A History of Philosophy
Volume VI, Part III: Immanuel Kant
Frederick Copleston, S.J.
Chapter XII: Scientific Knowledge
A. Space and Time
1. The only way in which our knowledge can related immediately to objects is by means of an
intuition
a. And it is by means of sensibility that objects are given to us and it alone provides us with
intuitions (235b)
b. Kant agrees with empiricists to the extent of saying that human cognition of objects requires
sensation (235e)
c. Sensation is a subjective representation but this does not mean that it is caused by the subject
(236a)
2. The object of an empirical sensuous intuition is called ‘appearance’, in which can be
distinguished 2 elements
a. Matter – that which corresponds to sensation (236b)
b. Form – that which enables the manifold of appearance to be arranged in certain relations
c. The form as distinct from the matter cannot be itself sensation
d. Hence, while the matter is given is a posteriori, the form must be a priori, constituting a
necessary condition of all sense intuition (236c)
e. According to Kant, there are 2 pure forms of sensibility, space and time
f. Thus, Kant parts company with the pure empiricists by finding an a priori element in all
sense-experience
3. Kant’s terminology (236d-237a)
a. Representation – covers a wide variety of cognitive states.
i. Therefore, ‘faculty of representation’ is almost equivalent to ‘mind’
b. Object – generally means ‘object of knowledge’
i. Can also mean a thing-in-itself
c. Kant distinguishes between appearance and phenomenon
i. Appearance – the content of a sense intuition when this content is considered as
‘undetermined’ or uncategorized
ii. Phenomenon – categorized objects
iii. But Kant often uses ‘appearance’ to mean both of these
4. We cannot advert to sensations without relating them in space and time
a. They constitute the framework in which the manifold of sensation is ordered or arranged
(238c)
b. This does not mean that we are at first aware of unordered sensations and that we then subject
them to the a priori forms of space and time
c. We are never faced with unordered sensations – we couldn’t be b/c Kant’s main point is that
space and time are a priori conditions of sense-experience (238d)
d. Therefore, what is given in empirical intuition is already ordered, which is a condition of
awareness/consciousness, not a consequence of it.
e. Space is the form of all appearances of the external senses
f. Time is the form of the internal sense; of the intuition of ourselves
5. In so far as Kant proceeds to say that time is the a priori formal condition of all appearances
whatsoever, whereas space is the a priori formal condition external appearances only sense, it
may appear that he is contradicting himself (239b)
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a. But he is not – all representations are determinations of the mind and as such, they belong to
our internal state and hence must be subject to time
b. But time is only the mediate condition of external appearances whereas it is the immediate
condition of all internal appearances (239c)
c. Space and time cannot be empirically derived nor are they general concepts – they are
particulars (240b)
6. Are space and time real for Kant?
a. In one sense, yes  Empirical reality is spatio-temporal and therefore space and time must be
said to possess empirical reality (240cd)
b. In another sense, no  inasmuch as space and time are a priori forms of human sensibility,
the range of their application is extended only to things as appearing to us (241b)
i. There is no reason to suppose that they apply to things-in-themselves, apart from their
appearance to us.
ii. You can say that all appearances are in time, but you cannot say that all things or all
realities are in time
iii. If there are realities which cannot affect our sense and which cannot belong to empirical
reality, they cannot be in space in time; they cannot have spatio-temporal relations (241c)
iv. By transcending empirical reality they transcend the whole spatio-temporal order
v. Space and time have no application to non-phenomenal reality
7. Kant’s formula: Space and time are empirically real but transcendentally ideal (241d)
a. Empirically real: What is given in experience is in space and time – they are not illusions
b. Transcendentally ideal: The sphere of phenomena is the only sphere of their validity
i. They do not apply to things-in-themselves
ii. But this leaves the empirical reality of the spatio-temporal order entirely unimpaired
(241e)
c. Kant’s Copernican revolution does not impair the empirical reality of the world of experience
(242a)
i. It is a question of explaining phenomena, not of denying them
ii. His view of space and time is capable of explaining the a priori knowledge founded on
these intuitions
B. Mathematics
1. The possibility of mathematical knowledge, which is synthetic a priori in character, can be
explained only on the theory that space and time are pure a priori intuitions (242d)
a. For Kant, mathematics is synthetic, require intuition and proceeding constructionally (244d)
i. ‘It is possible to construct a figure with 3 straight lines’ (242e)
ii. We do not deduce this proposition by mere analysis of the concepts of a straight line and
of the number 3 – we have to construct an object (triangle), a.k.a. give ourselves an
object of intuition.
