Kant’s Critique of Pure Reason
Analytic of Concepts: Chapter II: The deduction of the pure concepts of the
understanding
Section 1: The Principles of Any Transcendental Deduction
Summary:
Once again, Kant is addressing the problem of universals that arises from empiricism. As
he puts it, universal concepts (such as the necessity of a cause/effect) “must either be
grounded completely a priori in the understanding, or must be entirely given up as a mere
phantom of the brain.” Given this problem, Kant proposes that one must find the ground
of these concepts so that one may use them.
He begins by asserting that transcendental deduction is necessary to find the grounding of
a priori concepts. A transcendental deduction differs from an empirical deduction
because it is concerned with the conditions of knowledge itself and can therefore not rely
on empirical evidence, which presupposes and is made known by those conditions of
knowledge.
Next, he points out that there are two kinds of a priori concepts: those based on a priori
intuitions and those that make up the categories. The latter are the objects of interest in
this section, because Kant has already found the grounding for the former in the
transcendental deduction of sensibility. A transcendental deduction of the categories is
also necessary because even the concepts of space and time are contingent on these prior
categories. In fact, these categories are universal and are prior to all conditions of
sensibility (everything one can imagine or think is subject to them, otherwise it is
unintelligible and contradictory.)
In performing this transcendental deduction, he finds that representations must a priori
determine the object, for it is only possible to know anything as an object if a
representation is given. The first condition for this is the presence of a priori intuitions
and the second condition is the presence of a priori concepts. Concepts are the a priori
conditions of the possibilities of experience.
At the end, Kant addresses the errors of Locke, brought to light by Hume (inability to
explain verifiable a priori knowledge, like math). His goal is to find the determinate
limits of reason, so as to keep open the whole field of her appropriate activities”.
Detailed Outline of Section
B117
In law, one distinguishes between the question of right and the question of fact. How one
goes about proving each of these differs. The former requires a deduction, while the
latter requires an appeal to experience, which we trust without a deduction. There are
also some concepts, which are so universally recognized that we do not often ask for their
grounding, and when the question does arise, we are perplexed. Among these concepts
are the a priori concepts, which seem to be independent of all experience. Though we
often take them for granted, their ‘right to be employed’ really requires a transcendental
deduction. Because we understand them to be universal and necessary, an empirical
deduction will not be of use, but will only show the instances in which we can see them
at work.
B118
There are two kinds of a priori concepts that relate to objects: those arising from the a
priori intuitions of space and time, and those arising from the understanding. The former
are the forms of sensibility and the latter are the forms (or categories) of the
understanding. It is worthless to seek an empirical deduction of these, because they claim
universal validity. In experience, we can find occasions of their production, yet we do
not find their grounding as universally valid.
B120
While one may think that this kind of deduction is not necessary because we have trace
the concepts of space and time to their sources to show their a priori objective validity
before doing so, this is erroneous. These concepts have been validated because we have
shown their grounding in a priori intuitions. We have not yet found such a grounding for
the categories. Categories relate to objects universally and are not grounded in a priori
intuitions; they do not result from the intuitions of space and time.
B122
In the field of the understanding, the question of how the subjective conditions of thought
can have objective validity must be answered. That is, how can these categories set the
conditions for the possibility of all knowledge of objects? Let us take the example of
cause. While the objects of sensible intuitions must conform to the formal conditions of
the sensibility to be objects for us, they must also conform to the conditions of the
understanding if they are to become objects to us. The fact that appearance presents
cases where the rule of cause and effect are illustrated does not mean that the rule can be
deduced from our intuitions; rather, it means that our intuitions are formed into a unity by
the understanding and are understood according to these universal and necessary rules.
The concept of cause must be grounded completely a priori in the understanding, or it is a
fiction that only appears to have objective validity.
B125 Transition to the Transcendental Deduction of the Categories
There are two ways in which synthetic representations and their objects can be related to
each other. Either the object must make the representation possible or the representation
must make the object possible. If the object makes the representation possible, the
representation can never be a priori. Now, while the representation does not make the
object exist, it is through the representation that it is possible to know anything as an
object. Knowledge of an object requires an intuition, where the object is given as an
appearance, and a concept, through which the object that corresponds to the intuition is
thought. Given this order, one can say that all appearances agree with the formal
condition of sensibility and all objects agree with the antecedent conditions of the a priori
concepts. In other words, the concepts of objects underlie all empirical knowledge as its
a priori conditions and through them alone does experience become possible.
