Chapter II of the Transcendental Dialectic is entitled “The Antinomy of Pure Reason.” Its target is the division of metaphysics Wolff entitled “rational cosmology.” The intended object of rational cosmology is the totality of non-mental contingently existing things: the world, universe, or cosmos. Wolff’s notion of a world is that of an order (Reihe) of contingent things which stand alongside one another, succeed one another, and are collectively connected with one another (Deutsche Metaphysik, §544). Kant held that there are exactly four topics in rational cosmology, corresponding to the division of those categories which represent objects as standing in some kind of series. They are: the extent of the world in space and time, the division of objects in space, the series of causal conditions, and the world as a whole. In each case, there are two opposing “dogmatic” positions, neither of which is able to gain the advantage over the other.
The alleged rational doctrine of the world is said by Kant to have the same general basis as the illusory rational doctrine of the soul. There is an analogy between a form of inference and the application of categories to what could never be an object of experience. In the case of the rational doctrine of the soul, which Kant reprises at the beginning of the Antinomy, any series of categorical syllogisms must terminate with a judgment containing a subject which cannot in turn be a predicate of any other subject.
Kant thought that this logically ultimate subject could only be compared to a metaphysically ultimate subject, which is substance. In what amounts to a play on words, Kant held that the metaphysically ultimate subject must be the “subject” of presentations. (A406/B432). Moreover, he held that nothing material could play the role of subject of presentations, so that “the advantage is entirely on the side of pneumatism” (the view that the mind is an immaterial spirit), to the detriment of materialism (A406/B433).
The situation is different with the hypothetical syllogism. To its use corresponds “the unconditioned unity of the objective conditions in [the realm of] appearances” (A406/B433). Since the objective conditions in appearances are conditions of what is presented to the subject (rather than of the subject itself), there is no automatic reason to construe these conditions as spiritual. This allows an opposition between materialist and spiritualist construals of these conditions.
Each side is supported by laws of pure reason, so reason is in conflict with itself, a situation Kant calls “antinomy.” One classical response to antinomy is skepticism, according to which the intractability of the conflict shows the need to give up any pretensions to knowledge. Kant calls skepticism the “slumber” or even “euthanasia” of pure reason (A407/B434). The only way either side can be kept alive is through a “dogmatic defiance” in which reason will “rigidly stand up for certain assertions without granting a hearing or doing justice to the bases supporting the opposite” (A407/B434).
Each side purports to have a “transcendental idea” concerning “absolute totality in the synthesis of appearances” (A407-8/B434). Note the slide from talk of unconditioned unity of objective conditions to totality in the synthesis of appearances. Kant is assuming from the Analytic that the objective conditions of appearances embody syntheses and that unconditioned unity of conditions could only be the totality of these syntheses. This will become important in the arguments for purported principles of rational cosmology.
In the actual metaphysical systems before Kant that embodied the conflicting dogmatic positions, no such assumption was made. The philosophers treated the objective conditions in question as conditions of things in themselves. This will be of great significance when Kant diagnoses and tries to solve the antinomies. It will also explain some of the peculiar argumentation for one side of the antinomy.
Before beginning his treatment of the antinomies, Kant makes a distinction that will differentiate the “world concept” that is involved in the antinomies from an “ideal” which will be the topic of the third chapter of the Dialectic. The objective conditions of the world about which the philosophers have debated are all confined to the totality of the synthesis of appearances, while the ideal concerns “absolute totality in the synthesis of all possible things” (A408/B434-5).
The demand for unconditioned unity in the conditions of appearances arises from the fact that appearances are the result of synthesis. In human experience, we always occupy a certain point in the series that makes up the synthesis. From this point, we can, in our thinking about the appearances, either move backward or regressively through the series or else move forward or progressively through it. As noted in the previous document, there is an asymmetry here, in that reason demands that we trace the conditions backward but not that we trace them forward. Reason must determine what was needed to get us to the present point, but it is only optional that the conditions be traced forward.