iii. But this can’t be an empirical intuition b/c then it could not give rise to a necessary
proposition
b. Geometry, for example, is constructed a priori, but nevertheless, we know that its
propositions are necessary, in the sense that empirical reality must always conform to them
(243d)
c. The geometer determines a priori the properties of space, and his propositions will always be
true of the empirical spatial order
d. He can make these necessarily true a priori statements which have objective validity in
reference to the external, empirical world only if space (whose properties he determines) is a
pure form of human sensibility (243e)
2. Thus, Kant uses the a priori character of mathematics to prove his theory of space and time
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3. According to Leibniz,, we only need definitions and the principle of contradiction, and then we
proceed by analysis to mathematical propositions (244de)
a. For Kant, mathematics is synthetic, requiring intuition and proceeding constructionally
b. But if you accept the view represented by Bertrand Russell that mathematics is ultimately
reducible to logic, you shall naturally rejects Kant’s theory
4. Critics maintain that Kant’s theory of geometry has been discredited by subsequent developments
in mathematics (246d)
a. There may also be other reasons for denying Kant’s theory of the transcendental ideality of
space and time
5. If we assume that Kant has proved the truth of his theory of space and time, he may be said to
have answered his first question, namely how is mathematical science possible (246e)
C. The Pure Concepts or Categories of the Understanding
1. Human knowledge arises from 2 chief sources in the mind:
a. Sensibility: the power of receiving impressions via sense intuition – thru this an object as data
is given to us
b. Understanding: the power of thinking the data by means of concepts
c. The cooperation of both faculties is required for knowledge of objects (247c)
d. “Thoughts without content are empty; intuitions without concepts are blind…these two
powers or faculties cannot exchange their functions
2. Transcendental Logic – offered as a new and additional science to traditional formal logic (248a)
a. Concerned with a priori principles and concepts of the understanding and with their
application to objects in general
b. Transcendental aesthetic – studies the pure forms of sensibility as the a priori conditions
necessary for objects being given to us in sense intuition
c. Transcendental logic – studies the a priori concepts and principles of the understanding as
necessary conditions for objects being thought (248c)
d. Kant believed that there are in the understanding a priori concepts by which the manifold of
phenomena is synthesized, such as causality (248d)
i. Human knowledge necessarily synthesizes phenomena and makes knowledge possible.
3. Is there a way to ascertain the a priori concepts of the understanding? (249a)
a. Yes – via the faculty of judgment (a.k.a. the power of thought)
b. To judge is the same as to think – it is to unify different representations to form one cognition
by means of concepts
c. Cannot set a limit to the number of possible judgments, but you can determine the number of
possible ways of judging – in doing so is found the ‘transcendental clue’ needed to discover
the a priori concepts of the understanding (249d)
4. The understanding does not intuit, it judges. And to judge is to synthesize (249e)
a. It possesses an a priori categorical structure – it necessarily synthesizes representations in
certain fundamental ways, according to certain basic categories (250b)
b. The categories of the understanding are a priori conditions for knowledge – they allow for
the possibility of objects being thought (250c)
c. Kant makes a table of types of judgment and a table of categories, each of which corresponds
to a logical function: Quantity, Quality, Relation, Modality
i. This list contains all the original pure concepts of the understanding.
d. The third category in each triad arises out of the combination of the second with the first (e.g.
