Blogging through Critique of Pure Reason part 7: Cosmology and its Antinomies

Series Index

Criique of Pure Reason by Immanuel Kant (Hackett edition)

At this point it might take us longer to write these blog posts than it took Kant to write the Critique.

So it goes.

If it’s been a while since you read the last post (which is to say, if you’re reading these posts as we publish them), I recommend that you backtrack a bit with the Series Index and get a rolling start on this one.  As with before, we’ll give page numbers according to the A (1781) and the B (1787) editions.

What Is a Cosmological Idea?

When Kant critiqued reason’s capacity to think about the soul, the strong divisions between what experience could yield and what concepts must be in place for the subject to think he called amphibolies, contradictions between the experiencing self and the grammar within which we work when we talk and write about the self. When it comes to cosmology, Kant will deal with antinomies, contradictory claims about the spatial/temporal universe within which both sides cannot be true and each of the sides must be true.

When Kant writes about cosmology, he means the relationships between time and space, which he has established as conditioned by thought, and the things in themselves, about which the thinking subject can reflect indirectly but never in terms of experience or possible experience (A 412-3, B 439-40).  The questions that arise fall into four basic bins (A 415-16, B 443):

  1. Composition (the maginitude and duration, finite or infinite, of the totality of the universe)
  2. Division (the divisibility of objects, to a limit or infinitely)
  3. Arising (whether every appearance happens because of a previous cause or whether there is an absolute beginning)
  4. Dependence of the existence (whether or not the totality of appearances needs an uncaused cause to be intelligible)

Cosmoslogical thinking ultimately is never about a given thing among things but about the sum of all appearances, the absolute totality within which any appearance might make sense (A 419, B 447).  As Kant goes forward, he lays down four sets of antinomies, contradictory claims about reality as a whole and logically valid arguments that support both sides of the contradiction (A 421, B 448-49).  It’s the logical impossibility of such contradictions that lead Kant to his ultimate conclusion about cosmological claims and their relationships with pure reason, but the contradictions themselves will make more sense of that.

Four Cosmological Antinomies

“The world has a beginning in time and is also enclosed within bounds as regards space” (A 426, B 454).

“The world has no beginning and no bounds in space, but is infinite as regards both time and space” (A 426, B 454).

For each of the four antinomies, the Hackett and the Penguin editions of Critique of Pure Reason divides the page in half vertically, so that the left column contradicts the right at each step.  And after the book presents these claims–and their arguments–side by side, CPR discusses the logical validity of the arguments, also in parallel columns.  For the first antinomy, the arguments go something like this:

The world began and has bounds.  Because every event must have a cause, and because the whole span of time consists of all of its moments added up, any concept of time that is conceivable begins, which plays the part of the first cause allows for successive events to happen without resigning the whole of time to the unthinkable. Likewise, because the world is a whole, and because a whole must have boundaries at which the whole ends, the world must have spatial bounds.

The world has no beginning and no bounds.  Because every moment happens after another moment, any alleged first moment must have come after another moment, and because every place is next to another place, any alleged outermost boundary of the world has some kind of space beyond it, making both time and space infinite (A 427-430, B 455-458).

For the second antinomy, the arguments go thus:

Every composite substance in the world consists of simple parts, and nothing at all exists but the simple or what is composed of it.  To have a composite thing, that thing must be composed, at some level, of the absolutely simple, so to deny that at the root of things lie indivisible parts means that thinking the world is impossible.

No composite thing in the world consists of simple parts, and there exists in the world nothing simple at all.  To imagine any thing that has length or width means that there’s a midpoint along that length or width, which means that one could imagine dividing the thing at the midpoint into two smaller things.  Any provisional “elemental” particle becomes composite when one thinks about this reality (A435-437, B 463-466)

The third is like the first two:

The causality according to laws of nature is not the only causality, from which the appearances of the world can thus one and all be derived. In order to explain these appearances, it is necessary to assume also a causality through freedom. Each observed happening can and must be explained in terms of what caused it, but in order to get that chain of regress started, something must act free from external causes, which would by definition make it a free cause rather than a cause inherent in nature.

