Critique of Pure Reason
March 23rd, 2009
Taylor Black
Analytic of Principles: Section III “Systematic Representation of All Synthetic
Principles of Pure Understanding
Main Point/Summary of Section:
Kant’s concern in this section is with the faculty of judgment, “if understanding as such is explicated as
our power of rules, then the power of judgment is the ability to subsume under rules, to distinguish
whether something does or does not fall under a given rule.” This stage in Kant’s project then is to
analyze the formal/transcendental features of experience that enable judgment. Kant argues that there
are a number of principles that must necessarily be true of experience in order for judgment to be
possible. Kant’s analysis of judgment and the arguments for these principles are contained in this
section.
Kant first addresses the challenge of subsuming particular sensations under general categories in the
Schematism section. Transcendental schemata, Kant argues, allow us to identify the homogeneous
features picked out by concepts from the heterogeneous content of our sensations. Judgment is only
possible if the mind can recognize the components in the diverse and disorganized data of sense that
make those sensations an instance of a concept or concepts. A schema makes it possible, for instance to
subsume the concrete and particular sensations of an Airedale, a Chihuahua, and a Labrador all under
the more abstract concept of “dog.”
The full extent of Kant’s Copernican revolution becomes even more clear in the rest of the Analytic of
Principles. That is, the role of the mind in making nature is not limited to space, time, and the
categories. In the Analytic of Principles, Kant argues that even the necessary conformity of objects to
natural law arises from the mind. Thus far, Kant’s transcendental method has permitted him to reveal
the a priori components of sensations, the a priori concepts. In the sections titled the Axioms,
Anticipates, Analogies, and Postulates, he argues that there are a priori judgments that must necessarily
govern all appearances of objects. These judgments are a function of the table of categories’ role in
determining all possible judgments, so the four sections map onto the four headings of that table.
Detailed Outline of Section:
B198/A159
The pure understanding is the source of all principles, the faculty of rules in regard to that which
happens, and the source of the principles in accordance with which everything (every object) necessarily
stands under rules. What Kant means by this is that it is by the pure understanding that all appearances
can become objects. For example, when I catch a glimpse out of the corner of my eye of “something”
(aka an appearance) it is my pure understanding that is able to make that an understood object.
Laws of nature, as principles for use of the understanding, also carry with them a sort of necessity a
priori, prior to all experience. Even laws of nature stand under these higher principles of the pure
understanding however, because laws of nature apply only to appearances, whereas the higher
principles of the pure understanding alone provide the concept.
The principles of the pure understanding are derived from pure concepts and not from pure intuitions
because the pure understanding is a faculty of concepts.
B199/A160
Mathematics has similar principles, but the principles of mathematics presuppose the principles of the
pure understanding so Kant does not include them here.
The ground for the principles that he does include as principles of the pure understanding is that they
proceed from concepts to the intuition and not the other way around.
B200/A161 – B201/A162
These then are the rules of the objective use of the categories: 1) axioms of intuition, 2) anticipation of
perception, 3) analogies of experience, 4) postulates of empirical thinking in general. 1) & 2) correspond
to the categories of Quantity and Quality and Kant entitles them mathematical principles because they
allow of intuitive certainty of evidential force and a priori application to appearances. 3) & 4) are
entitled dynamical principles because they only allow of discursive certainty. Note however, that these
names are indicative only of their application, not their content; they are all principles of the pure
understanding.
B202/A162 – B207/A166
1) Axioms of Intuition: All intuitions are extensive magnitudes.
Kant’s proof for this is:
i) all appearances are extensive magnitudes
ii) consciousness of the synthetic unity of the manifold is the concept of magnitude
iii) therefore, appearances, as intuitions in time and space, must be represented through the same
synthesis whereby time and space are determined.
Kant defines a magnitude as extensive when the representation of the parts makes possible, and
therefore necessarily precedes, the representation of the whole.
There are no axioms of magnitude but there are some synthetic propositions.
Propositions of numerical relations are synthetic but are only formulae.
It is this transcendental principle of mathematics makes pure mathematics applicable to objects of
experience.