A94
A priori concepts are the a priori conditions of the possibilities of experience. One can
point to experience for their illustration, but one cannot deduce them from experience.
B127
Locke, however, did attempt to deduce them from experience, and Hume recognized that
this was impossible. Because he could not explain how these concepts could be universal
and necessary, he deemed them illusions that passed beyond the limits of experience.
This meant that he could not account for pure mathematics and the science of nature.
Kant’s solution, which places these a priori concepts within the understanding means that
they are only useful when they are applied to objects that come to us through intuitions,
but they are still known priori to these intuitions, rather than being deduced from them.
PP 276-296
The Amphiboly of Concepts of Reflection:
Arising from the Confusion of the Empirical with the Transcendental Employment of
Understanding.
Summary:
Reflection is a state of mind where we discover the subjective conditions under which we
are able to arrive at concepts. That is, it is the awareness of how we think and of the
various sources of our knowledge. We begin this reflection by asking how our
representations are connected. The point of this examination of judgment is to give
ourselves the grounding necessary to know that our judgments are true. As it is
concerned with the process of knowing, it can be called transcendental reflection. There
are four relations that rise in this reflection: those of identity and difference, agreement
and opposition, the inner and the outer, and the determinable and the determination.
These are the conceptions of comparison, which we use not only to compare different
representations, which we treat as being, but also to perform the activity of transcendental
reflection. They are different from the categories because they serve to compare the
manifoldness of =the representation to the concept of an object.
Now, an amphiboly is the “confounding of an object of pure understanding with an
experience”. This can occur in two ways, the first represented by the error of Leibniz and
the second represented by the error of Locke. According to Kant, Leibniz mistook
representations for which we require sensibility to be representations requiring only
understanding and Locke took representations requiring acts of the understanding to be
representations derived solely from sensibility. Here, Kant is more concerned with the
error of Leibniz than of Locke and uses the concepts of comparison to demonstrate why it
is erroneous and to argue that sensible intuitions are necessary for knowledge.
Detailed Summary:
B316
Reflection is the process that asks, “Under what conditions are we able to arrive at
concepts?” It is the consideration of the process of knowing that asks about the relation
of given representations to the different sources from which they come. We often accept
the validity of our judgments without examining their grounds, but all judgments require
reflection, and the act by which I determine whether a representation belongs to pure
understanding or sensible intuition is transcendental reflection. The right determining of
the relationship between the representation and the faculty to which it belongs depends
upon the use of the comparative concepts of identity and difference, agreement and
opposition, the inner and the outer, and the determinable and the determination.
B318
Given that the question of transcendental reflection concerns the content of the concepts
and their relation to our faculty of knowledge, one can use the abovementioned concepts
to distinguish how the representations relate to the faculties of sensibility and
understanding, respectively. While logical reflection is a “mere act of comparison” of
different things and presupposes the objectivity of those things, transcendental reflection
focuses on objects themselves and provides the ground for the possibility of comparing
objects with one another by establishing how we know each of them. Transcendental
reflection is a duty and no one can claim to make a priori about things without having
done so.
B320 Identity and Difference
When one object is presented to us on many occasions with the same qualities, the
understanding takes it to be one and the same. Even so, there are many of the same kinds
of things, and we are able to distinguish between them because of their position in space.
That is, because the sensibility plays a part in how we know. It is because of the faculty
of sensibility that we can justify two drops of water to be numerically different: if one
falls into the bucket before the other then they are intuited simultaneously in different
positions. Plurality and numerical difference are given by space as the condition of outer
appearances.
B321 Agreement and Opposition
If reality were given only by the understanding, we could not know oppositions that
cancel each other out (3-3=0). This is because realities cannot logically conflict given the
principle of non-contradiction. Sensible objects can oppose each other in a different way
than this; a feeling of pleasure can counter a feeling of pain, for example.
B322 The Inner and the Outer
We can have no concept of the outer without an experience of it. For this reason Leibniz
saw substances as monads, without outer relations. Object of pure understanding have
inner determinations, as do the monads (simple subjects with powers of representation),
as far as I can tell.
B323 Matter and Form
Matter signifies the determinable and form signifies the determination. In any judgment,
the concepts are the matter and their relation is the form (Bongo is a golden retriever).