Quantity: (i) Universal (ii) Particular (iii) Singular
D. The Justification of the Application of the Categories
1. Might not these objects, already given in sense experience, (a.k.a. appearances) be such that the
application of the categories of the understanding to them distorts of misrepresents them? (252b)
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a. What is the justification for the categories’ employment in synthesizing phenomena?
i. Kant justifies this via the transcendental deduction of the categories
b. But we can’t even have objects without the categories because the understanding effects the
unity of apperception (perceiving + thinking in one self-conscious subject) (255e)
Kant wants to show that the a priori concepts or categories of the understanding are a priori
conditions of the possibility of experience (252d) – transcendental deduction
a. Not concerned with justifying the application of the categories by showing that their
employment is empirically fruitful.
b. Rather, he wants to justify their application by showing that they are a priori conditions of all
experience
Space and time are also a priori conditions of experience, but they are conditions which are
necessarily required in order that objects should be given to us
a. Transcendental deduction is concerned with showing that the categories are conditions which
are necessarily required for objects to be thought.
b. Aims to show that objects cannot be thought (and hence known, b/c the thinking of objects is
required for knowledge of them) except thru the synthesizing categories of the understanding
(253a)
c. To show this is to show that the employment of categories is justified (253a)
Relation to Kant’s Copernican Revolution (253b)
a. The use of the categories cannot be justified on the assumption that the mind must conform to
objects
b. But if objects, to be known, must conform to the mind, and if this means that they must be
subjected to the categories of the understanding to be objects in the full sense, no further
justification of the use of the categories is required.
Argument of Transcendental Deduction
An object of knowledge is ‘that in the concept of which the manifold of a given intuition is
united’ – without synthesis there can be no knowledge of objects (253c)
a. A mere stream of unconnected representations could not be called knowledge
b. The connection of a manifold is an act of the understanding, which we call synthesis (253d)
i. All connection is an act of the understanding [B 129-30]
c. Connection: the representation of the synthetical unity of the manifold [B 130]
The idea of connection contains the representation of the unity of the manifold. The application of
any category of the understanding presupposes this unity. What is it?
a. It is the unity which consists in relation to one perceiving and thinking subjects – without this
unity, objects would be thinkable (254a)
i. ***In other words, the understanding’s work of synthesizing is not possible except
within the unity of consciousness
b. Thus, the manifold intuition is incapable of being thought and so becoming an object of
knowledge unless perceiving and thinking are so united in one subject that self-consciousness
is capable of accompanying all representations (254b)
c. “The I think must be capable of accompanying all my representations. For otherwise
something could be represented in me which could not be thought at all.”
d. It would be absurd to speak of my having any idea unless self-awareness could accompany it.
Kant calls this relation between the subject and the manifold of intuition ‘pure apperception’
(254e)
a. A.k.a. – It is the relation expressed by saying that the ‘I think’ must be capable of
accompanying all one’s representations.
b. Apperception: conscious perception  thinking + perceiving
c. For Kant, the possibility of an identical I think accompanying all representations is a
permanent condition of experience [think Marcel on faith, hope and love] (255a)
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d. And it presupposes a transcendental unity of self-consciousness which is the necessary
condition for their being any objects for me.
e. ***“Unless the manifold of intuition could be brought…to the unity of apperception, there
could be no knowledge…no objects” (255a) therefore, we need the understanding, b/c this
effects all connection (and hence, unity)
i. There must be one “I think” accompanying all representations b/c this is a condition of
experience.
8. So what does this have to do with justifying the application of the categories?
a. No knowledge of objects is possible unless the manifold of intuition is connected in one-self
consciousness
b. But all synthesis is effected by the understanding
c. Thus, it is by the understanding that the manifold of representations is brought into the unity
of apperception.
d. Now, the understanding synthesizes by means of its a priori categories
e. Hence, no knowledge of objects is possible except through the application of the categories
f. The world of experience is formed through the cooperation of perception and thinking
in the application of the a priori forms of sensibility and the categories of the
understanding
9. The categories of the understanding refer to objects because all objects, to be objects, must
conform to them
E. The Schematism of the Categories
1. How is the subsumption of the intuition to the pure concepts of the understanding possible, if the
latter can never be discovered in the former? How is the application of the categories to
appearances possible? (256a)
a. To solve this problem, Kant has recourse to the imagination conceived as a mediating power
or faculty between understanding and sensibility – the imagination mediates between the
concepts of understanding and the manifold of intuition (256e-257a)
F. The Possibility of the Pure Science of Nature
1. For Kant, there is a pure science of Nature in the sense that it consists of propositions which are
not empirical hypotheses but which enable us to predict the course of Nature, and which are
synthetic a priori propositions (265e)
2. While Hume contented himself with observing that we have a natural belief in the uniformity of
Nature and with attempting to give a psychological explanation of this belief, Kant attempted to
prove this uniformity (266d)
a. Argued that it follows from the fact Nature, as the complex of objects of possible experience,
must conform to the a priori conditions of objective experience
3. Kant raises the important questions whether natural science does or does not involve
presuppositions and if so, what is the logical status of these presuppositions (266c)
G. Phenomena and Noumena
1. The categories of the understanding, taken by themselves, give us no knowledge of objects (266e)
a. “The schematized categories apply only to the date of sense intuition, that is to say,
appearances.”
