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of our awareness of it. In this case the object is not created in the
process of knowing. When Kant says we “determine” an object and
its concept, he means we predicate one of a set of mutually exclusive
concepts to it. For example, in judging that a book is rectangular, I
am classifying it; my representation of it is determinate with respect
to its shape. We use theoretical reason when we make claims about
the properties of things we take to exist independently of us. Claims
of theoretical reason are “is” claims.
By contrast, practical reason concerns the thinking involved in act-
ing, when we decide what we ought to do. In this process, we bring
objective states of affairs into existence. Consider that in making a
decision (say, whether to keep a promise), one ¬rst has to appeal to
some rule concerning one™s values or desired goals. Kant calls such
The Prefaces and the Introduction 19
rules imperatives, because they express what one ought to do. (The
highest principle of morality for Kant is the categorical imperative,
but we also act according to non-moral or hypothetical imperatives.)
Now practical reason consists in making value judgments “ accept-
ing imperatives “ and applying them in making choices in concrete
situations. For example, if I decide to brush my teeth after eating
breakfast, it is because I accept a principle of the form “If you want
to be healthy, you should brush your teeth after meals.” When we
act, we change the objective situation by bringing about a new state
of affairs. In this sense the “object” of the judgment does not exist
prior to the judgment. For Kant, the state of affairs resulting from
the action also includes the state of our own will.
Kant believes that both theoretical and practical knowledge have
metaphysical parts. The metaphysics of each type of knowledge con-
sists in the a priori or pure rules originating in reason alone. The
Critique of Pure Reason is Kant™s account of the metaphysical foun-
dations of theoretical reasoning. Kant presents his metaphysics of
practical reason in The Critique of Practical Reason, where he argues
for the validity of the categorical imperative.
From Bxi to Bxiii Kant characterizes his new critical method as his
“Copernican revolution”: “reason has insight only into what it itself
produces according to its own design” (Bxiii). Kant accepts Hume™s
arguments that if theoretical knowledge depended solely on experi-
ence, we could never arrive at laws of nature: “accidental observations,
made according to no previously designed plan, can never connect
up into a necessary law, which is yet what reason seeks and requires.”
Inductive generalizations take the form “All Fs observed so far are
Gs” (e.g., “All crows observed so far are black”) rather than “All Fs are
necessarily Gs” (“All crows are necessarily black”). If necessary knowl-
edge cannot be derived a posteriori, from experience, then it must be
known a priori. As we shall see in the Introduction, one criterion of
a priori knowledge is its necessity.
With this point established Kant makes his famous claim to do
for philosophy what Copernicus did for astronomy. Kant effects his
Copernican revolution by rejecting a traditional assumption about
knowledge:
Up to now it has been assumed that all our cognition must conform to the
objects; but all attempts to ¬nd out something about them a priori through
concepts that would extend our cognition have, on this presupposition,
The Prefaces and the Introduction
20
come to nothing. Hence let us once try whether we do not get farther with
the problems of metaphysics by assuming that the objects must conform to
our cognition. (Bxvi)
All previous philosophers, rationalist and empiricist, assumed that
knowledge depends entirely on the world outside the perceiver.
Accordingly, our knowledge is of things as they exist independently of
us. Objective truth is independent of subjective conditions of knowl-
edge. In Kant™s terminology, this standpoint identi¬es the objects
of knowledge with things in themselves, that is, the ultimate reality
behind the appearances. Now although they disagreed about the roles
of reason and perception, both rationalists and empiricists assumed
that knowledge consists in discovering subject-independent truths.
Kant™s reason for giving up the assumption is this: if all cogni-
tion conforms to objects (depends on subject-independent truth),
then one could never establish the validity of a priori or necessary
knowledge. As mentioned earlier, Hume proved that experience at
best yields contingent truths. Now rationalists typically claimed that
knowers possess innate knowledge, the intellectual capacity to intuit
truths about existing things. But Kant rejects these claims. The prob-
lem with innate ideas is to account directly for their application to
the world. Both Descartes and Leibniz justify innate knowledge by
the goodness of God, thereby presupposing that reason can arrive
at truths about reality. Moreover, Kant agrees with Hume that no
knowledge of matters of fact can be obtained apart from a reliance on
the senses. Knowledge through pure thought either is analytic (i.e.,
of relations of ideas), or concerns the general form of thought itself
and does not inform us about actual existence. But a strict empiricism
leads to skepticism, the view that there is no objective basis for claims
to know necessary truths about existing things. Kant ¬rmly rejects
such skepticism.