The regressive tracing of the series of conditions that bring about the present situation of appearances can only stop when a totality has been reached. This totality must be “unconditioned,” since it comprises all of what is conditioned. Thus Kant lays down the principle of reason that “if the conditioned is given, then the entire sum of conditions and hence the absolutely unconditioned (through which alone the conditioned was possible) is also given” (A409/B436).
The unconditioned could be given in one of two ways. The most straightforward way is through the completion of the totality by the discovery of a first member, in the manner of Aristotle’s “prime” or “unmoved” mover, that moves but is not moved. The second way would be to regard the totality of the series as itself the unconditioned. In that case, “all the members would without exception be conditioned and only their whole would be absolutely unconditioned” (A417/B445). This would cover the case in which there is no first member of the series because the series is infinite as well as the case in which there is aEach side first member.
Kant must do a good deal of gerrymandering in order to produce a table of world-concepts (Weltbegriffe) corresponding to the categories. The first set of categories is that of quantity, which applied to appearances yields concepts of extensive magnitudes. Since what is at issue is the synthesis of appearances, the most obvious world-concept would be that of a completed series of events in time up to the present.
But space is not a series as such, in that all spaces co-exist together at any given time. To generate a world-concept, Kant resorts to saying that the synthesis in question is that of the measuring of space, which is successive (A412/B439). But this is not yet enough, as there is in measurement no distinction between progressive and regressive synthesis: one could measure in either direction from a given starting-point. So Kant avails himself of a further expedient, claiming that the series of one space being bounded by another is regressive. (More baldly, “the progression in space is also a regression” (A413/B440).) So we can form a world-concept of the spatial extent of the universe.
The second set of categories poses an even greater challenge. Quality, as applied to appearances, is manifest in their intensive magnitude, as in the degree of heat. What Kant is after, though, is the idea of the division of the world into spatial parts, which is a series of extensive, not intensive, magnitudes. Kant tries to tie the idea of division into the qualitative categories that concern degrees of reality by saying that in spatial division, we start with reality (a category of quality), and the result of division is less reality. When we complete the division, “the reality of matter vanishes either into nothingness or, at any rate, into what is no longer matter, viz., the simple” (A413/B440).
In the third set of categories, the relational, only the category of causality applies directly to a series. The relation of predicate to subject is one of subordination, not series. And the substances with which a given subject interacts are not its boundaries, though the spaces surrounding a body are its boundaries. So the world-concept include only the totality of the series of causes for a given effect.
Finally, we have the categories of modality: possibility, existence, and necessity. These pose the problem that modal categories do not enlarge the concepts of objects at all. So it would seem that there is no series to whose totality the modal categories would apply. But Kant professes to have found a loophole. He had stated in elucidating the principle of necessity that, “Everything that occurs is hypothetically necessary” (A228/B280). That is, every occurrence is dependent on some other occurrence. The totality of hypothetically necessary occurrences could be said to be unconditioned necessity.
So we can generate yet another table of concepts (here, transcendental ideas in the guise of world-concepts) based on the organization of the categories (A415/B443).
The completeness demanded by reason could be satisfied on one of two ways. The series could be terminated by one of its members, in which case it is finite. If there is no termination, it is infinite. Kant notes that the infinity of the series would have to be potential, since although the series must be considered complete, it could not be completed in a finite number of steps. If it can be completed (that is, if the series is finite), then the first idea (completeness of composition) is that of a boundary of the world, the second (completenss of division) is of something simple, the third (completeness of arising) is of freedom (absolute self-activity), and the fourth (completeness of dependence) is of natural (as opposed to supernatural) necessity.
Kant concludes his preparatory remarks by noting that the notion of a “world” has two different significations. In one sense, it would refer to the sum total of appearances, both in composition and division. In the other, it is nature, which concerns the unity of the successive ways in which appearances exist. This distinction between world and nature mirrors that between mathematical and dynamical principles of understanding. Although both kinds of concepts are appropriately called “world”-concepts, the distinction between world and nature allows us more precisely to call the second pair of world-concepts “transcendent natural concepts” (A420/B448). They are transcendent not in that they concern noumena, but because they “carry the synthesis up to a degree that surpasses all experience.”
