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K A N T ™ S CRITIQUE OF
PURE REASON




In this new introduction to Kant™s Critique of Pure Reason,
Jill Vance Buroker explains the role of this ¬rst Critique in
Kant™s critical project and offers a line-by-line reading of the
major arguments in the text. She situates Kant™s views in rela-
tion both to his predecessors and to contemporary debates,
and she explains his critical philosophy as a response to the
failure of rationalism and the challenge of skepticism. Paying
special attention to Kant™s notoriously dif¬cult vocabulary, she
explains the strengths and weaknesses of his arguments, while
leaving the ¬nal assessment up to the reader. Intended to be
read alongside the Critique, this guide is accessible to readers
with little background in the history of philosophy, but should
also be a valuable resource for more advanced students.

jill va nce buroker is Professor of Philosophy at
California State University. Her publications include Antoine
Arnauld and Pierre Nicole: Logic or the Art of Thinking (1996).
ca mbri dge i n trod u ct io n s to key
ph i los ophi c a l t e x ts


This new series offers introductory textbooks on what are considered to
be the most important texts of Western philosophy. Each book guides the
reader through the main themes and arguments of the work in question,
while also paying attention to its historical context and its philosophical
legacy. No philosophical background knowledge is assumed, and the books
will be well suited to introductory university-level courses.

Titles published in the series:
d esc arte s™s m e d i tat i o n s by Catherine Wilson
w it tg en ste in™s p h i l o s o p h i c a l i n v e s t i g at i o n s
by David G. Stern
wi t tg en ste in™s t r a c tat u s by Alfred Nordmann
aristotle™s n i c o m a c h e a n e t h i c s by Michael Pakaluk
spi n oz a™s e t h i c s by Steven Nadler
kan t™s c r i t i q u e o f p u r e r e a s o n by Jill Vance Buroker
K A N T ™ S CRITIQUE OF
PURE REASON
An Introduction


J I L L VA N C E B U RO K E R
California State University, San Bernardino
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
The Edinburgh Building, Cambridge cb2 2ru, UK
Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521853156

© Jill Vance Buroker 2006


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For Sophie
Contents




Acknowledgments page viii
List of abbreviations ix

1 Introduction to the critical project 1
2 The Prefaces and the Introduction 14
3 The Transcendental Aesthetic 36
4 The Metaphysical Deduction: identifying categories 73
5 The Transcendental Deduction of the categories 103
6 The Schematism and the Analytic of Principles I 136
7 The Analytic of Principles II 163
8 Transcendental illusion I: rational psychology 201
9 Transcendental illusion II: rational cosmology 226
10 Transcendental illusion III: rational theology 264
11 Reason and the critical philosophy 284
Conclusion: Kant™s transcendental idealism 305

Works cited 310
Index 317




vii
Acknowledgments




I am grateful to California State University, San Bernardino, for sab-
batical and research support while I was writing this book. I also thank
my colleague, Tony Roy, for helpful conversations, and students who
allowed themselves to be test subjects for various chapters. My inter-
pretation of Kant has been most heavily in¬‚uenced by Henry Allison,
Gordon Brittan, Jr., Lorne Falkenstein, Michael Friedman, Michelle
Grier, and Arthur Melnick. Gordon Brittan and Lorne Falkenstein
both made valuable comments on early drafts. I am indebted to Hilary
Gaskin of Cambridge University Press, and three readers for the press,
William Baumer, Fred Rauscher, and Lisa Shabel, for their sympa-
thetic criticisms and suggestions. I was especially fortunate to have
Angela Blackburn as my copy-editor. Finally, I want to thank Ed
McCann for his encouragement.




viii
Abbreviations




CPR Kant, Critique of Pure Reason
MFNS Kant, Metaphysical Foundations of Natural Science
NST non-spatial and non-temporal
(non-spatiotemporality thesis)
PD Principle of Determinability
Prolegomena Kant, Prolegomena to Any Future Metaphysics
PTD Principle of Thoroughgoing Determinability
t.u.a. transcendental unity of apperception
UT unknowability thesis




ix
chap t e r 1

Introduction to the critical project




1. ka nt™s lif e a nd works
Immanuel Kant was one of the greatest thinkers in the history of
philosophy. Unfortunately, he was not a good writer, and his works
are very dif¬cult to read. Not only did Kant write on most major
philosophical problems “ concerning knowledge, metaphysics, ethics,
aesthetics, religion, law, and government “ he also developed views
of extreme depth and subtlety. Especially impressive is the way Kant
uni¬ed his theories into a larger system, called an “architectonic.”
Although he sometimes appears to stretch his ideas to ¬t them into
his system, generally the unity in his views is not forced, and rests on
philosophical principles.
Kant lived from 1724 to 1804, during a period of enormous change
in science, philosophy, and mathematics. Kant himself was neither a
scientist nor a mathematician (although he did make a contribution
to cosmology). Nonetheless he shared the hopes of predecessors such
as Descartes and Locke to provide a philosophical foundation for
the new physics. The scienti¬c revolution, initiated by Copernicus™s
On the Revolutions of the Heavenly Spheres in 1543, put an end to
the Aristotelian worldview that had reigned for almost 2000 years.
The French philosopher Ren´ Descartes (1596“1650), a contemporary
e
of Galileo (1564“1642), was the ¬rst to attempt a systematic theory
of knowledge to support the Copernican astronomy. Descartes not
only invented analytic geometry, he also developed his own physics
and made important discoveries in optics, among them the sine law
of refraction. The power of mechanistic science became undeniable
with Isaac Newton™s formulation of the three laws of motion and
the law of gravitation, published in his Principia Mathematica of