The solution to proving the validity of a priori knowledge is to per-
form the same shift in perspective that the Polish astronomer Nico-
laus Copernicus made in his revolutionary theory. Before Copernicus,
astronomers assumed that the spectator on Earth is motionless, con-
tributing nothing to the observed motions. Accordingly, the observed
motions of heavenly bodies are in fact their true motions. On his
deathbed in 1543, however, Copernicus published On the Revolution
of the Heavenly Spheres, which replaced the Ptolemaic geocentric sys-
tem with the heliocentric or sun-centered system. The Earth is not
The Prefaces and the Introduction 21
motionless at the center of the universe, but rotates around the Sun
along with other heavenly bodies. Thus the motions of planets and
stars apparent to a spectator on Earth result from both their true
motions and the motions of the spectator. Kant believes that only
through a similar shift can we explain how we have a priori knowl-
edge. He will argue that empirical knowledge depends jointly on
what exists independently of us and on our nature as subjects. As this
reasoning implies, the features of objects known to be necessary are
those the subject contributes to experience. Contingent knowledge
is still dependent on our actual experience of objects.
In fact, Kant believes that the history of geometry, physics, and
chemistry lends support to this shift. At Bxi“xii he remarks that
geometry became a science of necessary truths only when geome-
ters stopped measuring objects to determine their properties, and
instead considered what was required to construct geometrical ¬g-
ures in space. Similarly, experimental results in physics and chemistry
achieved a ¬rmer footing when scientists such as Galileo, Torricelli,
and Stahl followed methods constrained by causal principles. In all
these cases the revolutionary shift consisted in the idea that reason
provides principles that govern the scientist™s demonstrations or use
of empirical evidence.
But this new critical perspective has some startling implications,
namely that “we can never get beyond the boundaries of possible
experience,” and that a priori cognition “reaches appearances only,
leaving the thing in itself as something actual for itself but unrecog-
nized by us” (Bxix“xx). Recall that the “thing in itself” (Ding an sich)
is whatever exists as it is independently of our cognitive access to it.
Appearances, as we shall see, are these existing things as they appear
to us. Once we no longer assume that empirical truth is independent
of our subjective capacities, it follows that knowledge does not reach
things in themselves. We must settle for knowledge of appearances.
The thesis that we cannot know things in themselves, called the
“unknowability thesis” (UT), is the most radical aspect of Kant™s
transcendental idealism and is rejected by many philosophers. But
it is a mistake to dismiss Kant™s philosophy because of it, especially
if one does not appreciate its role in his theory. First, UT is not
an assumption of Kant™s method, but rather a conclusion (I think
a plausible one) from his theory of cognition. Here Kant neither
assumes it nor argues for it; he merely alerts the reader that it in fact
The Prefaces and the Introduction
22
follows from his critical theory of knowledge. So anyone persuaded by
Kant™s analysis of human sensibility and understanding must logically
accept UT. But if these arguments are not convincing, then clearly it
is not necessary to accept UT (although one might hold it on other
grounds). It would be an error to dismiss Kant™s system because one
misunderstood the status of the thesis in his philosophy.
The real danger in reacting too strongly to Kant™s radical conclu-
sion is to close oneself off from the profound and subtle arguments
he makes throughout the Critique. It is hard to emphasize strongly
enough the care with which Kant considers his predecessors™ views,
the painstaking nature of his arguments, and the enormously rich and
powerful theory that results. Whether or not one agrees with Kant™s
theory, it is worthy of serious consideration. (Not to mention its enor-
mous in¬‚uence on the history of philosophy.) The truly disinterested
reader must go where the arguments lead. There are many grounds
for rejecting Kant™s arguments; throughout this guide I will pinpoint
the areas of greatest controversy. But at this point, it is important to
keep an open mind about what is to come.
Now back to UT. Kant also expresses it as a denial that we can
have knowledge of the unconditioned. He says: “For that which nec-
essarily drives us to go beyond the boundaries of experience and all
appearances is the unconditioned, which reason necessarily and with
every right demands in things in themselves for everything that is con-
ditioned, thereby demanding the series of conditions as something
completed” (Bxx). In Kant™s jargon, the “unconditioned” is any pre-
supposition of a cognitive claim, which itself has no presuppositions.
