Kant’s Solution to the Antinomies

A reader encountering the second half of the Antinomies is likely to feel a certain sense of culmination, perhaps even that Kant’s response to the Antinomies might have been his reason for writing the Critique. Certainly, the topics involved, the possibility of free will and the cogency of arguments in favor of a first cause among them, have a breadth of application adequate to the sweep of his critique. With the generality of its scope and the fundamentally constitutive nature of the problems it addresses in mind, Kant’s project may be seen as resembling Russell’s in his Problems of Philosophy: just as Russell attempted to provide answers to the most central problems in the history of philosophy using his new logic and the logical atomism he held to follow from it, so Kant uses the tools of transcendental philosophy in inventive and interesting ways to provide a new footing for philosophical study.

The content of the four antinomies themselves has been more fully discussed in a prior article. As might have been anticipated, his response has its basis in his transcendental turn. Let’s begin by taking a look at a general outline of the basic problem the Antinomies raise.

The Problem of the Antinomies

1. Each of the Antinomies involves a fundamental problem related to the project of discovering the underlying principles of our objective experience of the world in general, including: (a) whether the universe is infinite in its extent; (b) whether matter is infinitely divisible; (c) whether free will is possible; and (d) finally, whether there is a first cause of all existing things.
2. Thus, it might at first appear that reason and our understanding have a common goal in our investigation of the physical world: while reason attempts to ascend ever higher in the search for ultimate principles in order to bring unity to our understanding, our faculty of understanding seeks to encompass our experience through the investigation causal relationships in the search for complete intelligibility. However, in its search for first principles, reason inevitably seeks to grasp principles that take it further than our experience is able to provide an empirical foundation. For example, we might look to cases where a philosopher began (“dogmatically”) by providing definitions (for example, of the divine essence or of substance) as a starting point of a deductive system that, by its speculative nature, cannot be empirically grounded. In such cases, we find that reason “transcends” our experience. Although it may be enabled to create a perfectly consistent model of reality by supposing various axioms and definitions of the physical world, it nevertheless falls into the trap of supposing objects to have an existence and/or attributes our experience cannot confirm them to have.
3. Furthermore, our understanding operates through the categories and is determined thereby to understand the world in terms of the “principle of causality,” which serves to make our experience intelligible. The principle of causality, however, is an iterative, regressive principle: it always seeks some further explanatory cause for any given appearance. Thus, it can never arrive at a theoretical end point that can function as a first or originative cause, since to do so would be inconsistent with the very nature of the categorical nature of the principle itself. Just as reason is determined to search ever “higher” in the realm of principles, our understanding might be thought of as requiring further progress along the line of our experience toward an endpoint it can never reach.
4. It furthermore happens that all the Antinomies involve a conflict between iteration/regress on the side of our empirical understanding of the physical world (as seen in the antithesis portion of the Antinomies) and our rationalistic desire to complete our understanding by arriving at a first principle that will serve to encompass it (corresponding to the thesis. See B493-B494).
5. If that is the case, then the Antinomies point to a fundamental conflict between the rationalistic and purely empiricist approaches to the ultimate questions of the physical world. In the Antinomies, we have arrived at an impasse rooted in the very nature of our cognitive faculties.

In sum, the method of the empiricist leads us only in the direction of contingent causes of contingent effects by way of the causal principle, which requires an ever expansive reach of our experience. Hence, the empiricist, using purely empirical methods, cannot lead us to a necessary first cause, but only in the direction of further regress. The rationalist, on the other hand, solves cosmological problems by simply positing necessary first causes. But these are problematic because they attempt to find a solution that lies beyond the horizon of our experience and lacks adequate empirical grounding. In either case, experience is the necessary but missing ground. Neither can, by itself, lead to a solution because empirical methods require an indefinite search for further causal explanation in our experience and rationalistic methods merely suppose principles without adequate grounding in experience.

The basic moves that Kant makes in order to overcome this impasse may likewise be set out in a straightforward sequence.