b. “The categories can give us no knowledge of things ‘except in so far as they can be applied to
empirical intuition. That is to say, they serve only to make empirical knowledge possible, but
this is called experience.’” [B 147]
c. “Hence, the only legitimate use of the categories, with respect to the knowledge of things, lies
in their application to possible objects of experience.” (267a)
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d. “This, says Kant, is a very important conclusion b/c it determines the limits of the use of the
categories and shows that they are valid only for objects of sense. They cannot give us
theoretical or scientific knowledge of realities which transcend the sphere of sense.”
The same can be said of the a priori principles of the understanding – they apply only to possible
objects of experience, to phenomena
a. “The final conclusion of this whole section is, therefore, that all principles of the pure
understanding are nothing more than a priori principles of the possibility of experience; and
to this alone do all synthetic a priori propositions relate. Indeed, their possibility itself rests
entirely on this relation.” [B 294]
i. Hence, the principles, for example, which have reference to substance and to determined
causality hold good only for phenomena” (think God) (267b)
“Our knowledge of objects is thus restricted to phenomenal reality” (267c)
a. However, “although we cannot cross the bounds of phenomenal reality and know what lies
beyond them, we have no right to assert that there are only phenomena” – and thus Kant
introduces the idea of the noumena
“The notion that human beings enjoys or can enjoy an intellectual intuition of noumena is
precisely one of the positions which Kant is most concerned to exclude.” (267e-268a)
a. For Kant, all intuition is sense intuition
Transcendental object Vs. Noumena
a. A transcendental object is the completely undetermined idea of something in general – it is a
mere limiting concept (the unknowable X)
i. “To transform a the transcendental object into a noumenon, I must assume an intellectual
intuition in which the object can be given”
b. “The noumenon is conceived as an intelligible, a positive reality which could be the object of
an intellectual intuition.” (268c)
Kant then says that we possess no faculty of intellectual intuition (268d)
a. Further, even though the idea of a noumenon as a thing-in-itself does not contain a logical
contradiction, we cannot see the positive possibility of noumena considered as possible
objects of intuition and hence the division of objects into phenomena and noumena is not to
be admitted
i. [Because objects, by definition, cannot be noumena]
b. At the same time, the concept of the noumenon is indispensable as a limiting concept
Noumenon in the negative sense of the word: a thing in so far as it is not the object of our
sensuous intuition, thus abstracting from our mode of intuiting (269b)
a. This does not mean that we intuit the noumenon in a non-sensuous manner
b. Simply, we must understand by noumenon a thing in so far as it is not the object of sensuous
intuition – in so far as it does not appear – and at the same time make no assumptions about
the possibility of any other kind of intuition (269c) [B 307]
“Noumenon in the positive sense of the term would be an intelligible, an object of intellectual
intuition.”
a. “But, as according to Kant, we do not enjoy any such intuition, we can disregard for the
moment the positive sense of the term.” (269d)
Not only can we not know noumena in the sense of knowing their characteristics, but also we are
not entitled to assert dogmatically that they exist (270a)
a. The idea of the noumenon, or thing in itself, becomes a limiting concept [B 311, 312]
Kant started from the common-sense position that things produce an effect on the subject which
give rise to sensation (270c)
a. “But this common-sense point of view seems to involve the assertion that there are things-inthemselves. For it appears to involve inference from sensation as an effect to the thing-initself as cause.”