B207/A166 - B218/A176
2) Anticipations of Perception: In appearances, the real, that is, an object of sensation, has
intensive magnitude, that is, a degree
Proof:
i) Perception is empirical consciousness of sensation
ii) appearances are not pure intuitions like time and space rather they have in addition to intuition
the real of sensation (the matter of some object) as subjective representation
iii) from empirical consciousness to pure consciousness, a graduated transition is possible
iv) therefore there is also possible a synthesis in the process of generating the magnitude of a
sensation
v) therefore, since the sensation is not itself an objective representation, and since neither the
intuition of space, not time has met with it, its magnitude is not extensive, but intensive
What these Anticipations of Perception anticipate is all knowledge by means of which I am enabled to
know and determine a priori what belongs to empirical knowledge.
What corresponds in empirical intuition to sensation is reality.
A sensation occurs in an instant and not is not extensive through time.
The real, which corresponds to sensation in general, represents the concept which includes being.
Of magnitudes in general, we can know a priori only a single quality, that of continuity. In addition, in all
quality (the real in appearance) we can know a priori only their intensive quantity (that they have a
degree), all else depends on experience.
B218/A176 – B265/A218
3) Analogies of Experience: Experience is possible only through the representation of a necessary
connection of perceptions
Proof:
i) Experience is an empirical knowledge
ii) It is a synthesis of perceptions, not contained in perception but itself containing in one
consciousness the synthetic unity of the manifold of perceptions
iii) Since time itself cannot be perceived, the determination of the existence of object in time can
take place only through their relation in time in general. (Recall the importance of
measurement in human history) also only through concepts that connect them apriori.
iv) Therefore, since these always carry a necessity with them, experience is only possible through a
representation of necessary connection of perceptions
Kant proposes that there are three modes of time, namely: duration, succession, and coexistence.
The general principles of the three analogies rest on the necessary unity of apperception at every instant
of time.
These principles are not concerned with appearances, only with existence and relation in respect to
existence. Existence can never be known a priori. Existence cannot be constructed (like mathematical
principles) so these principles will only be regulative.
These analogies are valid only for empirical, not transcendental, employment of understanding.
In the principle, we as knowers, make us of the category but in its application to appearances, we use
the schema.
B224/A182 – B232/A189
Section 3A) First Analogy: Principle of Permanence of Substance: In all change of appearances substance
is permanent; its quantum in nature is neither increased nor diminished
Proof:
i) All appearances are in time. Time is the substratum in which alone coexistence or succession
can be represented.
ii) Time itself cannot be perceived. Therefore there must be in the objects perceived the
substratum which represents time in general.
iii) Therefore, the substratum of all that is real is substance. It is the permanent in relation to which
alone all time-relations of appearances can be determined.
Our apprehension of the manifold of appearances is always successive, always changing. We require an
underlying ground which exists at all times.
It is only in the permanent that relations of time are possible. Permanence expresses time in general.
Accidents are the determination of substance, the special way in which it exists.
Inherence is a special kind of existence of the real in substance, for example, motion as an accident of
matter. Inherence differs from subsistence in that it is the existence of a substance.
Alteration is but a state change, for all that alters persists. This notion is grounded on the recognition of
permanence and can be perceived only in substances. Coming-to-be is not alteration, it is absolute and
can never be a possible perception.
B233/A189 – B256/A211
Section 3B) Second Analogy: Principle of Succession in Time in Accordance with the Laws of Causality: All
alterations take place in conformity with the law of the connection of cause and effect
Proof:
i)
The preceding principle shows that all appearances of successions in time are alterations, not
coming-to-be
ii) I perceived that appearances follow one another, thus I am connection two perceptions and this
is a synthetic faculty of imagination
iii) The objective relation of appearance of succession is not determined through perception. In
order that this relation be known as determined, it must be so thought that it is thereby
determined as necessary which came first. Necessity can only come from a pure concept of
understanding. In this case it is cause and effect.
iv) The apprehension of the manifold of appearance is always successive.
v) Appearances, simply in virtue of being representations, are not in any way distinct from their
apprehension.
vi) We do not know if the parts of the object follow one another
a. Subjective Succession is arbitrary, like looking at a house from top to bottom or left to
right.
