all empirical use of the understanding, and create to themselves an object, the material of which is not taken from experience, and which is therefore a mere thing of the mind (blosses Gedankending). None the less the cosmological Idea of the fourth antinomy impels us to take this step. When sensuous appearances, as merely contingent, require us to look for something altogether distinct in nature from them, our only available instruments, in so doing, are those pure concepts of things in general which contingent experience involves. We use them as instruments in such manner as may enable us to form, through analogy, some kind of notion of intelligible things. Taken in abstraction from the forms of sense, they yield that notion of an absolutely necessary Being which is equivalent to the concept of the theological Ideal.

CONCLUDING COMMENT ON KANT’S DOCTRINE OF THE ANTINOMIES

We may now, in conclusion, briefly summarise the results obtained in this chapter. Kant fails to justify the assertion that on the dogmatic level there exist antinomies in which both the contradictory alternatives allow of cogent demonstration. His proofs are in every instance invalid. The real nature of antinomy must, as he himself occasionally intimates, be defined in a very different manner, namely, as a conflict between the demand of Reason for unity and system, and the specific nature of the conditions, especially of the spatial and temporal conditions, under which the sensuous exists. In this wider form it constitutes a genuine problem, which demands for its solution the fundamental Critical distinction between appearances and things-in-themselves, and also a more thoroughgoing discussion than has yet been attempted of the nature of Reason and of the function of its Ideas. It is to these connected questions that Kant devotes his main attention in the remaining portions of the Dialectic, so that in passing to the Ideal of Pure Reason he is not proceeding to the treatment of a new set of problems, but to the restatement and to the more adequate solution of the fundamental conflict between understanding and Reason.