TWENTY

Kant and the Antinomy of Pure Reason

Dr. Jean-Christophe Marchand conjectures that the Critique of Pure Reason was produced by a brain tumor. Until the age of forty-seven, the scientist Immanuel Kant wrote clearly. Astronomers recognize him as the inventor of the nebular hypothesis: planets, stars, and galaxies formed from dust that swirled together under the force of gravity. In the Natural History and Theory of the Heavens Kant writes, “Millions and whole myriads of millions of centuries will flow on, during which always new worlds and systems of worlds will be formed. . . . The creation is never finished or complete.”

Kant (1724-1804) had an active social life that consisted mostly of dinner parties. There are a few hints at romance. In one letter, dated June 12, 1762, Frau Maria Charlotta Jacobi sends Kant a kiss from her and her girlfriend. She suggests that Kant “may wind her watch” the next time they meet.

Kant continued to publish steadily until 1771. Then he fell into his silent decade. In 1781, Kant emerged with the Critique of Pure Reason. The topics are dizzyingly abstract. Sentences, tottering with jargon, soldier on for a whole page. German students prefer to read Norman Kemp Smith’s English translation; The Critique of Pure Reason loses something in the original.

Kant’s explorations of our innate cognitive architecture allow little role for emotions. This is salient in his subsequent ethical writings. Kant insists that morality is a matter of rigorous consistency. Cutting in line is wrong because you cannot consistently will that all members of the queue be permitted to occupy any position. Lying is wrong because you would fall into a contradiction if you willed that all testimony can be insincere. Kant explicitly forbids any exceptions. You cannot lie to save an innocent man from a murderer!

Kant emphasizes duty over kindness. Consider a lifeguard who rescues a boy. The less she likes the boy, the surer we can be that her motivation is moral. Rightness is a matter of following the appropriate rule. Like William of Ockham, Kant denies the moral relevance of consequences. The lifeguard deserves no more praise for a successful rescue than an unsuccessful rescue. What matters is following the correct maxims, not securing benefits that accrue from this obedience.

Granted, Kant stresses respect for persons. But often this is expressed negatively, as revulsion toward treating people as objects instead of free agents. He thinks our sensual side leads us to treat others as sexual objects. Kant compares womanizers to cannibals. Kant opposed birth control. He viewed sexual relations even within marriage as unsavory.

Many people are turned off by Kant’s loathing of our sensual side, by his stiff subordination of emotion to reason, and above all, by his inhumane writing style. They suspect something is wrong with Kant. The neuroscientist Michael Gazzaniga backs Marchand’s argumentum ad cranium:

Kant began to complain of headaches and other maladies and gradually lost vision in his left eye. Dr. Marchand deduced that Kant had a left prefrontal lobe tumor—growing slowly, but there. Damage to this area affects language ability and the ability of our emotional system to cue us toward good cognitive strategy. Is it possible that all those Kantians have saluted a man who was writing nonsense—a philosophy for those who do not have a normal cognitive and emotional system?

(1998, 121)

I think Gazzaniga’s query is answered by the continuity of Kant’s private correspondence. Kant’s letters from age 40 to 60 do not reveal any change in his linguistic competence. When addressing nonphilosophers, Kant abstains from technical terms and streamlines his syntax. His letters evince the normal emotional range of a busy Prussian academic. If Gazzaniga did not harbor antecedent doubts about the value of Kant’s philosophy, he would no more challenge Kant’s talk of the “transcendental unity of apperception” than he would challenge the cant of quantum mechanics.

Gazzaniga intimates that Kant’s disciples were so cowed that they could not detect a lapse into nonsense. Severely retarded sufferers of “chatterbox syndrome” have normal, even overdeveloped, linguistic faculties that enable them to pass as hypersophisticated conversationalists. They love big words. Listeners eventually detect empirical errors and a general failure to connect words with deed. Since philosophy professors are not expected to connect their esoteric discourse with practical affairs, it is more difficult to convict them of speaking nonsense.