1
Introduction to the critical project
2
1686. In providing a general explanation for Kepler™s laws of planetary
motion, Newton™s achievement brought to the fore questions about
the foundations of science. The new physics also depended on the
calculus, invented independently by Newton and Leibniz.
Immanuel Kant was born April 22, 1724, in K¨ nigsberg, the capital
o
of East Prussia (now Kaliningrad in Russia). He lived his entire life
1

in or near K¨ nigsberg, a thriving commercial city. His father was a
o
saddler, and Kant grew up in a working class family. Between the ages
of eight and sixteen, Kant attended the Friedrichskollegium, whose
principal was Albert Schultz (1692“1763). Schultz had been a student
of the Enlightenment philosopher Christian Wolff (1679“1754), him-
self a student of the great philosopher and mathematician Gottfried
Wilhelm Leibniz (1646“1716). The Friedrichskollegium was af¬liated
with Pietism, a seventeenth-century German Protestant movement.
It emphasized the “scrutiny of the heart,” and valued the active devo-
tion of the person. Kant rejected its more rigid practices, but evidently
admired its general principles. The school™s curriculum emphasized
religious instruction in Hebrew and Greek; non-religious subjects
were less important. In 1737, when Kant was thirteen, his mother died.
He was very close to her, and credited her with nurturing both his
spirit and his intellect. In 1740 Kant graduated second in his class from
the Friedrichskollegium, and entered the University of K¨ nigsberg.
o
There he was in¬‚uenced by another student of Wolff, Martin Knutzen
(1713“51), a professor of logic and metaphysics. Under Knutzen™s tute-
lage from 1740 to 1746, Kant studied philosophy, mathematics, nat-
ural sciences, and classical Latin literature.
Following his father™s death in 1746, Kant left the university to
support himself as a private tutor. In 1747 he completed his ¬rst
work, Thoughts on the True Estimation of Living Forces (published in
1749), in which he attempted to resolve a dispute between Leibnizians
and Cartesians over the formula for calculating force from mass and
velocity. Unfortunately Kant was ignorant of the correct solution,
proposed by d™Alembert in 1743. Nevertheless, this work, written in
German rather than the traditional Latin, marked the beginnings

1 Two excellent biographies are available in Ernst Cassirer™s Kant™s Life and Thought, and
Manfred Kuehn™s recent Kant: A Biography.
Introduction to the critical project 3
of Kant™s lifelong interest in the foundations of physics. During the
1750s he produced several scienti¬c treatises, the most important his
Universal Natural History and Theory of the Heavens (1755). His theory
of the formation of galaxies, later dubbed the “Kant-Laplace hypoth-
esis,” had a signi¬cant in¬‚uence on astronomy. In the same year Kant
completed his doctoral dissertation Meditations in which the Ether is
Succinctly Delineated, and his “habilitation” treatise A New Elucida-
tion of the First Principles of Metaphysical Cognition. The latter work
marks his earliest criticism of Leibnizian philosophy.
Although Kant began lecturing at the University of K¨ nigsberg
o
in the fall of 1755, he was practically destitute, depending on fees
from tutoring and lectures. After several unsuccessful applications for
professorships in logic and metaphysics, he received his ¬rst salaried
position in 1766 as assistant librarian at the palace library. Not until
1770, at the age of forty-six, was Kant awarded the professorship
he desired. His workload was formidable: he taught logic, mathe-
matics, metaphysics, physical geography, and foundations of natural
science. Eventually he added ethics, mechanics, theoretical physics,
geometry, and trigonometry. Despite the stereotype of Kant as rigidly
intellectual (and punctual), he was a great favorite both in and out
of the classroom. His lectures were renowned for erudition and wit.
But he was also quite sociable, sharing long dinners with friends and
frequenting the theater and casinos. He was highly prized for his
sparkling conversation in the most fashionable salons. This passage
from a student, the poet and philosopher Johann Gottfried Herder,
should put to rest the misleading stereotype:

I have had the good fortune to know a philosopher. He was my teacher.
In his prime he had the happy sprightliness of a youth; he continued to
have it, I believe, even as a very old man. His broad forehead, built for
thinking, was the seat of an imperturbable cheerfulness and joy. Speech,
the richest in thought, ¬‚owed from his lips. Playfulness, wit, and humor
were at his command. His lectures were the most entertaining talks. His
mind, which examined Leibniz, Wolff, Baumgarten, Crusius, and Hume,
and investigated the laws of nature of Newton, Kepler, and the physicists,
comprehended equally the newest works of Rousseau . . . and the latest
discoveries in science. He weighed them all, and always came back to the
unbiased knowledge of nature and to the moral worth of man. . . . No
Introduction to the critical project
4
cabal, no sect, no prejudice, no desire for fame could ever tempt him in the
slightest away from broadening and illuminating the truth. He incited and
gently forced others to think for themselves; despotism was foreign to his
mind. This man, whom I name with the greatest gratitude and respect, was
Immanuel Kant.2
Until the 1760s Kant was a devotee of Leibniz through the teach-
ings of Christian Wolff. In 1768 he published the short treatise On the
Differentiation of Directions in Space, in which he used the argument
from incongruent counterparts (objects like left and right hands) to
support a Newtonian theory of absolute space against Leibniz™s the-
ory of relational space. I argue in my Space and Incongruence: The
Origin of Kant™s Idealism that after 1768 Kant developed the incon-
gruent counterparts argument to reject Leibniz™s theory of the relation
between the sensibility and the intellect, and ultimately to support the
transcendental ideality of space and time. His introduction to Hume™s
Enquiry Concerning Human Understanding (published in 1748), prob-
ably around 1769, crystallized his misgivings about rationalism and
dogmatic metaphysics. Kant took his ¬rst step toward the critical
philosophy, the theory presented in his three Critiques, in his Inau-
gural Dissertation of 1770, On the Form and Principles of the Sensible
and Intelligible World. Here he radically distinguished the sensibil-
ity from the intellect, arguing that the former provides knowledge
only of phenomenal appearances. Nevertheless, he retained Leibniz™s
view that the intellect has access to noumena, the reality behind the
appearances.
In his February 21, 1772 letter to Marcus Herz, a former student
and friend, Kant lays out the questions haunting him since the dis-
sertation, which de¬ne the critical project:
In my dissertation I was content to explain the nature of intellectual rep-
resentations in a merely negative way, namely, to state that they were not
modi¬cations of the soul brought about by the object. However, I silently
passed over the further question of how a representation that refers to an
object without being in any way affected by it can be possible.3
Kant had come to see that he needed a more systematic treatment of
the intellect, in both its theoretical and practical activities. In the letter
Kant outlines a plan for his work, remarking optimistically that he
expects to complete the ¬rst part, on metaphysics, in three months.
2 3
Quoted in Cassirer, Kant™s Life and Thought, 84. Correspondence, 133.
Introduction to the critical project 5
In fact he did not produce the ¬rst edition of the Critique of Pure
Reason until 1781, almost twelve years after conceiving the project.
Unfortunately the work initially drew negative responses, both for
its obscurity and its conclusions. Eventually opinion shifted, and the
Critique began to exert its in¬‚uence in Germany and elsewhere. In
1786 Kant was made a member of the Berlin Academy of Sciences; in
1794 he was inducted into the Petersburg Academy, and in 1798 into
the Siena Academy.
Once engrossed in developing his critical philosophy, Kant became
a recluse. This is the only explanation for his enormous output
from 1781 to his death in 1804. These are the major works in that
period:
1781 The Critique of Pure Reason, ¬rst edition (referred to as A)
1783 The Prolegomena to Any Future Metaphysics (an obscure sum-
mary of the Critique)
1785 The Groundwork of the Metaphysics of Morals
1786 The Metaphysical Foundations of Natural Science
1787 The Critique of Pure Reason, second edition (referred to as B)
1788 The Critique of Practical Reason
1790 The Critique of the Power of Judgment
1797 The Metaphysics of Morals
1798 Anthropology from a Pragmatic Point of View
During this period Kant also wrote many shorter essays, among them
“The Idea for a Universal History with Cosmopolitan Intent” and
“What is Enlightenment?” (both 1784), Religion Within the Bounds of
Reason Alone (1793), On Eternal Peace (1795), and The Con¬‚ict of the
Faculties (1798).
His publication of the 1793 treatise on religion brought him into
con¬‚ict with a religious edict issued in 1788 by Frederick William II
(1786“97). Under Frederick William I (1713“40) and Frederick II, the
Great (1740“86), Prussia had been transformed from an authoritarian
state to a constitutional monarchy. Also known for religious tolerance,
it welcomed refugees from other countries, including Huguenots
from France, Catholics from Eastern Europe, and Jews. Despite these
progressive developments, the edict of 1788 put an end to religious lib-
eralism. Although the theology faculty of the University of K¨ nigsberg
o
declared that Kant™s treatise was not an essay in theology, the king
opposed its publication. During this affair, in June of 1794, Kant
Introduction to the critical project
6
published his second treatise on religion, the ironic The End of All
Things. In October of 1794 Frederick William II ordered Kant to
desist from such writing. Although Kant defended himself against
the charges, he agreed to renounce further essays on religion as long
as the king lived.
Kant™s last project, published as the Opus Postumum, was intended
as a bridge between the critical philosophy and empirical science.
Although he began the work in 1796, he was not to complete it. On
October 8, 1803, he became seriously ill for the ¬rst time. He died four
months later, on February 12, 1804. Thousands of mourners attended
his funeral procession on February 28. They took Kant™s body to the
professors™ crypt in the cathedral and university chapel of K¨ nigsberg.
o
A plaque later installed over the grave contains the famous quotation
from the Critique of Practical Reason: “Two things ¬ll the mind with
ever new and increasing admiration and awe, the more often and
more steadily we re¬‚ect on them: the starry heavens above me and the
moral law within me.”4