There is no freedom, but everything in the world occurs solely according to laws of nature. To say that some agent acted, one must posit the agent, and the agent must have come to be through laws of nature.  Moreover, whatever act the agent undertook would happen within the bounds of natural laws, once again putting any apparent freedom within the realm of explainable natural causes (A 445-447, B 472-474)

And what would a set of antinomies be without some mention of an absolutely necessary being?

There belongs to the world something that, either as its part or as its cause, is an absolutely necessary being.  Since the apparent world consists of a series of changes–whether geological, meteorological, biological, or other kinds of -logical–something must have caused the chain of causation to start up.  That something, whatever it is, will be that absolutely necessary being.

There exists no absolutely necessary being at all, neither in the world or outside the world, as its cause.  If such a being were inside the world, some more basic cause would be discoverable; if such a being were outside the world, some more basic cause might reside “behind” the being in that world (A 452-456, B 480-484).

So to reiterate: what makes these antinomies is that, playing by normal rules of logic, each of these claims contradicts its partner, and thus both cannot be true; yet each of these claims, on its own, allows for a logically valid demonstration of its truth.  The result is that any claims about the nature of the universe seem to be by definition non-logical, yet they are entirely logical.

Kant argues that different human motivations, themselves neither more nor less rational than their counterparts, drive certain people to prefer the thesis side of these claims and others the antithesis side.  For those more concerned to maintain some kind of moral order among human communities, the theses (that the universe began, that the will can freely make things happen, that there is an absolutely necessary being, and so on) allows for people to find in the metaphysical character of the world a basis for moral claims and thus to solidify morality (A 466, B 494).  On the other hand, those whose concerns are speculative, who seek always to challenge received opinions for the sake of precise history and empirical reasoning, tend to prefer the antitheses, which assume that any given thought is always susceptible to refutation or at least revision (A 468, B 496).  Since empiricism is inherently an investigative mode, eschewing the given in favor of the discovered, and since morality tends to begin with given principles and interpreting the given in light of the granted, reason can make equally compelling and in all cases logically valid cases for either of the antinomic pairs (A 474, B 502).

So that I don’t fall to the temptation to reproduce the entire text of the book here, I’ll just say that, as I read and reread the arguments for the antagonistic claims, I had to hand it to Kant: the logic really does hold in either direction, and although I could find extra-logical reasons to prefer one over the other, Kant’s pre-emptive psychological examination of why some prefer one and others the other stopped me in my tracks.  My hunch is that a reader with any imagination at all can at the very least imagine characters for whom each side of each antinomy is compelling, and one would be hard-pressed to say that either side of any pair is illogical.

Goldilocks and the Cosmological Concepts

True to the project of the Critique, the next move is not to solve the antinomies on their own logical terms but to examine them in terms of what the mind is and does.  First Kant distinguishes between cosmological ideas and empirical perceptions.  Ideas, by their character, assume totality and must posit (not imagine, as that’s an extension of sensory experience) limits to the concept (A 479, B 507).  Perceptions, on the other hand, relying on ideas of an absolutely whole universe but never perceiving totality, always seek beyond any given boundary and thus lead the imagination (now we are doing imagination) beyond any perceived boundary to what lies beyond, giving the mind the impression that any boundary must have something, rather than nothing, “beyond” (A 483-484, B 511-512).

The implications of perception’s tendencies and reason’s tendencies are that any cosmological idea that does not purge the sensory experience and become pure reason will always assume a world at once too large and too small for the concept “world” (A 487, B 515).  The concept will be too small because, once one imagines a boundary, the imagination always proceeds beyond it into something else, thus making any totality too small every time one imagines the edge of that totality.  The concept will be too big because empirical imagination cannot ever encompass totality but always focuses here or there within a totality.

Kant thus avoids treating all perceived objects as illusions, to fall into the trap of Descartes’s evil demon or even of Berkeley’s denial of matter.  If the mind can only imagine as a function of empirical perception, then objects of sense perception are actual (A 492, B 520); they are actual, however, not as things on their own terms but as objects, whose actuality is a function of a perceiving subject’s relation to them (A 492, B 520).  So the desk in front of me exists spatially only insofar as my mind or your mind, either of which experiences things in terms of extension and space, perceives.  To quote Kant, “objects of experience are never given in themselves, but are given only in experience and do not exist outside it at all” (A 492, B 521).  Whatever lies “beyond” or “behind” experiences, to use two metaphors also spatially conspicuous, can only be a concept, not anything perceived or imagined.