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b. In the Prolegomena, Kant writes that things in themselves are unknowable as they are in
themselves but that “we know them through the representations which their influence on our
sensibility procures for us” (Pro,13, remark 2)
c. “But talking in this way Kant obviously lays himself open to the charge of applying the
principle of causality beyond the limits which he lays down himself.” (270d)
d. “It has therefore been a common objection against the doctrine of noumena considered as
things-in-themselves that their existence is asserted as a result of causal inference, whereas on
Kant’s principles, the category of cause is only applicable to phenomena.” (270e)
e. In asserting the existence of the noumenon as a cause of sensation, it has therefore been said
that Kant contradicts himself, or is inconsistent with his own principles.
f. However, it is understandable that Kant talked in this way b/c he never believed that things
can be reduced simply to representations and it is therefore natural for him to postulate an
external cause of our representation – but this does not alter the fact that he is guilty of
inconsistency
11. However, when he discusses explicitly the distinction between phenomena and noumena, he
adopts a different approach (271b)
a. “The idea of the noumenon is represented as arising, not through inference to a cause of
sensation, but as an inseparable correlate to the idea of phenomenon.”
b. From this approach, we are not presented with subjective representations on the one hand and
their external causes on the other
c. “Rather, we are presented with the idea of an object which appears and corresponding to the
idea we have – as a purely limiting concept – the idea of the object apart from its
appearance.” (271c)
12. Kant also speaks – apart from talking about the noumenon as the thing which appears, apart from
its appearing – about the free, non-empirical ego and about God as being noumena and as
possessing noumenal reality, and occasionally of God as a thing-in-itself (271d)
a. Kant is justified on his premises in this way of talking, for God is not a phenomenon and
cannot possess phenomenal reality and must therefore be conceived as a noumenon, a thingin-itself, and not as something appearing to us.
b. Furthermore, everything said about the non-applicability of the categories to noumena holds
good in regard to God.
c. However, at the same God, if He is thought of at all, is not thought of as being simply a
correlate of spatio-temporal appearances – the concept of God is not the concept of a thing
which appears, considered as not appearing, for God cannot be said to appear [b/c He is not in
the spatio-temporal realm] and hence, the terms noumenon and thing-in-itself do not bear
quite the same meaning as earlier (272a)
H. The Refutation of Idealism
1. When Kant speaks of idealism (e.g. transcendental idealism), he is thinking of the doctrine of the
unknowability of things-in-themselves (272c)
a. He does not intend to assert that there are only the human ego and its ideas – he actually
attacks this doctrine
2. Kant attacks empirical or material idealism, in contrast with transcendental or formal idealism –
the acceptance of the latter involves the denial of the former (272d)
3. Kant distinguishes between 2 kinds of idealism (272e)
a. Problematic – attributed to Descartes: the existence of external things in space is doubtful and
indemonstrable, as there is only one certain empirical proposition, I am
b. Dogmatic – attributed to Berkeley: space, along with all the objects of which it is the
inseparable condition, is impossible, so that objects in space are mere products of the
imagination
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c. Kant says that dogmatic idealism is unavoidable if we hold that space is a property of thingsin-themselves, but it has already been shown that space is an a priori form of sensibility
which applies only to phenomena and not to things in themselves (273c)
4. Of problematic idealism, Kant says that Descartes’ approach is all wrong
a. Kant argues that internal experience is possible only thru external experience, as opposed to
Descartes who assumes that we first possess consciousness of ourselves independently of and
prior to experience of external things (273d)
b. The perception of my own existence in time is possible only through the existence of
something real outside of me, something permanent in perception (274a)
c. The point made by Kant is that I cannot be conscious of myself except mediately, that is, thru
the immediate consciousness of external things – “The consciousness of my own existence is
at the same time an immediate consciousness of the existence of other things outside me”
(274b) [B 276]
5. Kant makes a good point here, but to use this point against Descartes, he has to show that this
becoming aware of myself is impossible unless external things exist and are not merely my
representations or ideas.
a. Kant finds himself compelled to admit that “it does not follow that every intuitive
representation of external things involves at the same time the existence of these thing, for it
may be the mere effect of the power of imagination in dreams as well as in madness” [B 278]
b. “He argues, however, that these imaginative products are reproductions of previous external
perceptions, which would be impossible unless external objects existed” (274d)
c. “Our task here has been to prove only that internal experience in general is possible only
through experience in general.” [B 278]
6. Although his treatment of idealisms leaves a good deal to be desired, it shows Kant’s insistence
on the empirical reality of the world of experience as a whole