2 . th e criti c a l proj e ct
Kant™s critical philosophy attempts to show that human reason can
attain objective truths about the nature of reality as well as moral-
ity. Both types of knowledge are based on laws that are necessary
but known a priori, that is, independent of experience. Theoretical
knowledge is based on laws of nature, and moral knowledge on the
moral law. Neither rationalism nor empiricism explains how we have
such knowledge because both schools give mistaken analyses of the
human mind. Empiricists favor sense perception over the intellect,
and effectively deny the possibility of a priori knowledge. Rational-
ists recognize a priori knowledge, but have no coherent account of its
relation to experience. Kant originally intended the ¬rst Critique to
provide a philosophical justi¬cation for both theoretical and moral
knowledge. Recognizing after 1781 that morality required a distinct
foundation, Kant published the Groundwork of the Metaphysics of
Morals in 1785 and the Critique of Practical Reason in 1788. In the
Critique of the Power of Judgment of 1790 Kant broadens his project to

4 Practical Philosophy, 269.
Introduction to the critical project 7
include an analysis of teleological judgment at the basis of aesthetics
and empirical science. Although the three Critiques are the founda-
tion of Kant™s critical philosophy, the other works listed above on
morality and science expand his analysis of theoretical and practical
reason. In this section I will focus on the problems de¬ning Kant™s
critical theory of knowledge in the ¬rst Critique.
It is not misleading to view Kant™s critical philosophy as respond-
ing to the defects of rationalism and empiricism. The rationalists of
the modern period include Descartes, Baruch Spinoza (1632“77), and
Leibniz. In general they argue that knowledge derives from the intel-
lect, which may be aided or hindered by sense perception. Although
these philosophers differ on how the senses relate to the intellect, they
agree that the intellect alone can grasp truths about reality, through
innate ideas, prior to all sense experience. Descartes undoubtedly
provides the most famous arguments along these lines in his cogito
argument for his existence and his proofs for the existence of God.
Although the senses can contribute to physical science, Descartes
thinks sense perceptions are more likely to interfere with intellectual
intuition. Leibniz conceives the relation between the senses and the
intellect differently, taking sensory experience as a confused form of
thinking. Although he agrees that knowledge of noumena, or things
in themselves, is innate, depending entirely on the intellect, he holds
that there is a correspondence between noumenal reality and phe-
nomenal appearances. His Monadology (1714) is a paradigmatic ratio-
nalist attempt to base metaphysics on logical principles of identity
and non-contradiction.
In contrast to the rationalists™ optimism about the power of reason,
the British empiricists of the modern period “ John Locke (1632“
1704), George Berkeley (1685“1753), and David Hume (1711“76) “
emphasize the role of the senses. “Empiricism” is derived from the
Greek word for experience; on their view all ideas originate in sense
perception and re¬‚ection on our own minds. The intellect alone
cannot know reality; at best it can operate on ideas given through
the senses by such processes as association, comparison, abstraction,
and deduction. In his Essay Concerning Human Understanding (1689),
Locke argues, like Aristotle, that the mind is a tabula rasa or blank slate
at birth; all mental processes begin with sensory stimulation, and the
mind contains no innate ideas. Despite his empiricism, Locke accepts
Introduction to the critical project
8
many of Descartes™s metaphysical beliefs, such as the existence of
God, bodies, and causal connections. Although he thinks knowledge
of reality can never be certain, Locke does not question our capacity
to acquire scienti¬c knowledge, however fallible.
It is a paradox of empiricism that a commonsense theory of knowl-
edge leads ultimately to a profound skepticism. Berkeley takes the ¬rst
steps by arguing that belief in a mind-independent material world is
not only unjusti¬able but incoherent. Thus he rejects Descartes™s
substance dualism in favor of metaphysical idealism “ the view that
all reality consists of minds and their mental states. In his Principles
of Human Knowledge (1710) and Three Dialogues Between Hylas and
Philonous (1713), Berkeley rejects the existence of matter. Neverthe-
less, he retains Descartes™s beliefs in the existence of God and minds
as mental substances.
Hume, of course, argues for the most sweeping skepticism. In his
Treatise of Human Nature (1739), Hume argues against knowledge
of reality outside one™s perceptions, including minds, bodies, and
God. Against the rationalists, Hume makes devastating criticisms of
the capacity of “reason” as a purely intellectual faculty. In place of a
philosophical justi¬cation of metaphysics, he offers a psychological
account of its origins. Appealing to “reason” in a broad sense, includ-
ing the functions of the imagination, Hume claims that metaphysical
beliefs are “natural,” even if not strictly justi¬ed. Although his con-
temporaries failed to appreciate Hume™s brilliance, he effectively put
an end to rationalist metaphysics.
As we saw above, Kant was raised a Leibnizian, taught by stu-
dents of Wolff. Nevertheless, in the 1760s he recognized the power of
Hume™s attack on metaphysics. As he explains in the Prolegomena to
Any Future Metaphysics: “I openly confess that my remembering David
Hume was the very thing which many years ago ¬rst interrupted my
dogmatic slumber and gave my investigations in the ¬eld of specu-
lative philosophy a quite new direction.”5 Kant was less impressed,
however, by Hume™s psychological account of metaphysical belief. So
by 1769, Kant embarked on the ¬rst steps of his critical project.
Kant intends to defend metaphysics and scienti¬c knowledge by
providing an accurate analysis of human reason. His theory is based