However, after Kant entered his seventies, his followers were the first to detect cognitive decline. As Kant inched toward senility, acquaintances grimly joked that he was being “de-Kanted.” Even Kant’s dull-witted servant of forty years, Martin Lampe, began to exploit his master’s growing confusion. A former student, who was then overseeing Kant’s affairs, had to pension off Lampe. Kant continued to call his new servant “Lampe.” To compensate for his disintegrating short-term memory, Kant wrote himself copious notes. One of these resolves that “the name Lampe must now be completely forgotten.” In Kant: A Biography, Manfred Kuehn writes, “This kind of performative contradiction is perhaps more indicative of his condition than any of the other anecdotes that are told about the old Kant.” (2001, 417-18)

Augustine regarded vulnerability to paradox as a sign of fallen reason. And before Augustine, Sextus Empiricus pioneered the analogy between paradoxes and diseases. Kant breaks from this negative tradition by construing “the antinomies” of theoretical reason as a sign of mental normality.

THE FOUR ANTINOMIES OF PURE REASON

In the Critique of Pure Reason, Kant presented the four “antinomies of pure reason” as overextensions of reason’s pursuit of completeness. By antinomy, Kant means a pair of apparently impeccable arguments for opposite conclusions. His formulation of the arguments was affected by a recent, titanic debate between Gottfried Leibniz and Samuel Clarke (a spokesman for Isaac Newton). After discussing the four transcendental ideas that underlie the antinomies, Kant presents the pros and cons side by side.

THESISANTITHESIS
The world has a beginning in time, and is also limited as regards space.The world has no beginning, and no limits in space; it is infinite as regards both time and space.
PROOFPROOF
If we assume that the world has no has no beginning in time, then up to every given moment an eternity has elapsed, and there has passed away an infinite series of successive states of things. . . .For let us assume that it has a beginning. Since the beginning is an existence which is preceded by a time in which the thing is not, there must have been a preceding time in which the world was not, i.e.an empty time. . . .

Each competing proof takes on the air of a reductio ad absurdum. Instead of directly deducing the conclusion, the arguments suppose the opposite of what they are designed to prove and then deduce a contradiction.

In this first antinomy, Kant supposes, for the sake of contradiction, that there is an infinite past. He then infers there must have been an infinite wait to reach the present moment. An infinite wait cannot be complete. Yet here we are at the present moment. So the wait must have only been finite.

The antithetical arm of the antinomy supposes that the world has a beginning. Prior to the commencement of time,there must have been a stage in which there was no time. Change implies time. Nothing can happen in a timeless era. History would be stalled at the starting line!

These arguments about time have implications for space. To conceive of the universe as containing infinitely many things, you must imagine an inventory being made of all the objects. But if you only have finite time to make a list, that survey can only be finitely long. Therefore, a universe that contains infinitely many things is inconceivable.

To establish that the totality of things in space is infinite, we extract an absurdity from the supposition that this totality is limited within infinite space. Consider the region of space in which there are no longer any objects. This region is a vacuum. But a vacuum is nothing and nothing cannot limit anything.

Something has gone wrong! It is possible for there to be two valid direct arguments for incompatible conclusions, for one of the arguments could have a false premise. But an indirect argument has no premises. In particular, a reductio ad absurdum just supposes a proposition, deduces a contradiction without the help of further premises, and then infers the negation of that conclusion. Any pair of valid reductios must yield compatible conclusions. If both arguments really are reductios, then the problem cannot be a false premise. The problem must be purely logical.

The riddle behind the second antinomy is, Does everything divide up into discrete atoms or is there some continuous “gunk” that is infinitely divisible? The thesis of the second antinomy is atomism: every composite object is composed of simple parts. If there were no simple things, then there would have to be infinitely small things. But to be infinitely small is to be of no size. A collection of nothings, even infinitely many nothings, cannot add up to something. Since there is obviously something rather than nothing, there must be a limit to how far things can be divided.

The antithesis is that everything is infinitely divisible. If there were simples, then we would have something in space. Space is continuous. Given this infinite divisibility of space, we can divide the simple thing into different parts. There will always be a difference between, say, the left side of the object and its right side.