The General Strategy Behind Kant’s Response: Strategic Agnosticism

1. We must begin by setting our view of the physical universe on a sound transcendental footing.
2. We may do so by recognizing that the objects that appear to us in our experience are always subject to the principle of causality. This means that there are going to be cases (such as when we might contemplate whether the universe is infinite in its extent), where speculating beyond the horizon of experience cannot yield and determinate result.
3. Furthermore, whether considered as effects or as causes, perceptual appearances should be considered as representations rather than things in themselves. As representations they may be understood in terms of the categories, which provide the conceptual framework of our capacity for understanding. Things in themselves, however, cannot be known, even in principle, inasmuch as they lie outside our capacity to access them through the forms of our perception or the categories of our understanding. What we may know at all can only be known by the particularly human way we are able to access the world epistemically.
4. We fall into the trap of treating appearances as if they were things in themselves whenever we contemplate the reality of a primary cause that transcends our experience as if it had an objective reality. Such a principle can be contemplated purely intellectually and speculatively, but it is something to which we have no access at all. Even the big bang, for example, takes us only as far back as the first principle of the expansion of our universe. But the principle of causality enjoins us to go beyond this relative first principle to something always beyond our horizon.
5. Thus, if we were to make any claims about the objective reality of a first principle we can only contemplate speculatively, we would fall into the trap of supposing the existence and reality of something we cannot know to be the case. Furthermore, we should keep in mind that according to pure empiricism, we cannot have any justification for the existence of such a first principle at all: any such principle would violate the principle of causality.
6. Hence, any solution that attempts to grasp the totality of our experience from a vantage point beyond the horizon of experience whether by supposing a first principle of a particular kind or its necessary impossibility will draw us into unresolvable difficulties. To do so is precisely what draws us into transcendental illusion and precisely the error the parties to the theses and antitheses of the Antinomies have committed.
7. Once we recognize this difficulty, we are provided with a justification for taking up an agnostic stance toward the nature of first principles as contemplated in the Antinomies. That is to say, we are provided with a justification for not deciding between either rationalism or empiricism, or again, between the objective necessity of a first principle and the possibility of an infinite regress in empirical causes. This follows from the fact that in every case the antinomies set a rationalistic solution to the problem of causal regress in opposition to empiricist skepticism about the very possibility of a first principle. 
8. Finally, as will be seen, this transcendentally grounded agnosticism allows Kant to say either that the claims of the opposed parties are either both false or somehow both true. 

Consider Kant’s text in connection with these points:

“It is not therefore surprising that in dealing with a member of the empirical series, no matter what member it may be, we are never justified in making a leap out beyond the context of sensibility. To do so is to treat the appearances as if they were things in themselves which exist apart from their transcendental ground, and which can remain standing while we seek an outside cause of their existence.” B591

“[Transcendent ideas] no longer serve only for the completion of the empirical employment of reason – an idea of completeness which must always be pursued, though it can never be completely achieved. On the contrary, they detach themselves completely from experience and make for themselves objects for which experience supplies no material and whose objective reality is not based on completion of the empirical series but on pure a priori concepts. Such transcendent ideas have a purely intelligible object; and this object may indeed be admitted as a transcendental object, but only if we likewise admit that, for the rest, we have no knowledge in regard to it, and that it cannot be thought as a determinate thing in terms of distinctive inner predicates.“ B593

Both of the quotes above take us back to the central problem of the Antinomies: the conflict between empiricism and rationalism, and confirm that the first principles contemplated in the Antinomies are considered as purely intelligible objects, as opposed to objects that might be theorized about on the basis of existing empirical evidence. There is furthermore a way in which the principles of Kant’s transcendental philosophy follow directly from a meditation on this conflict. Anything grounded transcendentally is grounded in the categorical concepts of our understanding and in the forms of our sensibility. But if we try to imagine something like a pure idea that can also function as a cosmological first principle, then in order to remain true to those very concepts, we must limit ourselves to formulating an idea that would be consistent with the categories of our understanding and the forms of our sensibility, but cannot treat it as though it were anything more than a speculative idea (see B567ff.). This is essentially what the rationalist does when he falls prey to a transcendental illusion. Instead, we should recognize that this limitation is a limitation of human reason.

The First Antinomy

Like all the other Antinomies, the First Antinomy involves a dilemma created by a rule for the conduct of reason in general: that we ought to precede “up“ to the unconditioned in a series of conditions whenever we wish to discover the principle underlying them. In fact, reason compels us to seek some first principle among the conditioned nature of the world of appearances about us. Yet, the “unconditioned“ (i.e. the first cause) among cosmological conditions (dependent causes of evident effects) is in each case something beyond our grasp, an object of speculation. Indeed, in a way that echoes the opening lines of Aristotle’s Metaphysics, in his introduction to the first edition Kant writes,

Human reason has this peculiar fate that in one species of its knowledge it is burdened by questions which, as prescribed by the very nature of reason itself, it is not able to ignore, but which, as transcending all its powers, it is also not able to answer.