5 Theoretical Philosophy after 1781, 57.
Introduction to the critical project 9
on his discovery of synthetic a priori knowledge, judgments that are
both informative and necessary. The problem is to explain how such
judgments arise, as well as to give an account of their truth. Agreeing
with Hume that experience cannot be their source, Kant takes the
“critical turn,” locating such knowledge in the subject. But equally
unhappy with rationalism™s appeal to innate principles, Kant must
offer a new theory of the mental faculties. The key is his view that
human reason, both theoretical and practical, produces synthetic a
priori principles in the course of its natural activities. The Critique of
Pure Reason argues that the necessary mathematical and metaphysical
principles underlying all theoretical knowledge originate in the pure
forms of sensibility and the intellect.
From Kant™s point of view, all thought before him is pre-critical:
he was the ¬rst to offer a systematic, functional justi¬cation of pure
concepts and principles. To do this, Kant invents a new type of
argument, which he calls a “transcendental deduction.” His strat-
egy is to show that a certain type of experience has particular nec-
essary conditions. Thus anyone who accepts the “fact of experience”
must agree that its transcendental conditions or presuppositions are
true. All previous philosophers assumed that there were only two
alternatives: either accept some substantive beliefs dogmatically as
self-evident, or fall into an in¬nite regress of justi¬cation. One hall-
mark of Kant™s brilliance is the way his critical method sidesteps this
dilemma, by exploiting assumptions necessary to frame the skeptical
challenge.
Kant™s view that synthetic a priori knowledge originates in the sub-
jective capacities of the knower results in transcendental idealism.
This is the position that all theoretical knowledge is only of appear-
ances, and that things in themselves are unknowable. Despite its radi-
cal nature, Kant™s idealism offers solutions to two skeptical challenges.
First, while it sets clear limits to metaphysics and empirical science,
it explains how humans can attain knowledge of the spatial-temporal
world. Second, it provides the basis for claiming that knowledge of a
world governed by causal necessities is compatible with the practical
freedom required by the moral law. These interwoven strands of the
critical philosophy “ the analysis of human reason, the justi¬cation
of synthetic a priori knowledge, and transcendental idealism “ will
serve as main themes in this guide.
Introduction to the critical project
10

3. t he struct ure of t h e c r i t i q u e o f p u r e r e a s o n
As mentioned above, Kant™s philosophy is noteworthy for its system-
atic nature. The Critique of Pure Reason is organized around several
fundamental distinctions. After the two Prefaces (the A edition Pref-
ace of 1781 and the B edition Preface of 1787) and the Introduction,
the text is divided into the Doctrine of Elements and the Doctrine
of Method. The ¬rst part explains the a priori contributions of the
mind to experience, and the legitimate and illegitimate use of these
representations. Kant further divides the Doctrine of Elements into
the Transcendental Aesthetic and the Transcendental Logic, re¬‚ect-
ing his basic distinction between the sensibility and the intellect. In
the Transcendental Aesthetic he argues that space and time are pure
forms of intuition inherent in our sensory capacities, accounting for
the a priori principles of mathematics. The Transcendental Logic
is divided into the Transcendental Analytic and the Transcenden-
tal Dialectic. The former defends the legitimate uses of the a priori
concepts, the categories, and their correlative principles of the under-
standing, in attaining metaphysical knowledge. The section titled
the Metaphysical Deduction explains the origin of the categories;
in the Transcendental Deduction, Kant makes the central argument
justifying their application to experience. Following this, the Ana-
lytic of Principles contains detailed arguments for the metaphys-
ical principles correlated with the categories. This section begins
with the Schematism, which explains how the imagination functions
in applying pure concepts to the sensible data given in intuition.
Then follow the detailed arguments for the a priori principles corre-
lated with the schematized categories. The last part of the Doctrine of
Elements, the Transcendental Dialectic, explains the transcendental
illusion that motivates the misuse of these principles beyond experi-
ence. Kant™s most signi¬cant arguments are the Paralogisms of Pure
Reason, the Antinomy of Pure Reason, and the Ideal of Pure Reason,
aimed against, respectively, traditional theories of the soul, the uni-
verse as a whole, and the existence of God. In the Appendix to the
Critique of Speculative Theology Kant explains the positive role of
the transcendental ideas of reason. The Doctrine of Method, which
takes up no more than a sixth of the text, contains four sections, of
Introduction to the critical project 11
which the ¬rst two are most signi¬cant. The Discipline of Pure Rea-
son contrasts mathematical and philosophical methods of proof, and
the Canon of Pure Reason outlines the relation between theoretical
and practical reason, in preparation for the critical moral philosophy.
Here is an outline of the text, listing the main discussions:

1. First and second Prefaces
2. Introduction
3. Doctrine of Elements
A. Transcendental Aesthetic
B. Transcendental Logic
(1) Transcendental Analytic
a. Analytic of Concepts
i. Metaphysical Deduction
ii. Transcendental Deduction
b. Analytic of Principles
i. Schematism (bridging chapter)
ii. System of Principles of Pure Understanding
a. Axioms of Intuition
b. Anticipations of Perception
c. Analogies of Experience
d. Postulates of Empirical Thought (Refutation of
Idealism)
iii. Ground of Distinction of Objects into Phenomena
and Noumena
iv. Appendix on the Amphiboly of the Concepts of
Re¬‚ection
(2) Transcendental Dialectic: Transcendental Illusion
a. Paralogisms of Pure Reason
b. Antinomy of Pure Reason
c. Ideal of Pure Reason
d. Appendix to Critique of Speculative Theology
4. Transcendental Doctrine of Method
A. Discipline of Pure Reason
B. Canon of Pure Reason
C. Architectonic of Pure Reason
D. History of Pure Reason
Introduction to the critical project
12
4. th e second (b ) e d i ti on versi on
The ¬rst important review of the Critique appeared in the January
19, 1782, edition of the G¨ttingischen Anzeigen von gelehrten Sachen.
o
The review was originally based on a sympathetic exposition of Kant™s
arguments by Christian Garve (1742“98), a moral philosopher. The
published version, however, rewritten by J. G. H. Feder (1740“1820),
omitted most of Garve™s interpretation, and emphasized three objec-
tions. First, it mistakenly assimilated Kant™s idealism to Berkeley™s
idealism, which analyzes spatial objects as collections of sense data.
Second, based on this reading, it charged that Kant™s theory could
not distinguish between the real and the imaginary. And ¬nally, it
attacked the distinction between theoretical and practical philoso-
phy, on the grounds that morality is based on common sense. This
misreading and Kant™s own dissatisfaction with the Transcendental
Deduction prompted him to publish a revision in 1787.
In his revised (or B) edition Kant separates his transcendental
idealism from Berkeley™s “empirical” idealism, and reworks several
key arguments. The second edition Preface presents Kant™s critical
approach through the startling metaphor of the Copernican revolu-
tion. Kant also expands his arguments in the Introduction and the
Transcendental Aesthetic. The two major changes in the Analytic
are a completely revised Transcendental Deduction of the categories,
and a new section, the Refutation of Idealism, added to the Ana-
lytic of Principles. Kant reworks the Transcendental Deduction to
address two defects of the earlier edition: a failure to make the unity
of self-consciousness the foundation of the argument, and a lack of
connection to the theory of judgment. In the Refutation of Idealism
Kant clari¬es his idealism. Although the proof is aimed at Descartes™s
view that knowledge of the external world is less certain than self-
knowledge, Kant elucidates the difference between his and Berkeley™s
idealism as well. Because of this addition, Kant also revised the Par-
alogisms section of the Dialectic.
In this text my main purpose is to explain Kant™s arguments intel-
ligibly to the student who has some familiarity with the history of
philosophy. In keeping with the principle of charity, I attempt to give
Kant™s views the most plausible interpretation consistent with the
texts. At the same time I indicate the main strengths and weaknesses
Introduction to the critical project 13
in his views. While it is impossible to evaluate the many criticisms
leveled against Kant, I point out both some clear misunderstandings
and many reasonable questions raised by commentators. And since I
believe it is impossible to understand a philosophy without knowing
the issues engaging the philosopher, as well as the legacy, in general
the discussion situates Kant™s arguments in the context of his times.
c h a p t er 2

The Prefaces and the Introduction




1 . t he a ed ition pre face : th e probl em
of h u ma n re a s on
In the ¬rst edition Preface Kant explains why a critique of human
reason “ the power to know “ is necessary. At Avii he says it is the
nature of reason to ask questions it cannot answer. Although he gives
no examples, these questions are the basis of traditional metaphysical
disputes Kant examines in the Transcendental Dialectic: is the uni-
verse ¬nite or in¬nite in space and time? Is matter in¬nitely divisible
or composed of simple parts? Do humans have free will or are we
determined by causes outside our control? And does the existence of
the universe presuppose a necessarily existent being? We can see how
these questions arise in our everyday thinking. Consider the princi-
ple underlying scienti¬c investigation: “Every event has a cause.” We
“naturally” ask: what caused the earthquake? What causes the earth
to revolve around the sun? What caused the universe? But if these
questions arise naturally, then what is the problem?
In the Dialectic, Kant describes how, in trying to explain reality,
reason ends up in a dilemma: either the explanatory chain contin-
ues forever, or it must end somewhere. The temptation is to ¬nd a
stopping place, to invent an “absolute” to end the series. Examples of
such “absolutes” are God as the cause of the universe, and freely acting
souls as the causes of human actions. The problem with such answers
is that they cannot be veri¬ed by experience. Humans cannot experi-
ence the entire history of the universe, or God, or an immaterial soul
as they can experience everyday events in space and time. As Kant
puts it, once we have conjectured about the existence of things that


14
The Prefaces and the Introduction 15
are not possible objects of experience, then reason has overstepped its
bounds, namely “all possible use in experience” (Aviii).
This is why the traditional metaphysical debates have never been
resolved. Since the Greeks, philosophers have inquired about the
ultimate nature of reality, but once they posited the existence of
“absolutes,” their answers could not be tested by experience. So meta-
physicians could only conjecture rather than make genuine claims to
knowledge. Worse, different philosophers gave opposing solutions,
and thus human reason “falls into obscurity and contradictions”
(Aviii). Because Kant treats these questions at length in the Tran-
scendental Dialectic, here he only points out that the unresolved
debates of metaphysics show that philosophers have been using the
wrong methods. In particular, he will argue that all cognitive claims
must be decidable by reference to experience. (A version of this idea
gains prominence as the “veri¬ability principle” of meaning espoused
by twentieth-century positivists.)
From Aix to Ax Kant describes the battles between dogmatists “
rationalists such as Plato, Descartes, and Leibniz “ and skeptics “
empiricists who questioned the ability to discover the nature of reality.
Kant mentions that Locke attempted a “physiology” of the under-
standing, but this settled nothing, since Locke wrongly assumed that
the answer lies in analyzing how experience arises historically. In fact,
none of Kant™s predecessors identi¬ed the necessary conditions for
knowledge. Until this is done, the traditional problems of metaphysics
cannot be resolved.
Philosophy must start all over again by examining reason itself to
discover what it is capable of knowing. Here as well as in the deduc-
tion of the categories, Kant uses the metaphor of judicial claims to
describe his task, since he thinks of reason as having to establish its
rightful claim to knowledge. As he explains at Axii, a critique of reason
by reason would examine the sources, extent, and limits of our cog-
nitive capacities. More speci¬cally, the critique would answer these
questions:

1. What can reason know independently of experience?
2. Is metaphysical knowledge possible? Are metaphysical questions
meaningful and decidable?
The Prefaces and the Introduction
16
3. What are the limits of knowledge by reason alone? In particular,
Kant is concerned about whether humans can attain knowledge
of things in themselves, or things as they exist independently of
human perceivers.