b. Objective Succession is that order in the manifold of appearance according to which, in
conformity with a rule, that which happens follows that which it precedes. Applies to
events.
c. Appearance never goes backwards to some preceding time, but it does stand in relation
to some preceding time.
d. There must lie in that which precedes an event, the condition of a rule according to
which this event necessarily follows.
e. The event, as conditioned, thus affords reliable evidence of some condition. This
condition is what determines the event.
f. We have to show that we never ascribe succession to the object.
g. When I perceived that something happens, this representation contains the
consciousness that there is something preceding. Only by reference to what preceded
does the appearance acquire its time relation.
h. The rule that the condition under which an event necessarily follows, lies in what
precedes the event. This is called the Principle of Sufficient Reason and it is the ground
of possible experience.
vii) Therefore, the relation of cause to effect is the condition of the objective validity of our
empirical judgments.
If it were not for cause and effect we could not perceive anything as an event, only unrelated
perceptions. It is the condition of all experience.
The cause and effect may be simultaneous. It is the order of time, not the lapse of time that is
important.
The Empirical Criterion of Substance is that wherever there is action there is substance. Action is a
sufficient empirical criterion to establish the substantiality of a subject because the substratum of
everything that changes is the permanent.
Coming-to-be is always alteration but never regarding substance. How anything can be altered is an
empirical question. The form of alteration, that is, the conditions under which alteration can take place,
can be considered a priori according to the law of causality and the condition of time.
The Law of Continuity of all Alterations is that all alteration is possible though a continuous action of the
causality which, insofar as it is uniform, is entitled a moment. The alteration does not consist of these
moments, but is generated by them as their effect.
How can this principle be known a priori? Every transition in perception is a determination of time
through the generation of this perception. Since time is always a magnitude, the generation of a
perception is always a magnitude. This reveals the possibility of knowing a priori a law of alterations, in
respect to their form.
B257/A211 – B265/A218
Section 3C) Third Analogy: Principle of Coexistence in Accordance with the Law of Reciprocity or
Community: All substances, insofar as they can be perceived to coexist in space, are in thoroughgoing
reciprocity
Proof:
i) Things are coexistent when in empirical intuition the perceptions of them can follow upon one
another reciprocally.
ii) We cannot assume that because things are set in the same time that their perceptions can
follow reciprocally, because time itself cannot be perceived.
a. Influence is the relation of substances in which one contains the ground of the
determinations/accidents of the other.
b. Community or Reciprocity is the relation of substances where each contains the ground
of the determinations of the other.
iii) We know two substances are in the same time when the order in the synthesis of apprehension
of the manifold is a matter of indifference.
iv) If each is completely isolated, (none receives reciprocal influences) coexistence would not be a
possible perception. Therefore, there must be something through which A determines B and
vice versa, namely, its position in time.
v) Only that which is the cause of another determines the position of the other in time.
vi) Therefore, it is necessary that the substances stand immediately or mediately in dynamical
community if their coexistence is to be know in any possible experience.
They thereby constitute a whole.
There are three dynamical relations: Inherence, Consequence, Composition: the appearances stand
outside of one another and yet in connection, constituting a composite.
B266/A218
4) The Postulates of Empirical Thinking in General
The categories of modality do not enlarge the concept to which they are attached as predicates. They
express the relation of concept to the faculty of knowledge. Thus the principles of modality are only
explanations of the concepts of possibility, actuality, and necessity in their empirical employment.
i)
First Postulate: That which agrees with the formal conditions of experience, that is, with the
conditions of intuition and of concepts, is possible.
A concept may be impossible because, while containing no contradiction, it would be impossible to
construct in space. For example, two lines forming a figure.
A concept may be groundless although free from contradiction, because it cannot be based on
experience. For example, reading other minds.
ii) Second Postulate: That which is bound up with the material conditions of experience, that is,
with sensation is actual.
In the mere concept of a thing, no mark of its existence is to be found.
This Postulate does not demand immediate perception, for example, iron filings show us a magnetic
field.
Refutation of Idealism:
Problematic Idealism: (Descartes) there is only one empirical assertion that is certain: “I am”.
Existence of objects is doubtful or undemonstrable.