Also, unlimited reality was viewed as the matter of possibility and its limitation was the
form. Further, in order for the understanding to determine anything something must first
be given; it is matter to be formed. Consequently, Leibniz first assumed things to be
monads with a power of representation that founded their outer relations upon this basis.
Kant finds this problematic and says that the form precedes the things and determines
their possibility because it is a subjective condition and a formal intuition.
B325
The place where we assign a concept, either to sensibility or pure understanding is its
transcendental location. The decision as to its location is made according to the rules
denoted by the transcendental topic. This topic, which allows one to distinguish the
cognitive faculty to which each concept belongs, acts as a safeguard against error. It
contains the four aforementioned distinctions. These concepts are not categories because
they are not concerned with what constitutes the concept, but rather, how to distinguish
between the manifoldness of the representation prior to and the concept of the object.
This requires a determination of where the things that are being compared belong- either
to the pure understanding or sensibility. This process is important because without this
reflection, one risks mistaking an object of pure understanding with an appearance.
B327
The error of Leibniz is exactly this. He has erected “an intellectual system of the world”
on which he believed he could obtain knowledge of the inner nature of things by
comparing objects only with the understanding, and the formal concepts therein. The
table of the concepts of the reflections, however, point out his error.
1. We can see that Leibniz saw the conditions of sensible intuition as a confused
mode of representation rather than a separate source of representations. Leibniz
compared objects of the senses with each other merely in regard to understanding.
That is, he could not think of their position in intuition and has no explanation of
how any drop of water is different from any other.
2. It is a true proposition that concepts can never logically conflict but it is not true
that reality cannot conflict. Leibniz’ system does not account for this.
3. For Leibniz’ monads, substances have a simple internal nature and are free from
outer relations. There seems to be a problem of communication of intelligibility
here.
4. Leibniz’ doctrine of time and space: the intelligible form of the connection of
things in themselves. For him, the senses only confused and distorted
representations.
B333
Essentially, Kant says that the demand that we should be able to know things without
senses demands a faculty of knowledge that is very different from the human. Further,
even if the whole of nature were revealed to us, we would still be unable to answer those
“transcendental questions which go beyond nature.” We can never know the relationship
of sensibility to an object and the transcendental grounds of this unity. If we can only
know ourselves through our inner sense and as appearance, then our sensibility cannot be
treated as a tool for discovering anything except other appearances. Thus, while
appearances are not things-in-themselves within the objects of pure understanding, they
are the only objects that our knowledge can possess.
B337
While it is true that whatever universally agrees or contradicts a concept also agrees with
or contradicts every particular under it, this is not to say that whatever is not included in
the universal concept cannot be included in the particular. Concepts are particular
because they include in themselves more than is in the universal. Leibniz confuses these,
saying that if a distinction is not found in the concept of a thing in general, it is not to be
found in things themselves. The mere concept abstracts from the many necessary
conditions of its intuition. One example is the distinction of location through which one
can differentiate between two similar objects. Similarly, just because conflict is not
found within the concepts of reality is to say that reality is all in agreement with itself.
B339
Kant shows how Leibniz’ contentions would be justified if one only had access to mere
concepts and again affirms that something is contained in intuition that could never be
known through mere concepts: space and time.
B343
Merely intelligible objects are impossible because the employment of concepts of the
understanding require intuition; if we abstract from intuition, the concepts have no
relation to any object. The categories do not extend beyond the conditions of the
sensibility- they do not lead to knowledge of things in themselves. If we speak of
noumena, the categories are not valid; the noumenon is not an object. The noumenon is
“a problem unavoidable bound up with the limitation of our sensibility.” We do not
know whether it would cease to exist without sensibility or whether it would remain; it is
an empty concept that is of no service except to mark the limits of sensible knowledge
and to open a space that we can fill neither through possible experience nor thought pure
understanding”. When we determine an object by thought alone, we are giving a logical
form without content, and this is empty. Goodbye metaphysics.
A290
Without having decided whether the noumenon is something or nothing, we can draw
table that divides up the concept of nothing.
1. An empty concept without an object (opposite of all, many, and one)
2. An empty object of a concept (absence of an object- shadow, cold)
3. An empty intuition without an object (pure space, pure time)
4. An empty object without a concept (this contradicts itself- a two sided rectilinear
figure).
We can do it!!
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