Like many of Kant™s key terms, the term “reason” (Vernunft) has
several meanings. Kant uses “reason” in three important senses. In
its broadest use, “reason” refers to all subjective processes involved in
knowing. The second sense is less inclusive, and refers to intellectual
as opposed to sensory capacities. The third and narrowest sense of
“reason” refers to the inferential operations involved in logical justi-
¬cations and explanations; in this sense reason is distinguished from
the understanding as the faculty of judging. Kant attributes the errors
of traditional metaphysics to reason in the narrowest sense.
At Axiii Kant makes this extravagant claim: “In this business I
have made comprehensiveness my chief aim in view, and I make bold
to say that there cannot be a single metaphysical problem that has
not been solved here, or at least to the solution of which the key
has not been provided.” Now since philosophers before Kant spent
several thousand years wrangling over metaphysics, the immodesty
of his statement cannot fail to strike the reader. But the next sentence
explains Kant™s optimism. Pure reason is “such a perfect unity” that
its principle supplies the solutions to all metaphysical problems. This
means that the solutions to the metaphysical debates depend on what
the subject contributes to knowledge. Kant will argue that human
reason is governed by a single principle, that it has one and only one
function. Once we understand that function, we can decide which are
the rightful claims to knowledge. (In brief, reason functions to provide
the forms of knowledge.) In any case, an accurate analysis of reason
will guarantee a correct, complete system of metaphysics. Kant will
conclude that some traditional metaphysical claims (e.g., “Every event
has a cause”) are legitimate, whereas others (e.g., “God exists”) are not.
Finally, at Axvi“xvii Kant describes two sides to the deduction of
the categories (a priori concepts), one objective, the other subjective.
The aim of the former is to demonstrate the “objective validity”
of the categories, that is, their applicability to objects of experience.
The latter explains how a priori representations arise from subjective
cognitive processes. Since the Critique ¬rst appeared, commentators
The Prefaces and the Introduction 17
have debated whether Kant™s subjective analysis contains a “faculty
psychology,” like Hume™s theory of custom and association, which
would beg questions at issue in the Critique. As we shall see in chapter
5, although the two sides are interdependent, Kant clearly intends his
account to be epistemological rather than psychological.