The riddle behind the third antinomy is the classic dilemma of freedom or determinism. The thesis is that there are some uncaused causes, in particular, acts of freewill. Think of the difference between raising your arm and your arm rising. When you raise your arm, a free choice enters the causal order. That intervention does not itself have a cause. If your arm passively rises, then you look for a cause such as involuntary contraction of your arm muscles. This cause must itself have a cause. The explanation is open to continuation by a third cause. On and on we go down the chain. We can arbitrarily break off the inquiry because of limited resources. But the only principled way of completing the inquiry is to anchor the chain of events in a decision by a free agent. Thus, it is incoherent to suppose that the world could be composed solely of passive causes. By calling the chain of passive causes a “world,” you imply it is a complete collection of events. But to be an uninterrupted story, there must be at least one active cause to originate the series.

You are not merely a passive puppet that moves because of an action instigated by a puppeteer. You are an autonomous agent. Most things are mere patients whose behavior must be totally explained by causes outside of them. You know by introspection that you are one of the rare exceptions.

Could there be world that never had any agents? There could be a puppet whose strings are pulled by another puppet. And that puppet could in turn be manipulated by another puppet. But we cannot continue this series indefinitely. Sooner or later, we must postulate a puppeteer—at least in the past. Only free actions have the self-explanatory nature that can halt an infinite regress.

The antithesis denies that there is freewill. There is only the passive kind of causation in which each event wholly depends on some earlier cause. If agents introduced new energy into causal order, there would be something coming from nothing. An absolutely free act would violate the principle of sufficient reason: there must be a reason for every event.

Gottfried Leibniz illustrated the principle of sufficient reason with Archimedes’ deduction: a scale with equal weights must be balanced because there is no more reason for one side to go up rather than the other. Samuel Clarke agreed that the scale must be at rest because it only involves passive objects. If an agent is confronted by equally balanced alternatives, he can arbitrarily choose one over the other. (In the 1950s, existentialists amplified this point: we sometimes choose the less weighty alternative because of weakness of will—or sheer defiance. Freedom is the silver lining in every irrational cloud.)

Leibniz denies that an arbitrary choice would differ from mere behavior. If your body moves randomly, the “act” is not yours. If you try to make it your act (rather than one of your effects) by claiming it is caused by your character, then you are no longer conceiving of the act as an uncaused cause.

Clarke admits that the self-motion associated with freewill is somewhat mysterious. But so is gravity. The movement of falling objects appears to require action at a distance. That is so strange we would be quite skeptical of gravity if it were a rare phenomenon. But falling apples are common. So are free choices. We should accept both without pretending to understand their deeper natures.

Kant thinks the proofs for freedom and determinism are equally forceful. He cites side motives to explain why people accept one argument rather than the other. Freewill is a requirement for being morally responsible. Freewill is also an asset in building a case for the existence of God. Suppose we follow Isaac Newton in picturing the universe as a big machine. Given that we also accept the requirement that every explanation be anchored with an act of freewill, we are poised to infer that there is a maker of the machine.

Leibniz complained to Clarke that acts of freewill have the same stupefying effect as miracles. If God can intervene anywhere and at anytime, why should we push our inquiry through the anomalies experience presents? It is self-defeating to rescue the natural order by postulating supernatural causes.

Kant regards the moral and religious aspects of freewill as potent distractions. The steadiness of our convictions as rationalists or empiricists is traced to the steadiness of our biases: “If men could free themselves from all such interests, and consider the assertions of reason irrespective of their consequences, solely in view of the intrinsic forces of their grounds, and were the only way of escape from their perplexities to give adhesion to one or other of the opposing parties, their state would be one of continuous vacillation.” (1965 A475-B503) What matters in the third antinomy is the transcendental aspect of freewill. Reason is stymied because agency seems to block the quest for completeness and yet also seems essential to this quest.

The riddle behind the fourth antinomy is whether there is a necessary being or just an endless chain of contingent beings. If all beings were contingent, then each thing would depend on something that depended on yet a third thing. There would be no bottom to the sequence.

The antithesis argues against the existence of a necessary being. Only a field of contingent beings can form a unified whole. If the necessary being is part of the empirical universe, then it is the sort of thing whose existence is open to empirical confirmation or refutation. But only contingent beings satisfy this condition of possibly not existing. If the necessary being is outside the empirical realm, then it is not the sort of thing that explains an empirical sequence of events. Once you start an explanation within the empirical realm, you cannot hit an eject button and whoosh up to the realm of necessary beings.