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in the opening sentence. But whereas for Aristotle the desire to understand gives reason its wings to explore speculative realms and is seen mainly as an inspiration toward knowledge, for Kant the inspiration that impels reason forward is tempered by a fuller understanding of its limitations and its “peculiar fate” as quoted above.

The problem for reason is its compulsion toward the realization of totality in the development of its concepts (see B593): totality can only be attained by grasping a first cause and yet, our inability to do so experientially is precisely what makes the cosmological questions considered in the Antinomies problematic. Kant writes that it is “an idea which must always be pursued, though it can never be completely achieved” (B593) foregrounding the point that reason cannot, in principle, know whether has grasped totality as such in its speculations, though it is bound to go on attempting to do so. The question for philosophy is, for Kant, how to deal with its problematic nature.

If he has been successful in arguing that the Antinomies are, moreover, fundamentally unresolvable, then some way beyond the arguments advanced by the partisans of empiricism and realism must be found who are caught up in the conflicted nature of human reason. Kant’s move is to embrace the problematic nature of the Antinomies as a brute fact, a fact of our lack of epistemic access to an understanding of the totality of conditions that would otherwise make the physical nature of the universe actually intelligible with respect to its origin, necessitating factors, and continuance. 

Let’s consider this issue of epistemic access with regard to the First Antinomy. Kant’s argument is that, first of all, all our experience of phenomena in the world is representational. This means that they may be interpreted transcendentally so that the conclusions of the transcendental aesthetic may apply to them and be understood in terms of the transcendental categories. This, in turn, means that they must, in order to appear to us at all and be understood in terms of their appearance, appear to us in space and time, subject to the regulative principle of causality. 

Thus, if we are to inquire into the possibility of an absolute limit of space and time, we must recognize that any potential limit of an empirical regress must also appear to us in space and time. The alternative, that we might perceive some ultimate cause in the series of causes that is not in space and time is for Kant simply an impossibility [see B545]. The transcendental position thus implies that we cannot presuppose a limit to the universe, since any perception we might have (through a telescope, for example) must also be in space and time without any known limit. The aesthetic/causal principle does not, by itself, preclude the possibility that the universe is somehow limited in its extent. Hence, any such limit can be considered, but never concluded to exist a priori.

Either option leads to a regress into the in fact a priori unknown, and for Kant, the unknowable nature of the universe. What we may know of the extent of the universe, considered as a regress, is simply what we are at present able to observe and confirm through observation. It’s actuality, to the extent that we may know it, extends no further than our actual experience of the regress itself. For example, we might be able to conclude that the Big Bang actually occurred at some point in the distant past. But nothing precludes (a priori) the possibility of some series of prior physical causes that brought the Big Bang itself into being. There is no reason why an infinite series of causes could not have preceded it. We simply cannot speculate on the point further than our experience can actually serve to confirm our speculations. 

Again, to affirm the point that totality as described is in principle unknowable or unattainable as an a priori principle when applied to the physical universe, consider that Kant writes,

“since the world can never be given as complete, and since even the series of conditions for that which is given as conditioned cannot, as a cosmic series, be given as complete, the concept of the magnitude of the world is given only through the regress and not in a collective intuition prior to it” [B550].

We are, nevertheless, perfectly justified in taking up an agnostic position as to whether the universe is infinite in extent or in time. In such a case, both those who profess a priori knowledge that it either is or is not limited do so falsely. Thus we are led back to the strategic agnosticism discussed in the first section. 

The Second Antinomy

The second Antinomy concerns the diversity of matter and whether, in the process of the division of bodies in space, simple (indivisible) bodies are ever to be met with.

Kant’s approach is to proceed by a method which has been discussed in prior articles as the via negativa, according to which, after rejecting possible answers we may eventually make progress along more fruitful lines. Some may recognize this as a familiar procedure from the platonic dialogs. In this case, the topic of discussion is, at first, what kind of thing is the subject of division in order to arrive at simple, elementary bodies.