2. the b edition pre fac e : ka nt ™s
copernic a n revolut ion
In the 1787 Preface Kant approaches the problem of reason from a dif-
ferent angle. He ¬rst asks whether metaphysics can attain the certainty
of science, or must continue to grope for knowledge. The model used
for comparison is logic, the science of the formal rules of thought.
Kant believes this system “ the elaborated Aristotelian system of syl-
logistic inference “ is complete and certain. It owes its success to the
fact that it abstracts completely from the content of thought, and
merely codi¬es the forms of valid inference. For example, the argu-
ment form modus ponens consists of two premises, one a conditional
“If P, then Q”, the other the antecedent “P” of the conditional, and
the conclusion, the consequent “Q”. Any argument having this form
is deductively valid: if the premises were true, then the conclusion
would have to be true. So, for example, the following two arguments
are both valid because they have the form modus ponens:
1. If the Sun does not revolve around the Earth, then the Earth
revolves around the Sun.
2. The Sun does not revolve around the Earth.
3. Therefore, the Earth revolves around the Sun.
and:
1 . If the universe exists, then it must have been created by an in¬nite
spirit, God.
2 . The universe exists.
3 . Therefore, it must have been created by an in¬nite spirit, God.
The two arguments differ not in validity or logical correctness, but
in the actual truth value of the premises. The ¬rst argument is sound,
since it is valid and the premises are in fact true. Whether the second
argument is sound is controversial, because the ¬rst premise is clearly
The Prefaces and the Introduction
18
debatable. In general, logic cannot decide on the soundness of an
argument, since determining the truth value of claims about reality
requires factual or empirical knowledge. Nevertheless, Kant thinks
any discipline aspiring to be a science must aim for the completeness
and certainty exempli¬ed by logic. Now this strikes contemporary
readers as ironic, since only a century later, the German philosopher
Gottlob Frege inaugurated the development of modern logic by
demonstrating the inadequacies of the logic in which Kant had so
much con¬dence. Despite the limitations of his logic, Kant had a
clear idea about what a formal science was supposed to do.
Although he does not complete the comparison here, Kant™s point
is that if metaphysical knowledge is possible, it will share some char-
acteristics of logic but diverge in others. For Kant, any science must
be based on necessary principles. If scienti¬c principles were only
contingent, one could never be certain that the theories were true.
For this reason all scienti¬c knowledge must be based on a uni¬ed
system of formal rules of thought. But unlike logic, which is purely
formal, metaphysics has a content because it is the science of reality.
We shall see below what kinds of objects metaphysics studies.
At Bix“x Kant distinguishes theoretical from practical reason, a
distinction at the foundation of his entire critical system. Kant bor-
rows this distinction from Aristotle, although he expresses it rather
differently. Essentially the difference is between representing existing
states of affairs, and representing states of affairs that ought to exist.
As Kant puts it, we may know objects in two ways. In the ¬rst, we
apply a concept to an object that is given or exists independently
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
The Prefaces and the Introduction 29
representations such as concepts. In fact he will argue that synthetic
a priori judgments rest on a priori intuitions and on a priori con-
cepts. Although many philosophers reject Kant™s view that there are
a priori intuitions and concepts, the distinction between necessary
and contingent judgments is generally accepted. Which judgments
are necessary, and whether there are synthetic a priori judgments are,
however, controversial issues.
Kant™s second major distinction is between analytic and synthetic
judgments. Unlike the distinction between a priori and a posteriori
representations, which concerns the origin of cognition, this distinc-
tion is logical and concerns the content of judgment. It does, how-
ever, have epistemological consequences. Kant™s ¬rst characterization
is based on the idea of conceptual containment. Regarding af¬rmative
subject-predicate judgments, Kant says those in which the predicate
is (covertly) contained in the subject are analytic; those in which the
predicate is not contained in the subject are synthetic. His exam-
ples are “All bodies are extended” and “All bodies are heavy.” Kant
thinks the concept “body” includes the concept “extended” but not
the concept “weight.” Analytic judgments are merely clarifying since,
if one already understands the concepts, the judgment adds no new
knowledge. Synthetic judgments, however, are ampliative, since the
predicate concept adds something that is not part of its content to
the subject concept.
From the notion of concept containment, Kant moves to the more
general idea that analytic judgments are those whose truth value can
be determined by means of the law of non-contradiction, the logical
principle that a judgment P and its negation not-P cannot both be
true simultaneously. At A7/B10, he points out that if the predicate is
contained in the subject, then the predicate would be identical with
at least part of the subject. And in these cases, one already has in
the subject all the information one needs to make the judgment “in
accordance with the principle of contradiction” (B12). In synthetic
judgments, there is no identity between the subject and predicate, and
so the principle of non-contradiction is not suf¬cient for determining
their truth values.
Now there are several remarks to make here. First, although Kant™s
intentions are clear, his account is not general enough. (This is in
fact a problem in Hume™s discussion as well.) First, Kant makes the
The Prefaces and the Introduction
30
original distinction in terms of subject-predicate judgments. But he
also recognizes more complex forms of judgments such as conditionals
(“If . . . then . . .”) and disjunctions (“Either . . . or . . .”). And it is
not clear how “concept containment” would work for these complex
forms. Second, Kant admits that he is only considering af¬rmative
subject-predicate judgments, although he claims it is easy to apply his
distinction to negative judgments. In other words, it seems we would
want to label the judgment “No bachelor is married” analytic rather
than synthetic, although the concept of being married is clearly not
contained in the concept of bachelor. A third problem concerns the
relation between analyticity and truth. Again, it looks as if the concept
containment criterion works only for analytically true (af¬rmative)
judgments in which the predicate is in fact contained in the subject.
But the analytic-synthetic distinction should apply to both true and
false judgments. Since the logical character of the judgment is at stake
here, we should consider judgments in pairs, so that any judgment
P and its negation not-P would fall under the same classi¬cation.
That is, because the truth of “All bachelors are unmarried” entails
the falsity of “Some bachelor is married,” we should recognize both
analytic truths and analytic falsehoods. In both cases the truth value
of the judgment can be determined by the principles of logic and the
meanings of the terms alone. Fortunately, there is a way to generalize
Kant™s distinction to incorporate all judgments, simple and complex,
af¬rmative and negative, true and false.
Following Kant™s reference to the principle of non-contradiction,
we can reformulate the distinction this way: a judgment and its nega-
tion are both analytic if and only if one of the pair is self-contradictory,
or false by virtue of the de¬nitions of words or its logical form. (This
is actually close to one of Hume™s criteria for relations of ideas.) Thus
the judgments “All bachelors are unmarried” and “Some bachelor is
married” would be analytic: the ¬rst is true and the second is false
(actually self-contradictory) by the de¬nition of “bachelor.” By con-
trast, Hume™s famous examples “The sun will rise tomorrow” and
“The sun will not rise tomorrow” are synthetic, since neither judg-
ment is self-contradictory. Mere de¬nitions of terms or logical form
are not suf¬cient to determine the truth values of synthetic judg-
ments. In this particular case, actual experience is required to know
which of the pair will be true.
The Prefaces and the Introduction 31
This reformulated criterion can also be applied to complex judg-
ments. In some cases complex judgments will be analytic by virtue
of their logical form, or the meanings of logical operators, regard-
less of the content of their constituent judgments. For example, the
judgment “Either the sun will rise tomorrow or the sun will not
rise tomorrow” will be a true analytic judgment since it has the form
“Either P or not-P” which is logically true in classical systems of logic.
And by the same token the conjunction “The sun will rise tomorrow
and the sun will not rise tomorrow” will be a false analytic judgment
because judgments of the form “P and not-P” are self-contradictory
or logically false. In other cases, complex judgments would be ana-
lytic by virtue of the meanings of non-logical terms: “If something
is red, then it is colored” would be a true analytic judgment, and “If
something is round all over, then it is square all over” would be a false
analytic judgment. Finally, this way of making the distinction would
make all existence claims about logically possible objects synthetic,
which is in fact Kant™s view. This characterization, then, ¬ts consis-
tently with both his examples and his arguments for synthetic a priori
judgments. Based on textual grounds as well as the principle of char-
ity, we shall treat the analytic-synthetic distinction as reformulated
here.
In principle, with two sets of distinctions, it looks as if there could
be four kinds of judgments: analytic a priori, analytic a posteriori,
synthetic a priori, and synthetic a posteriori. In fact, however, only
three kinds of judgments are possible. At A7/B11“12 Kant discusses
the possible combinations and explains the problematic character of
synthetic a priori judgments. First he notes that there are no analytic
a posteriori judgments. All judgments of experience or a posteriori
judgments are synthetic, “For it would be absurd to ground an analytic
judgment on experience” since determining their truth value requires
appealing only to logical form or meanings of terms. Just as it is
obvious how we come by analytic a priori judgments, it is obvious
that synthetic a posteriori judgments such as “Some swans are white”
are based on experience, both for their content and their truth value.
The problematic case is synthetic a priori judgments, since neither
meanings of terms nor experience can account for their features.
Because they are synthetic, their truth value cannot be based logically
on their content; nor can it be derived from experience, since they are
The Prefaces and the Introduction
32
a priori and hence thought with necessity. In the judgment “Every
event has a cause,” there is no logical connection between the concepts
of an event in time and being caused: an uncaused event is conceivable.
But experience cannot ground this judgment either, since it cannot
confer necessity and universality on the principle. As Kant poses
the problem at A9/B13, “What is the unknown = X here on which the
understanding depends when it believes itself to discover beyond the
concept of A a predicate that is foreign to it yet which it nevertheless
believes to be connected with it?” In short, how can there be ampliative
or informative judgments that are nevertheless necessarily true? This
is the technical problem driving the critical philosophy.
Another approach to the problem of synthetic a priori judgments
concerns their necessity. This point is important because it is the sub-
ject of some misunderstanding among commentators. Recall that for
Kant all a priori judgments are necessary. Now this is easily under-
stood with analytic judgments, since their necessity is clearly logical
or conceptual. But the necessity characteristic of synthetic a priori
judgments cannot be logical necessity. Kant admits that an uncaused
event is logically possible, and yet we think it necessary that every
event has a cause. So an alternative description of Kant™s project is to
account for this peculiar kind of non-logical necessity. As we examine
his arguments we will begin to appreciate what kind of necessity this
is. For now let us call it an “epistemic” necessity.
In section V Kant takes a preliminary stab at convincing the reader
that mathematics, natural science, and metaphysics in fact contain
synthetic a priori judgments. Although mathematical inferences may
rely on logical principles, the fundamental propositions of arithmetic
and geometry are synthetic a priori. First he claims that arithmetic
formulae such as “7 + 5 = 12” are not analytic, despite their necessity,
because the mere concept of 7 + 5 does not determine the distinct
individual that results from the act of addition: “no matter how long I
analyze my concept of such a possible sum I will still not ¬nd twelve in
it” (B15). Similarly, he argues that postulates of geometry are synthetic:
“That the straight line between two points is the shortest is a syn-
thetic proposition. For my concept of the straight contains nothing
of quantity, but only a quality” (B16). Kant thinks the arithmetical
sum and the geometrical lines both have to be constructed with the
aid of sensible intuition, which adds a non-conceptual content to our
The Prefaces and the Introduction 33
cognition. Now these controversial claims are based on Kant™s com-
plex theory of mathematics, which he details only in the Discipline
of Pure Reason in the Doctrine of Method. In both the Aesthetic
and the Analytic, he sketches the process of construction required for
mathematical knowledge. In general, the informative character of all
synthetic judgments depends on the role of intuition.
Kant also claims from B17“18 that physics and metaphysics con-
tain synthetic a priori judgments. The examples from physics are
conservation principles: in all physical interactions the quantity of
matter remains constant, and action and reaction are always equal in
communication of motion among particles. Kant believes these prin-
ciples are actually physical versions of the metaphysical principles “In
all change of appearances substance persists, and its quantum is nei-
ther increased nor diminished in nature” and “All alterations occur in
accordance with the law of the connection of cause and effect.” Kant
argues for these latter principles in the section titled the Analogies of
Experience, in the Transcendental Analytic.
In the closing sections VI and VII Kant returns to Hume, whose
arguments he obviously takes seriously. He notes here, as elsewhere,
that Hume saw the problem of how we could make informative
judgments that we believed to be necessarily true, but did not arrive
at the correct solution to the problem. Hume concluded that our
belief in necessary connections of existing things arises from a psy-
chological association based on repeated experiences. For Kant, this
is tantamount to explaining an objective necessity in terms of a psy-
chologically subjective necessity. Thus Hume regarded metaphysical
knowledge as a “mere delusion” (B20). In fact, in the last paragraph
of the Enquiry Concerning Human Understanding, Hume writes:
If we take in our hand any volume; of divinity or school metaphysics, for
instance; let us ask, Does it contain any abstract reasoning concerning quan-
tity or number? No. Does it contain any experimental reasoning concerning
matter of fact and existence? No. Commit it then to the ¬‚ames: For it can
contain nothing but sophistry and illusion.