For example, the idea of a ¬rst or uncaused cause is one example of the
“unconditioned” since it is a cause unconditioned by any prior cause.
In the case of appearances and things in themselves, Kant sees the
latter as the condition of the former, since (as he says at Bxxvi“xxvii)
it would be absurd to think that there could be appearances without
anything that appears. In other words, the existence of things in them-
selves is a logical presupposition of the fact that something appears to us.
The claim that things in themselves exist has struck many readers as
unjusti¬ed and even inconsistent with other views Kant holds. Before
we can form an opinion on the matter, however, we need to be clear on
what this position involves. First, it means we are logically justi¬ed in
making the minimal existential assumption that something exists that
The Prefaces and the Introduction 23
has its own nature. (In terms of quanti¬cational logic, Kant is simply
asserting that we have the right to take some domain as existing,
and to quantify over it.) This assumption, however, implies nothing
about our ability to know the nature of these things in themselves.
Some commentators claim that even the minimal thesis that things in
themselves exist violates UT. But this ignores the fact that knowledge
consists of true predications, and to claim that things in themselves
exist is to predicate nothing about their natures. When we make
empirical existence claims, such as “Cats exist,” we are (according to
modern logic) asserting that something that exists has the properties
of a cat. In fact Kant was clear that existence is not a real predicate of
things (or, as we would say, a ¬rst-order predicate), and so it gives us
no information about the nature of things in themselves.
In spite of this solution, Kant™s various statements about things
in themselves raise a host of questions. As we shall see, although we
must assume that things in themselves exist, Kant will argue not only
that we can know nothing about them, but also that they cannot
have features essential to appearances, i.e., they cannot be spatial or
temporal, or quanti¬able, or substances standing in causal relations.
At the same time, Kant clearly thinks of things in themselves as
the basis of appearances. His view of the relation between things
in themselves and appearances has stimulated a lively debate among
commentators. We shall return to these issues in chapter 3, after
examining the ¬rst arguments for these conclusions. In my concluding
remarks following chapter 11, I also offer a general overview of the
coherence of Kant™s idealism.
In any case, at Bxx Kant repeats his ¬rst Preface point about the
contradiction that results when we assume that we can know things
in themselves. It is an indirect proof of the critical position that
the contradiction vanishes if we deny the assumption. But he then
remarks at Bxxi that although theoretical reason cannot know things
in themselves (the “supersensible”), practical reason, which does not
depend on sensory experience, can make claims going beyond expe-
rience. In particular, Kant has in mind the con¬‚ict over free will and
determinism. As he says at Bxxvii“xxix, one key conclusion in the
Critique will be that appearances are subject to causal laws. But this
principle also applies to our own actions as we experience ourselves.
From the standpoint of theoretical reason, we must always understand
The Prefaces and the Introduction
24
our actions as effects of antecedent states such as desires. But if we
consider the human will not as it appears to us, but as a thing in itself,
it is possible to think of ourselves acting freely. This is why Kant says
that although one cannot cognize freedom as a property of things
in the world of sense, “nevertheless, I can think freedom to myself, i.e.,
the representation of it at least contains no contradiction” (Bxxviii).
This example of the debate over free will indicates one way the critical
method will resolve traditional metaphysical problems.
At Bxxv“xxvi Kant states the precise views at the basis of UT.
These are “that space and time are only forms of sensible intuition,”
and therefore apply only to appearances, and that we can apply con-
cepts of the understanding to objects only “insofar as an intuition
can be given corresponding to these concepts.” He derives the thesis
concerning space and time in the Transcendental Aesthetic, which
analyzes human sensibility and its capacities. Kant argues for his view
of concepts of the understanding in the Transcendental Analytic.
Here, again, he is only anticipating the main results of his arguments
to come.
Before we go on to the Introduction, it will helpful to put Kant™s
transcendental idealism in historical perspective, to give us a sense
of both the continuity between Kant and his predecessors, and the
radical nature of his idealism. In general the issue between realists
and idealists concerns the metaphysical status of certain entities or
properties. But often these metaphysical questions arise because of
views about knowledge, and so the realism-idealism controversy is
often linked to epistemological issues as well. To begin, let us start
with a baseline realist position, which I shall call “naive realism.”