He begins by rejecting the idea that space in general should be considered the subject of division since space is, by its very nature, divisible and cannot be divided out of existence since it is, along with time, a transcendental foundation for our perception. An alternative subject however, allows for a way forward: it cannot be known a priori whether an organized body in space is infinitely divisible with respect to its parts. While every body must necessarily take up a certain amount of infinitely visible space, 

“we cannot assume that every part of an organized hole is itself again so organized that, in the analysis of the parts to infinity still other organized parts are always to be met with; in a word that the whole is organized to infinity“ [B554]. 

Again, we arrive at a place where, as in the first Antinomy, the possibility exists for either an infinite continuation of parts within parts or of its termination. This is the important point behind the phrase “we cannot assume…”. Nothing in the notion of an organized body or in our experience allows us to predetermine an answer to the question as was the case with space in general. As in the first Antinomy, we arrive at a case where there is an undecidability regarding the two possible outcomes. 

This is precisely the topos Kant is looking for in order to apply his transcendental solution. His answer echoes the point already made in the discussion of the First Antinomy where it was said that when we are considering the extension of space and time as a regress, what we may know about it can only extend as far as our experience of the regress itself justifies drawing any conclusions about how it may or may not proceed. Accordingly, Kant finally writes, 

“How far organization can go in an organized body only experience can show; and although, so far as our experience has gone, we may not have arrived with certainty at any inorganic part, the possibility of experiencing such parts must at least be recognized.“ [B555]

Again, Kant’s agnostic resolution points in one direction: any dogmatic solution to the question that decides in favor of either an infinite series or of its termination fails to respect the natural limitations of reason itself in relation to our understanding, as was discussed in above.

Mathematical vs. Dynamic Series

The third and fourth antinomies involve a transition from a “mathematical“ to a “dynamic” concept of a series. The two terms refer to the type of synthesis involved. The extent of space, the order of events in time, or the division of their parts involve types of conditional series whose members must all be of one kind, empirical, just as in the construction of Euclidean line, all of its parts must be points of a certain kind. In a word, they must be homogeneous. In this case, only a point existing in space and time that has material properties can act upon other material objects as an efficient cause of their motion. By the same token, because of their homogeneity, they may be treated as points/units amenable to mathematical speculation.

By contrast, the so-called “dynamical” syntheses, so he argues, may admit of heterogeneity among their members. This means, in concrete terms, that while some members may be sensible, others may be purely intelligible. This specific heterogeneity might well remind some readers of Descartes’ dilemma involving the problem of how the mind, which is one kind of substance, is able to interact with the body, which is another kind of substance. For now, it should be seen that while Kant’s transcendental solution to the first two antinomies involves the crucial point that any endpoint in a series of conditioned conditions (i.e. caused causes) would necessarily have to occur in space and time, Kant argues this need not be the case with dynamic regressive series leading back to the origination of a free will in us or of the universe itself, since a dynamic series allows us to suppose an intelligible cause outside the physical world.

The Third Antinomy (On the Question of Free Will)

The Third Antinomy, then, concerns the possibility of free will. The possibility of free will becomes a philosophical problem once it it understood as the supposition that an uncaused cause exists in an empirical universe in which every cause must be treated as an effect of some prior cause. Kant’s solution involves the supposition of a purely intelligible, spontaneous cause of our action that is capable of acting upon the physical world from “outside” its causal matrix.

A basic condition for the freedom of the will must be that whatever causes our actions must not be determined by some prior cause. But if what we call our will, the source of spontaneous action in us, also exists in space and time, then it too must have some antecedent determining cause or causes like all other things existing in space and time.I’d that were the case, then the activity of our will would not truly be free, but would have to be thought of as causally determined by something prior to it. Kant shows that free will can be retained as a possibility by supposing our freely willed actions to be the result of an intelligible cause whose ontological standing is as a thing in itself in relation to the appearance of free will in us.  

Let’s consider Kant’s full argument against the oppositional elements in the Third Antinomy as distilled into a few points:

An Outline Kant’s Solution to the Third Antinomy

1. The world about us is a world of appearances.
2. Appearances are not things in themselves but representations subject to the forms of perception and categories of understanding.
3. As such, it is only within our world of representations that events can be understood as determined by other prior causal circumstances.
4. Appearances may nevertheless (for all we know) appear to us as a result of things in themselves, which exist outside our perception, to which we lack epistemic access.
5. This possibility allows for an intelligible cause of our activity that is not subject to empirical laws.
6. Hence, there exists the possibility that there exists a non-sensible, intelligible cause of our actions in us that is not subject to the empirical law of causality.