Each of the transcendental world-concepts (in the broad sense) is consistent with two opposing doctrinal prinicples. One of the doctrines may be called a “thesis,” the opposition between a thesis and its opposing doctrine can be called “antithetic,” and what is opposed to the thesis is thus the “antithesis.” The thesis considers the reference of the world-concept to he a finite world, while the antithesis takes it be an infinite world. Neither thesis nor antithesis is presumed at the outset of examination to have any superiority over the other. They cannot be either confirmed or refuted by experience, and each has equally good reasons for asserting its truth. They are the result of natural and unavoidable illusion.
The basis for antithetic is placed by Kant in the relation between understanding and reason. The principles of the unity of experience belong to the understanding. Anything that satisfies them will be “too small” for the demands of reason. But the principles of the absolute totality of conditions belong to reason, and they are “too great” for the understanding. “And from this there must arise a conflict that cannot be avoided, no matter how one goes about doing so” (A422/B450). Using a military analogy, Kant notes that the last argument to be presented will win so long as no other arises to challenge it, since either reason or the understanding will be satisfied. He holds out the hope that both sides will give up the combat and “part as good friends” (A423/B451).
The method of letting the dispute play out in the hopes of showing that it is insoluble is called “skeptical.” Kant carefully distinguishes the skeptical method from doctrinal skepticism, which he calls a principle of ignorance which undermines the foundations of all cognition. The skeptical method instead aims at certainty. It is of no use in mathematics, where there are no disputes. In science, we always have experience to settle any dispute, as is also the case with morality. Only transcendental assertions must be approached through the skeptical method, since they lie beyond the scope of intuition and experience.
The First Antinomy concerns the extent of the world in time and space. The thesis states that the world has a beginning in time as well as a boundary in space. The antithesis (which is also a thesis in the sense of a doctrine) is the denial of the thesis: the world has no beginning in time or boundary in space.
In Section III of the Antinomy, Kant explains why one might come down on the side of the thesis or the antithesis. The antithesis has the formal advantage of uniformity: each member of the series is exactly like the rest. In the present case, if the world has no beginning in time, there would be no moment which is distinguished from all others in that it is not preceded by an earlier moment. Kant associates the side of the antithesis, which postulates that experience is uniform, with empiricism, since each member of the series is accessible to at least a possible experience. The thesis side, which, to satisfy reason, postulates a condition which is not accessible to possible experience, is associated with dogmatism.
Dogmatism has certain material advantages over empiricism. It provides support for morality and religion. In the case of the thesis of the First Antinomy, a beginning in time would make a doctrine of creation more plausible than would an infinite past. It also has the advantage that the whole series is finite and hence can be comprehended clearly. Further, it is in step with popular opinion, which always demands in any endeavor some fixed point from which to proceed.
But empiricism is not without its own material advantage, though this feature of empiricism works against morality and religion. It allows us to pursue empirical investigation secure in the knowledge that each step in the investigation is covered by uniform laws. We will never come to an abrupt halt by venturing to a point (like a beginning in time) beyond which the laws of nature have no further application.
The argument of the thesis of the First Antinomy, denying that the world has a beginning in time, may be reconstructed as follows.
As for space, a similar argument can be reconstructed, with the recognition that not space itself, but only the boundaries of spaces, present us with a series.
Kant in the Comment on the First Antinomy claims that previous philosophers have relied on a false notion of the infinite to derive the same conclusion. According to this view, the infinite is the greatest magnitude, one that could not be made any bigger by the addition of a new part. The argument would be that the universe cannot have a greatest magnitude, since a part could always be added to it. Kant’s objection is that the infinite signifies an uncompletable task, not the completion of a task that allows no further addition to it.
The argument of the antithesis assumes that the universe has a beginning or boundary and purports to derive a contradiction from this assumption.
The corresponding argument for the spatial infinity of the world is somewhat trickier, since space is not a series.