What holds for space is also true of time, another function of the mind.  Thus the desk’s duration in time, as remembered or anticipated, is a function of our sense of time without being proper to the thing itself (A 495, B 523).  The desk is not unreal as an illusion is unreal but, as a matter of constitution, a result of senses and concepts and imaginations, not the thing itself.  As a purely negative thought one can speculate that there is some thing that’s not the appearance and not the spatial extension and not the temporal duration, but as soon as one imagines what that thing might be, the thing becomes again an object of the mind, thus giving another kind of objective knowledge, not the thing in itself.

Cutting the Antinomian Knot

So two realities confront this exploration of reason’s capacity: as purely negative concepts, time and world must have limits in order for causality and continuity to make sense.  And as extensions of perception into memory and anticipation, any posited limit to time will lead the mind to imagine moments before and after, and any posited limit to space will lead to the mind’s imagining space beyond the limits of space.  Appearances on their own cannot resolve this dispute, as any experience must happen within a world comprehensive enough to encompass the experience (A 499, B 527).

The logical oddity of cosmological claims is that reason can rule the claims “the universe is finite” and “the universe is infinite” both as false (A 504, B 532).  For both of these claims treat the universe as a thing in itself, neither as an idea that transcends the possibility of perception nor as an “empirical regression of the series of appearances” (A 505, B 533).  In other words, once again, Kant turns to the nature of thought and of reason and of perception to note that the realities in question, when one makes cosmological claims, are not things in themselves but functions of different kinds of reasoning.

The important implication here is that the contradictory cosmological claims are not deceptive but logically valid, and do not deceive but stand as well-founded (A 507, B 535).  When the speculative mind says that the universe is finite and must be, that’s right.  And when the imaginative mind insists that, beyond any imagined boundary, there is space, that’s right.  Thus Kant’s next move is not going to be to choose one side or the other but to draw more precise boundaries around what kinds of moves are possible, intellectually speaking.

Kant calls those boundaries the regulative principle, not a body of content but rules that define what can and cannot be valid intellectual content.  One of those rules is that, in a series of regressive causes, no conceivable cause can be absolutely unconditioned (A 509, B 537).  So in intellectual terms, one can posit negatively that an infinite series is impossible, since some sort of first cause is necessary in order for further causes to happen, but a positive account of what that first cause might be is by definition unintelligible.  On the other hand, the mind’s inability does not mean that the regress of causes is infinite; Kant prefers to call regressions of causes and effects indeterminate (A 512, B 540), since any given instance admits of one more but not causes without limit.  By contrast, the series of whole numbers in mathematics is a truly infinite series, since any given number by definition has unlimited numbers after it.  The difference between the two kinds of regression has to do with the conditions for the concepts: in order to imagine a number, one must imagine its place in a series extending infinitely, while to imagine a human being involves imagining one more generation than what’s present in the current thought but not necessarily an infinite series of ancestors (A 513, B 541).

The rule works out in terms of the universe’s boundaries (in space) and beginnings and endings (in time) as well: when one imagines a boundary in space or a beginning-moment in time, reason requires that we inquire after another boundary or a moment before that moment (A 517, B 546).  On the other hand, when we conceive of the whole world as a concept rather than as a mental image, we can in fact say that, without being able to picture how, the universe is a unity (A 519, B 547).  Therefore the world itself is neither bounded nor unbounded (A 522, B 550).  With that in place, the world’s boundedness is real, because concepts are real, and the world’s boundlessness is real, because intuitions of space are real, but neither reason’s concepts nor the empirical faculty’s intuition has any access to the thing itself.

Kant goes on, as I will not, to apply the same mode of argument to the question of particles’ divisibility.  Empirically one can always imagine a distance half the magnitude of any given distance, but conceptually there must be indivisible quanta.  As with the arguments about the universe’s duration and magnitude, so with the limits of smallness: the unconditional always lies beyond regress but does not stand susceptible to intuition, only negatively to conceptualization (A 531, B 559).  To shift back into human language for just a moment, the rule for thinking about the limits of reality have to do with what the mind, which has access only to its constructions and perceptions and objects, does with reality.  To conceptualize matter’s nature is to assume that there are in fact quanta, limits beyond which division cannot occur, because only after that is in place can one conceptualize matter built up of those smallest, most basic particles. But to imagine any given particle as the quantum limit, the smallest possible object, is to invite the spatial intuition (the way we imagine space) to picture a particle exactly half as large as the smallest-possible-particle that one just imagined.