Might the necessary being be the whole sequence of contingent events or the fusion of all the contingent beings? No, reasons Kant, the whole can be necessary only if one of its parts is necessary.

ORIGIN OF THE ANTINOMIES

Kant formulates the antinomies in the technical vocabulary of his grand architectonic system. But he thinks these paradoxes arise from natural, universal thought patterns. Even children think, What happened before that? This can be asked of any event. One does not need to be a philosopher to think, What is beyond that? This makes sense whenever asked of a point in space.

The concepts originating the four antinomies are; before, part of, caused by, and depends on. Each of these can be driven to a “logical conclusion” in two absurd ways. We argue for the thesis by showing how the antithesis generates a vicious infinite regress. We argue for the antithesis by showing how the thesis implies a viciously ad hoc stopping point (a first moment, an indivisible part, a spontaneous cause, a causer who cannot have failed to exist).

We drive the concepts onward because the ideals regulating inquiry command completeness. You achieve your goals by always reaching further, endlessly expanding the application of each of the four powerful ideas before, part of, caused by, and depends on. An antinomy is “not arbitrarily invented but founded in the human reason as such.” (1950, 337–38)

The dialectical origin of each idea arises from a combination of technical proficiency and selective attention. Logic professors teach us how to construct arguments. That skill has been applied to articulate each arm of the antinomies. By focusing on one intrinsically attractive alternative, you can mine evidence favoring just one side of the debate. If you do this systematically across a wide range of antinomical issues, the result is a sweeping metaphysical system.

Kant believes that rationalism flowered by defending the thesis of each antinomy. In reaction, empiricism developed by refining arguments for each antithesis. The rationalists believed that central features of nature could be ascertained by reason alone. They built upon our cognitive geography in one direction. The empiricists believed that all knowledge of nature relied on experience. They built in an opposed direction. Rationalism, taken alone, would be decisively proven. But the same could be said for empiricism. Thus, their powerful arguments cancel out.

This mega-application of Sextus Empiricus’s method of equipollence first occurred to Kant as he analyzed the public correspondence between the rationalist Gottfried Leibniz and the empiricist Samuel Clarke. Each of these scholars argued masterfully from their classic perspectives. But “there arises an unexpected conflict which never can be removed in the common dogmatic way; because the thesis as well as the antithesis, can be shown by equally clear, evident, and irresistible proofs. . . . ” Rationalists and empiricists try to pull each other down through ever more intricate debate. Kant regards these tactical refinements as futile: “all the metaphysical art of the most subtle distinction can not prevent this opposition. . . . ” (1950, 337-38, 339–40)

The rationalists and empiricists were like two evenly matched teams in a tug of war. Ironically, the competing parties are kept standing by their opposing efforts. Kant’s strategy is to cut the rope.

KANT’S COPERNICAN REVOLUTION

As a scientist, Kant had a sleepy sympathy with empiricism. He was shaken by David Hume. Kant believed Hume drove empiricism to its logical conclusion: the skepticism of Sextus Empiricus. As a scientist, Kant also thought we have plenty of knowledge. He was so confident in scientific progress and common sense that his inquiry just presupposes that we know about as much as the scientists of his era believed we knew. To avoid skepticism, Kant swung to rationalism. Rationalists correctly believed that there are synthetic a priori propositions. But Kant believed Hume had also demonstrated that there is no reason why a mind-independent reality must live up to expectations of reason. The best we can expect from a world we did not create is indifference.

When Copernicus had trouble accounting for the movements of stars with the hypothesis that they are all moving around the observer, he tried the reverse hypothesis: The observer is moving and the stars are at rest. Kant was encountering parallel difficulties accounting for a priori knowledge on the hypothesis that our ideas of objects must conform to the objects. His Copernican revolution was to try the reverse hypothesis that objects must conform to ideas of objects. From this inverted perspective, experienced reality is a collaboration between our minds and external causes. As the empiricists emphasized, we cannot check the faithfulness of our ideas by comparing them with what they represent. We are trapped in the circle of our own ideas. Traditional metaphysics aims at studying a mind-independent world. But all we can know about things in themselves is that they exist and have some causal influence over our perceptions. Therefore, traditional metaphysics is a hopeless enterprise.