What Kant has done here is to use the distinction between appearances and things in themselves to argue in favor of the possibility of free will, based upon our lack of any knowledge of things in themselves.

He does, in fact, take the step of arguing that things in themselves are the basis for representations as may be seen in a quotation from B535: 

“If… appearances are not taken for more than they actually are; if they are viewed not as things in themselves, but merely as representations, connected according to empirical laws, they must themselves have grounds which are not appearances.“ B535

Notice that if the cause were homogeneous with its effects, it would not be capable of spontaneous, uncaused causality because it would necessarily have to be subject to the empirical law of cause-and-effect that determines the nature of appearances in space and time. 

But there is a final point: Kant’s argument is one drawn up in favor of a compatibility between an intelligible cause of our actions and a strictly empirical explanation of causal events [see B568]. He argues that there need be no inherent conflict between an the idea of an effect being (a) the result of an unknown, uncaused cause outside our perception (hence, outside the causal matrix), such that (b) it fits perfectly within the chain of necessitated natural causes. The possibility of a compatibility between a spontaneously acting will and the causal matrix of the empirical world is a sufficient basis for arguing in favor of the compatibility of a freely acting will. 

The Fourth Antinomy

The Fourth, I like the Third Antinomy, is based upon the distinction between a mathematical and a dynamic series. In the latter case—the one before us—Kant sees a way to solve the Fourth by supposing an intelligent cause/ground that stands entirely outside the empirical world, thus leaving the internal logic of unnecessitated contingency intact, as was the case with the Third Antinomy.

But the Fourth Antinomy, by contrast, deals with the problem of contingent regress in its widest possible scope. It contemplates the logical consistency inherent in supposing a necessary ground with the entirety of contingent appearances in the world about us. Kant’s aim is to find a way to introduce such a ground into his ontology while also leaving the world of appearances empirically grounded in the principle of causality. The latter requirement entails that no matter how far we might pursue a chain of causes back to an expected initial cause, we will be bound to continue searching for some further determining cause. Obviously, such a requirement conflicts with the supposition of a necessary first cause as long as that cause falls within a series of causes. What Kant does in order to solve this difficulty is to point out that the supposition of a purely intelligible cause (for us) outside the entire contingent chain of causal events is not inconsistent with the supposition of its existence outside a purely contingent series.

It is the contingency of appearances within the world that makes this seem like a difficult problem. Their contingency requires that no member of a series of contingent appearances can be considered necessary. That, in turn, implies that there can be no absolutely first cause among the series of contingent causes.

This means that if we are to imagine a physical world consistent with the principle of causality, we cannot contemplate an absolutely contingent series of causes as leading back to an unconditioned first cause in the same way as was done in the answer to the Third Antinomy. Here is Kant:

“This way of conceiving how an unconditioned may serve as the ground of appearance differs from that which we followed in the preceding subsection, in dealing with the empirically unconditioned causality of freedom. For there the thing itself was as cause (substantia phenomenon) conceived to belong to a series of conditions, and only its causality was thought as intelligible.” B589

The last sentence requires close reading if Kant is to be properly understood. In the case of the Third Antinomy, our free will is conceived as a genuine condition among the series of conditioned causes. If it were not part of the series, it could not be thought of as having any part to play in a case where our reason appears to decide in favor of one alternative over another. If our will, free or determined, is to be capable of willing anything effectually, it must be capable of initiating a causal series and so to be in some sense a member of the series. But Kant denies that this can be the case with a necessary primary being because such a being is conceived as the absolutely first cause.

Here what is being sought is some sort of cause that would not only stand outside the causal matrix of the physical world, but do so in such a way as not to entail any need for ongoing compatibility with the flux of the physical world in its causal activity. In fact, the absolute independence and self-sufficiency (B589) of such a being must hold if it is to suffice as the “ground of the possibility of all appearances” (B590). Thus, in contrast to the way Kant thinks of the nature of our will, he conceives of a necessary primary being as not only purely intelligible with respect to its causality, but also with respect to its being.