Where Philosophy Hits Justice

All of that might seem like so much nosebleed-high speculation or, even worse, dated disputes that now we solve simply by asking an astrophysicist or a quantum physicist.  (Todd might have something to say about all of this, is what I’m saying.)  But the last of the cosmological antinomies–contradictory pairs, each element of which happens to be true–gets at some problems of living in human community that bear even on those who don’t spend a great deal of time thinking about galaxies and subatomic particles.

Here’s the last antinomy: in order to conceptualize nature, one must think of the chains of causes and events entirely continuous.  In other words, nothing in this world happens unless something caused it, and any cause itself has a cause, and the regulative principle kicks in at some point: whenever we imagine any given cause as the unconditioned cause, reason requires that we imagine what caused that one (A 533, B 561).  But here’s the problem: if everything in the world, including what I do next, has a chain of causes regressing far past the moment when I think I intended to do something, then whatever I think I willed actually had material causes extending backwards in time to moments long before I had the capacity–or the existence–to intend anything.  Therefore, since I could not have done otherwise than what causes and effects made to happen, I do not bear real responsibility for any act that I commit (A 534, B 562).  Yet, in order to live together as human beings, we must treat acts as free deeds of particular persons, subject to praise and blame, reward and punishment (A 537, B 565).

Kant’s solution, as before, is to affirm both the freedom and the caused-effect character of every act (A 542, B 570).  Following the regulative principle which he has already articulated, Kant insists that any given act which seems to originate in a moment that we call “decision” or “will” in fact has another, prior cause before it, and so on backwards, not an infinite regression but without a doubt an indefinite regress (A 543-44, B 571-72).  In terms of appearances, the stuff of empirical perception and anticipation and memory, no event can have an absolute beginning, and thus there can be no truly free will.  Yet in terms of reason, which thinks non-empirical realities, any given person ought to act in certain ways, and thus a person who acts as she ought or as he ought not stands as a genuinely free agent (A 548, B 576).  Thus scientific inquiry, which always seeks to discover the cause prior to the cause at hand, can co-exist with jurisprudence, which treats acts as free and thus subject to reward and punishment, so long as neither purports to deal with the act itself but with some next-door neighbor of the thing, either a concept or an appearance of an act.

Irrespective of empirical causes, in other words, reason can and must blame criminal acts in terms of freedom (A 555, B 583).  Freedom, as Kant locates freedom, is neither an actuality (which would put it in the realm of appearances, thus make it subject to regress of causes, thus remove its freedom) nor a possibility (which would not free any actual act from the same chain of causation) but a transcendent idea, a negative concept which we can posit but never picture (A 558, B 586).  Thus, for Kant, explaining material conditions that led to a crime ultimately do not remove the transcendent (beyond cause and effect) reality that a person ought to be one way and ought not to be another.  The idea does not make anything happen, but it does lend intelligibility to freedom without compromising the continuous totality of nature as we know it.

Kant ends this section reminding the reader that these cosmological claims, contradictory at every turn, do not deal with any thing or even any concept or even any appearance but only the conditions in which concepts can locate the negative “space” where a thing might be and in which the same concepts allow for appearances to occur to the mind (A 564, B 592).  The point of all of this meditation on contradiction, as far as I can tell, is analogous to what’s going on with the amphibolies of the mind: because the project of the Critique is to lay down limits to what reason can do and remain reason, unalloyed by perception.  Because so many cosmological disputes in fact do not deal with pure reason but with that mixture of empirical imagination and real, conceptual reasoning, Kant demonstrates that the antinomies are only apparently intractable and in fact fall in place if only we can keep in mind what counts as ideas, what as intuitions of time and space, what anticipations and memories of empirical happenings.  With everything in its place, both the amphibolies and the antinomies turn out to be errors, not limitations of reason, and reason can go about its real work, not saying what is (in terms of cause and effect) but what ought to be (in terms of freedom).

Well, that was a terribly long blog post, and I thank you for riding it out.  In our next episode, Todd will no doubt best me in brevity as he starts to dig into what Kant calls theological reasoning, the world of ultimate ideals.

 

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