Should ordinary people be shocked that the external world is so intransigently unknowable? Kant believed that we are normally concerned with “phenomenal reality”—the world as it appears to us. Plato dismissed the realm of appearances as mere shadows of the real world of the forms. But the introspective Augustine made appearances a world of their own. The Augustinean reads “There appears to be a square in figure 20.1” as a correct description of an appearance rather than a hedged report of a square that is actually not there. Even after we realize that we are projecting the square into a sequence of bars, we still “see” the square. Similarly, Kant continues to see the objects in his room configured in space even though he believes he is just projecting spatial relations onto objects.

Fig. 20.1

René Descartes’s meditations further persuaded philosophers that this world of appearances provides our only available premises for conclusions about noumenal reality (the mind-independent realm of things in themselves). We must excogitate the external world from inner certainties. George Berkeley boldly disagreed on both the need and possibility of this escape to the external world. Although Berkeley believes that there are cherries and fireplaces, he thinks “material object” is an incoherent philosopher’s term. If you take away how the cherry tastes and feels and sounds, you take away the cherry. Kant does not go that far. He believes the noumenal realm is real. He just insists that we are radically overopinionated about it. We can know virtually nothing about things in themselves.

The feeling that we know much about noumenal reality is due to the “transcendental illusion” of construing a subjective condition of our conceptual scheme as an objective feature of reality. We are a bit like the astronomer Percival Lowell. When peering at Venus through his giant telescope, he regularly claimed to see “spokes.” It turns out that he was seeing shadows cast by the blood vessels in his own eye. Astronomers speculate that a physician might have been able to diagnose Lowell’s hypertension by studying his diagrams of Venus.

Kant has a stronger version of the projection thesis than scientists accept. They grant that secondary qualities such as color are projected onto the world. But they believe that objects really have primary qualities such as weight, solidity, and electric charge. Physicists take pride in telling us how things are in themselves. Kant thinks this is metaphysics masquerading as physics. Observation and science only inform us about phenomenal reality.

In addition to yielding particular facts, phenomenal reality is also open to the more abstract kind of investigation that we associate with the theory of perspective. Since the Renaissance, artists have worked out principles of representation. Their aim was simply to draw better pictures, but they were actually engaged in a mathematical enterprise. Kant portrays number theorists as unconsciously working out the structure of time and geometers as working out the structure of space.

External things contribute to the content of experience, but the mind regulates the form those experiences must take. Appearances are situated in an arena of space and time. For material things, it is always proper to ask what is next to an object, what is the left side, and where was it before. By conceiving of something as a substance, one acquiesces to the legitimacy of questions about its parts, questions about its location, and so on. Material things also must fit into a unified casual order. Your left shoe did not just pop into existence. It had to be cobbled into existence. The raw materials must have themselves been brought into existence by other causes.

Just as Euclid perfected geometry by articulating the inner rules for constructing spatial experience, Aristotle perfected logic by articulating the inner rules of inference. In the preface to the second edition of the Critique of Pure Reason, Kant says that after Aristotle, logic has not needed “to retrace a single step, unless, indeed, we care to count as improvements the removal of certain needless subtleties or the clearer exposition of its recognized teaching, features which concern the elegance rather than the certainty of the science.” (1965, B viii) The status of the logical paradoxes had declined to such a low level that Kant’s optimism could be taken seriously. The liar paradox, the paradoxes of identity, and the problem of negative existentials were not even regarded as anomalies. They were stale sophistries with no more significance than parlor tricks.

KANT’S CONFLICTING SOLUTIONS

One mark of a paradox is that different thinkers “solve” it in incompatible ways. A stronger mark of a paradox is that one and the same thinker “solves” it in incompatible ways.