Kant remarks in his preface to the Prolegomena of 1783, that Hume
“threw no light on this kind of knowledge; but he certainly struck a
spark from which light might have been obtained, had it caught some
in¬‚ammable substance and had its smouldering ¬re been carefully
The Prefaces and the Introduction
34
nursed and developed.” So although Hume showed that metaphysical
knowledge could not be justi¬ed by rational insight into the nature
of things, his account of metaphysical beliefs went seriously astray.
Finally, in section VII, Kant describes the critical theory as “tran-
scendental” philosophy. The term “transcendental” is a key term,
which has several uses depending on the context. Here Kant says, “I
call all cognition transcendental that is occupied not so much with
objects but rather with our mode of cognition of objects in so far as
this is to be possible a priori” (A11/B25). He means that the Critique
contains a theory about the necessary conditions for knowing objects
rather than adding to our knowledge of them. If knowledge of objects
is empirical (or ¬rst-order) knowledge, then the critical philosophy
is a (second-order) theory about such knowledge. In general Kant
uses the term “transcendental” to characterize the necessary condi-
tions of cognition. It is important not to confuse this with the term
“transcendent,” which usually means going beyond experience. For
theoretical reason, the idea of God is a transcendent idea.

4. th e a na ly t ic-s ynt h e ti c con t rovers y
Kant™s views about synthetic a priori knowledge raise questions that
are still debated by philosophers. Two contested aspects of his theory
concern the analytic-synthetic distinction and his theory of mathe-
matics. Here I shall brie¬‚y discuss the ¬rst issue, treating the second
question in chapter 3. Following Kant, the analytic-synthetic distinc-
tion became a staple of contemporary philosophy, largely accepted
(with some rede¬nition) by Frege and the logical positivists. But in
1950 Morton G. White published “The Analytic and the Synthetic:
An Untenable Dualism,” which rejected the notion of analytic state-
ments. Two years later Willard Van Orman Quine took up the attack
in his classic paper, “Two Dogmas of Empiricism.” After arguing that
the de¬ning process cannot give us an account of analyticity, Quine
rejects the view that one can separate linguistic from factual compo-
nents of the meaning of a statement. Because knowledge is a “web
of belief,” underdetermined by experience, there are no statements
immune to revision in the future, including the laws of logic. Not all
philosophers were persuaded by these attacks. In 1956 H. P. Grice and
P. F. Strawson published “In Defense of a Dogma,” in which they offer
The Prefaces and the Introduction 35
an alternative de¬nition of synonymy to save the analytic-synthetic
distinction. Similarly, in “The Signi¬cance of Quine™s Indeterminacy
Thesis,” Michael Dummett points out that in “Two Dogmas,” Quine
himself de¬nes an analytic statement as one such that no recalcitrant
experience would lead us to regard it as not true. Moreover, in his later
work Word and Object, Quine explicitly allows for stimulus-analytic
sentences. Thus there are good reasons to reject Quine™s argument in
“Two Dogmas.”

5. su mma ry
In the Prefaces and the Introduction Kant lays the foundation for his
critical theory. The Prefaces introduce the problem of metaphysics
through the idea that reason naturally poses questions about reality
that are not easily answered. Since ancient Greece, philosophers have
debated whether a priori knowledge is possible, as well as what it
consists in. The second edition Preface explains the problem in terms
of the Copernican revolution: a priori knowledge is possible only if
the subject contributes features to experience, so that what appears
depends on the subject™s cognitive capacities. This requires giving
up the traditional assumption that knowledge conforms to things
as they exist independent of the subject. And this, in turn, leads to
Kant™s transcendental idealism, the view that knowledge is only of
appearances, and that things in themselves cannot be known. The
Introduction presents the technical analysis at the basis of the criti-
cal philosophy. This requires two fundamental distinctions, between
a priori and a posteriori representations, and between analytic and
synthetic judgments. Of the three possible types of judgment, the
problematic case is synthetic a priori judgments, since they are both
informative and necessary. Kant argues that this is the proper classi-
¬cation of metaphysics and mathematics. The task for the Critique
is to show that there is such knowledge, and to justify its application
to experience.
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