It is interesting to note that the first of these two arguments for the antithesis is a variant of one given by Leibniz (though for a different purpose, which was in effect to deny the existence of empty time). But although Leibniz applied the argument to space as well (see his Third Paper in response to Clarke, §5), Kant did not. The basic reason for this is that Leibniz thought that there would have to be a condition sufficient to determine the location of the world in empty space. But for Kant, the only conditions which determine existence are temporal ones, so he was forced to invent a new argument.
In the Comment on the First Antinomy, Kant takes note of Leibniz’s position, which is that “a boundary of the world as regards both time and space is indeed entirely possible without one’s needing to assume an absolute time prior to the beginning of the world, or an absolute space spread outside of the world” (A431/B459). He agrees with Leibniz that such a space and time are impossible, as space and time are mere forms of intuition which have no application beyond appearances. Still, he claims that there have to be absolute space and time under the assumption that the world has a boundary in space and time, because appearances can only be presented in space and time.
The reason the Leibnizians deny this is because they are engaged in “subterfuges” (A431/B459). Their claim is that the world is finite because it has a “limit,” rather than a boundary. Anything beyond the limit would be part of an intelligible, rather than a sensible, world. Since a void space and time are unintelligible, it is claimed, they do not lie beyond the limit. Kant rejects this view because we have no insight into an intelligible world, and we can only relate objects in space and time to other such objects or (problematically) to their conditions, space and time themselves.
In his discussion of the solution to the First Antinomy (Section IX), Kant provides an alternative proof of the Antithesis. The original proof proceeded in accordance with the common and dogmatic way of presenting it
(A521/B549). The conclusion of the argument is that the world is infinite, i.e., occupies all times and all places without limit.
The new argument is more in accord with Kant’s own system. It begins as with the first proof, assuming that the world has a first beginning in time or a boundary in space. If so, it would be bounded by an empty time or space, respectively. Since the world is not a thing in itself but only appearance, there would have to be a boundary of appearances given in possible experience. But an empty time or space cannot be given in possible experience, because in that case the experience would be empty and hence not an experience at all. This means that an absolute boundary of the world is impossible empirically
, and since there is no other way in which it could be bounded, the world is not bounded in any respect, i.e., absolutely
(A524/B552). This argument would not establish the infinity of the world as would the initial, dogmatic, argument purports to do.
Kant held that both sides of any antinomy present equally persuasive arguments. If their conclusions contradict each other, however, there is something wrong with both of them. In the case of the First Antinomy (and the Second as well), the problem is that the premises treat appearances as things in themselves.
Let us begin with the thesis. The postulation of a boundary is incompatible with the conditions of experience (and hence impossible, by the principle of possibility), because “in the empirical regress we can encounter no experience of an absolute boundary, ” since an empty time or empty space cannot be perceived (A517/B545). So no matter how far back we go in the regressive series of conditions, we must seek yet another condition. The antithesis argument is correct on this point. On the other hand, we cannot perform an infinite regression. In this respect the argument of the thesis is correct.
So the two arguments destroy each other. The reason they do so is that they share a common false assumption. This assumption is that “the world” is a concept that is significant independently of the series of syntheses. In both cases, then, the world is treated as a thing in itself, rather than the sum-total of appearances. The assumption is that the world-series is “given wholly,” rather than being the product of successive synthesis. If we keep the concept of the world within its proper bounds, we can say instead that the magnitude of the world is indefinite.
The Second Antinomy is in some respects parallel to the First. The thesis is that all composite beings have simple parts, and the antithesis is that there is nothing simple in the world. The proof of the thesis is based on the premise that unless there are simple parts, nothing would remain if we thought away all compositeness. This is an argument modeled on Leibniz’s argument for monads. The proof of the antithesis rests on the fact that any part of a being in space is in space itself, and hence is composed of parts.
The solution is to hold that the division of a composite being exists only insofar as a decomposition takes place—a condition holding for appearances and not for things in themselves. (The decomposition of a composite would have to be a kind of “reverse synthesis,” so to speak, whereby we cognize an object by cognizing two objects which are its parts.) So bodies are indefinitely decomposable because there is a process of division—a process which always has a next step—and we will never encounter a simple. On the other hand, bodies are not infinitely divided.