Naive realism includes any philosophy that considers things as they
appear to us (however this may be) to be these things as they exist
independently of knowers. This realism accepts without quali¬cation
the assumption that all knowledge conforms to objects. Such a theory
assumes that we only discover characteristics of real things, that our
perceptual or other cognitive processes do not distort or conceal their
real properties, or contribute new features to the appearances. So, for
example, a naive realist would hold that physical objects have exactly
the shapes, sizes, colors, and so on that we sense in them. To the
extent that Aristotle accepted this view, his position falls under naive
realism.
The Prefaces and the Introduction 25
The ¬rst step away from naive realism is scienti¬c realism. It appears
as early as ancient atomism, but the scienti¬c realists most familiar
to Kant were Descartes and Locke. They believe that some of the
properties objects appear to have are in fact properties they possess
independently of being perceived. Other properties of appearances are
not real properties of the objects, but result merely from the perceptual
process. In Cartesian dualism, for example, things in themselves are
divided into two sorts of substances, minds and bodies. With respect
to physical substances, Descartes argues that every particle of matter,
whether it is perceived or not, really has such properties as exten-
sion in space, size, shape, and rest or motion. Locke added solidity
to this list of real physical properties. Thanks to Robert Boyle, these
properties became known as “primary qualities.” Other perceived
properties, however, such as colors, odors, sounds, and the heat and
cold we sense, were analyzed as subjective effects in perceivers caused
by the real properties of the particles. Although different philosophers
de¬ned the terms somewhat differently, in general these sensory qual-
ities became known as “secondary qualities.” For the scienti¬c realist,
then, the primary qualities are real properties of physical things, but
the secondary qualities (as we perceive them) are only subjective or
ideal. That is, if there were no perceivers with visual organs, colors
as they appear would not exist. So scienti¬c realists maintain that
some features of appearances are also real features of things in them-
selves, but others are not. But they also hold that it is possible to
get “behind” the appearances, so to speak, to discover the natures of
things in themselves.
The phenomenalism of George Berkeley is idealistic in a different
sense, since for Berkeley the only things that exist are minds and their
ideas. Berkeley argues that the entities we call physical objects really
are nothing more than collections of ideas in a mind. Thus he denies
that what we take to be physical objects in space really are material,
extended things existing independently of human perceivers. Berkeley
does not deny that objects such as trees, rocks, tables, and chairs really
exist; he only denies that they are non-mental. In his phenomenalism,
what we mistakenly consider material objects are nothing more than
collections of sensible ideas. Furthermore he sees no difference in the
metaphysical status of primary and secondary qualities “ all are merely
ideas in perceivers™ minds. But Berkeley agrees with realists that we
The Prefaces and the Introduction
26
can know the true nature of the minds and ideas that constitute things
in themselves.
An even more radical idealism is found in Leibniz™s philosophy,
since Leibniz thinks both space and time are ideal. It is no accident
that this version is closest to Kant™s, for Kant was educated by students
of the Leibnizian Christian Wolff. Although Kant rejects Leibniz™s
epistemology, he borrows much of his terminology. Leibniz is a ratio-
nalist who believes that sense perception is a confused or degraded
form of intellection. In his metaphysics, called the monadology, the
ultimately real substances are monads, indivisible “intelligible” or
“noumenal” entities of which everything is composed. Leibniz argues
from basic logical principles that these entities are not themselves in
space and time. Rather, spatial and temporal features emerge from
the perceptual process; thus Leibniz classi¬es space and time as ideal
or “phenomenal.” Despite their subjective nature, however, spatial
and temporal properties correspond to real features of monads. Leib-
niz expresses this in the view that space and time are “well-founded
phenomena.” So Leibniz™s idealism is more radical than Berkeley™s,
although he also maintains that reason can know things in them-
selves.
In Space and Incongruence I argue that Kant™s idealism resulted from
his rejection of Leibnizian idealism. A key step in Kant™s reasoning
was rejecting Leibniz™s theory that sense perception is merely a con-
fused form of intellection. Despite this difference, Kant did maintain
part of Leibniz™s idealism, namely the view that objects of experience
are merely phenomenal manifestations of underlying, non-spatial,
non-temporal entities. Kant differs from Leibniz in concluding that
we cannot posit any correspondence between phenomena and the
underlying noumena, or in Kant™s vocabulary, between appearances
and things in themselves. In any case, Kant takes Leibniz™s ideal-
ism one step further, to UT. From the epistemological standpoint,
Kant™s idealism is the most radical, since he ends up denying that
we have any knowledge of things in themselves. From the metaphys-
ical standpoint, Kant™s idealism is less radical than Berkeley™s, since
Kant will argue that space and material objects are no less empirically
real than minds and their ideas. In short, the history of philosophy
before Kant leads to ever more idealistic forms of philosophy. Tran-
scendental idealism is the ¬rst idealism to deny that we can draw any
The Prefaces and the Introduction 27
theoretical conclusions about things in themselves. Let us now turn
to Kant™s ¬rst steps in arguing for this position.