Dogmatic Idealism: (Berkeley) Space is impossible. Unavoidable if space is interpreted as a property
of things in themselves.
Thesis: The mere, but empirically determined, consciousness of my own existence proves the
existence of objects in space outside of me.
Proof:
a. I am conscious of my own existence in time
b. All determination of time presupposes something permanent in perception
c. Therefore, it is only through this permanent that my existence in time can be
determined.
The game played by idealism has been turned against itself. Inner experience is itself possible only
mediately, and only through outer experience.
This thesis agrees with all our experiences. The representation “I” is not an intuition, it is an
intellectual representation of the spontaneity of the thinking person.
It does not follow that every intuitive representation of outer things involves the existence of those
things.
iii) Third Postulate: That which in its connection with the actual is determined in accordance with
universal conditions of experience, is (exists as) necessary.
The necessity of existence can never be known from concepts, but always only from connection with
that which is perceived.
It is not the existence of substances that we can know necessarily, only the existence of their state in
accordance with the law of causality.
Four Propositions of Nature:
a. Nothing happens through blind chances
b. No necessity in nature is blind, but always conditioned and therefore intelligible
necessity
c. Principle of Continuity forbids any leap in the series of appearances
d. Principle of Continuity forbids any gap in the series of appearances
There is not more that is possible than is actual.
Why does Kant refer to these as postulates?
The Principles of Modality are not objectively synthetic: they do not enlarge the concept to which they
are applied, they are subjectively synthetic, and they predicate the action of the faculty of knowledge
through which a concept is generated.
We may postulate the Principles of Modality since they do not increase our concept of things, but only
show the manner in which it is connected to the faculty of knowledge. In mathematics, a postulate
cannot be proved because the procedure requires the same procedure through which we generated the
concept.
B288-294
General Note on the System of Principles
1) The possibility of a thing cannot be determined from the category alone and in order to exhibit
the objective reality of the pure concept of understanding we must always have an intuition.
2) For the same reason it follows that no synthetic proposition can be made from mere categories.
3) In order to understand the possibility of things in conformity with the categories, and so to
demonstrate the objective reality of the categories, we need outer intuitions.
4) All principles of the pure understanding are nothing more than a priori principles of the
possibility of experience.
5) All synthetic a priori propositions are related to the principles of the pure understanding alone,
indeed, their possibility itself rests entirely on this relation.
Questions, Notes:
Talk about Kant’s Notion of Judgment
What is “pure” reason?
What is Transcendental Aesthetics about?
Why does Kant insist that knowledge must be both synthetic and a priori and what effect does that have
on his answer to whether or not metaphysics is possible?
Why are a priori synthetic judgments necessary for doing science?
What is the difference between the transcendental imagination in the Critique of Pure Reason Part A vs
Part B?
What are the categories?
Name the four heads of the categories and give some examples of them.
How do geometry and algebra fit into Kant’s categories?
How does Kant express the Copernican Revolution in his Critique?
Is freedom in the first Critique the same as freedom in the Groundwork?
What does Kant think that we should not do proofs for the existence and nature of God? (Immortality
and Freedom)
Can we know God, freedom, and the will?
Is metaphysics as a science possible?
How does Kant feel about the use of examples in moral theory?
What is Kant’s problem in the Critique of Pure Reason initially?
What does Kant mean by “transcendental” “analytic” “synthetic”
Distinguish synthetic/analytic and a priori/a posteriori judgments.
How does Kant reject simple empiricism?
What are the categories without sensibility and vice versa?
Compare the way in which Kant says we come to know things and the way Aristotle does.
What is Kant’s argument in the Groundwork?
What is Kant’s categorical imperative?
Differentiate between categorical and hypothetical imperatives.
What is a maxim?
What is a synthetic a priori judgment? Is mathematics an example of it?
Explain how we get the categories, why these 12?
How do categories apply to the intuition?
What role do space and time play in the intuition? How does Kant relate geometry and algebra to space
and time?
How is the Critique of Pure Reason a drama? (following Aristotle’s Poetics)
What is the difference between the hypothetical imperative and the categorical imperative?
What is the good will for Kant?
What is the importance of intuition and judgment? What are their necessary components? How does
Kant hold intuition and judgment together?