Kant’s older and simplest solution takes a cue from Aristotle: the antinomies confuse a potential infinity with an actual infinity. Although the chain of temporal order (or division or causation or dependence) can be continued without end, we cannot infer that it ever actually reaches infinity. The imperative to extend the domain of the concepts is a regulative ideal. Unfortunately, these ideals have been reified into impossible limit-objects. Thus, each antinomy rests “on a mere delusion by which they (the conflicting dogmatists) hypostatize what exists merely in thought, and take it as areal object existing, in the same character, outside the thinking subject.” Under this solution, all of the arguments composing the antinomies are sound. Each antinomical issue is analogous to the riddle “What happens if an irresistible force meets an immovable object?” The two answers to this “antinomy” appear to be contradictory:

Thesis:If an irresistible force meets an immovable object, then the immovable object moves.
Antithesis:If an irresistible force meets an immovable object, then the immovable object does not move.

Yet each side can be soundly argued. Proof of the Thesis: An irresistible force can move anything. So if there is an immovable object, it is an object and so it must move. Proof of the Antithesis: An immovable object cannot be moved by anything. So if there is an irresistible force, even that cannot move it. The conclusions of the proofs are compatible because they are conditionals with impossible antecedents. It is possible for there to be an irresistible force and it is possible for there to be an immovable object. But they are not co-possible. The riddle tricks you into assuming that the confrontation could take place. Anything follows from an impossibility. Even contradictory consequences. Garbage in, garbage out! If you do not realize what is going on, you will try to defend one of the consequences. You will slant the evidence so that it seems to confirm your answer and disconfirm the “contrary” answer. But both thesis and antithesis are true.

Although Immanuel Kant never retracts this solution, he becomes nervous. If the necessary being is a limit-object and limit-objects are delusions, then Kant is heading toward atheism. Kant rejects all metaphysical arguments for God’s existence, but he is eager to leave room for God as a possibility. Indeed, he softens the impact of criticisms of the ontological argument and of the cosmological argument by claiming that these destructive points clear the way for faith.

There is more bad news if freewill is a limit-object. For then Kant gets all the pain of hard determinism without the cold satisfaction of putting everything in its place.

To rescue the possibility of God and the possibility of freewill, Kant suggests that the phenomenal/noumenal distinction affects the third and fourth antinomies. On this softer, second solution, there are two kinds of causes. In addition to phenomena causing other phenomena, noumena cause phenomena. Thus, it is possible that your noumenal self causes phenomenal effects. (The self you see in the mirror and experience through introspection is your phenomenal self, your noumenal self is what lies beneath these appearances.) Freewill is possible because noumenal causation might spontaneously originate effects. Similarly, Kant rescues the possibility of a necessary being with a distinction between noumenal dependence and phenomenal dependence. God could be the being that rests at the bottom of a noumenal chain of dependence.

So on this second solution, the arguments composing the third and fourth antinomies are not sound. If the phenomenalnoumenal duality is understood as forcing different senses of “cause,” then the arguments commit the fallacy of equivocation. If that duality is understood as revealing that there are two species of causation, then the arguments have false premises or embody an invalid inference.

Kant suggests that we can accept freewill and accept determinism as a principle that applies to phenomenal causality. Similarly, we can accept the necessary being and respect a prohibition against accepting phenomenal stopping points.

Although Kant does not think freewill and God can be proved, he does think they can be articles of faith. Indeed, he thinks practical reason makes them part of a “rational faith.”

Kant’s Critique of Pure Reason continues to inspire. I leave you with V. Alan White’s “Antinomy” (sung to the tune of “Chimchiminey” from the film Mary Poppins):

Antinomy, antinomy, antinomy—

it’s not merely one but it’s two QEDs—

antinomy, antinomy, antinomy—

contradictory results from the same premises!

(Despite what one thinks—both can’t be believed!)

Immanuel Kant said the world can’t begin

then thought better of it, and said it can’t end;

how better adjoin separate theses as these

but publicize them as Kant’s antinomies?

Old Zeno thought space a remarkable thing

(somewhat as we think of a pig on the wing);

Achilles could not catch a Testudines

if burdened by so many antinomies!

We search for the truth till the end of the day—

but closer approaching seems farther away—

an infinite effort our destiny be—

the lover of wisdom’s own antinomy!