3. t he introd uc tion: th e proble m of s ynth eti c
a p r i o r i know le dg e
It is impossible to understand Kant™s arguments that reason supplies
formal features of experience unless one grasps his technical notion
of synthetic a priori knowledge. It is no exaggeration to say that the
precise motivation for Kant™s Copernican revolution is his conviction
that no predecessor had explicitly recognized this kind of knowledge.
Although synthetic a priori knowledge can provide a foundation for
science, it is not obvious how we come by it. Kant™s new critique
of reason undoubtedly arises from his recognition of the peculiar
properties of such cognitions.
The main task of the Introduction is to provide a new classi¬cation
scheme of judgment, and to identify the best candidates for synthetic
a priori cognition. Kant™s account rests on two distinctions, the ¬rst
between a priori and a posteriori cognitions, and the second between
analytic and synthetic judgments. Leibniz and Hume offer similar
analyses, but each makes only one distinction. Leibniz classi¬es all
propositions as analytic or synthetic; Hume divides all beliefs into
relations of ideas (a priori beliefs), and matters of fact (a posteriori
beliefs). On Kant™s view both philosophers mistakenly collapse what
should be two distinctions into one. This is the reason each fails to
recognize the peculiar nature of synthetic a priori knowledge.
Kant begins by distinguishing a priori or pure from a posteriori or
empirical cognition. First he agrees with the empiricists that all cog-
nition begins with experience, because he accepts a stimulus-response
model in which all cognitive processes are triggered by the reception
of sensory input. “As far as time is concerned, then, no cognition in
us precedes experience, and with experience every cognition begins”
(B1). But the second paragraph maintains that although all cognition
is temporally dependent on experience, it does not follow that it is
logically dependent on it. It is possible that the content of cognition is
not all derived from sense impressions. This would be so if the subject
supplied representations in addition to the sense impressions arising
from contact with objects. Here Kant explicitly offers an alternative
The Prefaces and the Introduction
28
to Hume™s theory that all simple ideas are only copies of antecedent
simple impressions.
The question to be investigated in the Critique is whether any
cognition is logically “independent of all experience and even of all
impressions of the senses” (B2). Kant calls such cognition a priori,
in contrast to empirical or a posteriori cognition, which is dependent
for its source and content on experience. In the last two paragraphs
he distinguishes two senses of “a priori,” one relative and the other
absolute. He points out that sometimes we classify cognition as a
priori relative to some general principle: we say someone should know
that undermining the foundations of his house would cause it to fall
before he actually did it. But this is not absolutely a priori knowledge,
because experience is required to know that bodies are heavy. The
a priori knowledge Kant is concerned with is absolutely prior to
all experience, not just prior to some particular experiences. In the
last two sentences of this section, he also speci¬es that by “pure” a
priori cognition he means cognition having “no admixture of anything
empirical.” The proposition “Every alteration has its cause” does not
qualify as pure in this sense, because Kant thinks the concept of an
alteration can be derived only from experience of events in time. Now
in general we, like Kant, will ignore this caveat in the rest of the text.
In The Metaphysical Foundations of Natural Science, Kant clari¬es his
view of the a priori status of the laws of physics. For our purpose we
can safely equate pure with a priori knowledge.
Section II of the Introduction explains that the criteria of a priori
judgments are necessity and strict universality. Unlike a judgment based
on experience, which is only contingent, an a priori judgment is
“thought along with its necessity” (B3). Moreover, such judgments
are also recognized to have a “strict” rather than “merely comparative”
universality. As we saw earlier, Kant accepts Hume™s argument that
inductive generalizations from experience are only contingent. And
because they are based only on observed instances, they are restricted
in scope. But science presupposes necessary judgments, which do
not allow for exceptions. For example, the principle of causality “
“Every event has a cause” “ is assumed to be necessarily true of all
events in time. Obviously it cannot be based on observed instances.
In the last paragraph, from B5 to B6, Kant points out that the term “a
priori” applies not only to judgments, but also to non-propositional

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