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Norman Kemp Smith.

A commentary to Kant's 'Critique of pure reason,' online

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emphasis upon time, but that need not have involved so
exclusive a recognition of its field and function. Possibly
Kant's very natural preoccupation with his new and revolu-
tionary doctrines of inner sense and productive imagination
has something to do with the matter.

Though the definitions given of the various schemata,
especially of those of reality and existence, raise many diffi-
culties, consideration of them must be deferred. 2 They can
be properly discussed only in connection with the principles
which Kant bases upon them. Only one further point calls
for present remark. Kant does not give a schema for each of
the categories. In the first two groups of pure conceptual
forms, those of quantity and of quality, he gives a schema
only for the third category in each case. Number is strictly
not the schema of quantity as such, but of totality. The
schema of quality is a definition only of limitation? This
departure from the demands of strict architectonic is made
without comment or explanation of any kind. Kant delights
to insist upon the confirmation given to his teaching by the
fulfilment of architectonic requirements ; he is for the most
part silent when they fail to correspond. This architectonic
was a hobby sufficiently serious to yield him keen pleasure in
its elaboration, but was not so vital to his main purposes as
to call for stronger measures when shortcomings occurred.

1 Cf. above, pp. 240-3.

2 For comment upon the definition of number, which Kant takes as being the
schema of quantity, and upon the view of arithmetic which this definition may
seem to imply, cf. above, p. 128 ff. 3 Cf. above, p. 192.



342 THE ANALYTIC OF PRINCIPLES '

In concluding this chapter Kant draws attention to the
fact that the sensuous conditions which serve to realise the
pure concepts also at the same time restrict their meaning.
Their wider meaning is, however, of merely logical character. 1
Their function, as pure concepts, lies solely in establishing
unity of representation ; they d.o not therefore suffice to yield
knowledge of any object. Objective application "comes to
them solely from sensibility." In these statements Kant
expounds one of his fundamental doctrines, but in a manner
which does less than justice to the independent value of pure
thought. As he elsewhere teaches, 2 it is not sense that sets
limits to understanding ; it is the pure forms of thought that
enable the mind to appreciate the limited and merely pheno-
menal character of the world experienced.

1 Cf. above, pp. 339-40, and below, pp. 357, 404 ff.
2 Cf. above, pp. 20, 25, 290-1 ; below, pp. 407, 412, 414-17.



CHAPTER II

SYSTEM OF ALL PRINCIPLES OF PURE UNDERSTANDING

The introductory remarks to this important chapter are
again dictated by Kant's architectonic, and set its actual
contents in an extremely false light. Kant would seem to
imply that as the Analytic of Concepts has determined all the
various conceptual elements constitutive of experience, and
has proved that they serve as predicates of possible judgments,
it now remains to show in an Analytic of Principles what a
priori synthetic judgments, or in other words what principles,
can actually be based upon them. Though this is a quite
misleading account of the relation holding between the two
books of the Analytic, it has been accepted by many com-
mentators. 1 For several reasons it must be rejected. The
pure forms of understanding are not predicates for possible
judgments. They underlie judgment as a whole, expressing
the relation through which its total contents are organised.
Thus in the proposition " cinnabar is heavy " the category of
substance and attribute is not in any sense the predicate ;
it articulates the entire judgment, interpreting the experienced
contents in terms of the dual relation of substance and attri-
bute. Judgment, its nature and conditions, is the real problem
of the misnamed Analytic of Concepts. As already indicated, 2
the two main divisions of the Analytic deal with one and
the same problem. But while doing so, they differ in two
respects. In the first place, as above noted, the Analytic of
Concepts supplies no proof of the validity of particular cate-
gories, but only a quite general demonstration that forms of
unity, such as are involved in all judgment, are demanded for
the possibility of apperception. The proofs of the indispens-
ableness of specific categories are first given in the Analytic
of Principles. Secondly, in the Analytic of Concepts the
temporal aspect of experience falls somewhat into the back-
ground, whereas in the Analytic of Principles it is emphasised.

1 E.g. Riehl, Philos. Krit. 2nd ed. i. pp. 535-6. 2 Above, pp. 258, 332-3.

343



344 THE ANALYTIC OF PRINCIPLES

From these two fundamental points of difference there
arises a third distinguishing feature. When the categories,
or rather schemata, are explicitly defined, and receive indi-
vidual proof, they are found to be just those principles that
are demanded for the possibility of the positive sciences. This
is, from Kant's point of view, no mere coincidence. Scientific
knowledge is possible only in so far as experience is grounded
on a priori conditions ; and the conditions of ^^-experience
are also the conditions of its conceptual interpretation. But
while the Analytic of Concepts deals almost exclusively with
ordinary experience, in the Analytic of Principles the physical
sciences receive their due share of consideration.

First and Second Sections. The Highest Principles of Analytic
and Synthetic Judgments. These two sections contain nothing
not already developed earlier in the Critique. Though the
principle of non-contradiction is a merely negative test of
truth, it can serve as a universal and completely adequate
criterion in the case of all judgments that are analytic of
given concepts. The principle of synthetic judgments, on
the other hand, is the principle whereby we are enabled to
advance beyond a given concept so as to attach a predicate
which does not stand to it in the relation either of identity
or of contradiction. This principle is the principle of the
possibility of experience. Though a priori synthetic judg-
ments cannot be logically demonstrated as following from
higher and more universal propositions, 1 they are capable of
a transcendental proof, that is, as being conditions of sense-
experience.

" The possibility of experience is what gives objective reality to
all our a priori knowledge." 2 "Although we know a priori in
synthetic judgments a great deal regarding space in general and the
figures which productive imagination describes in it, and can obtain
such judgments without actually requiring any experience ; yet even
this knowledge would be nothing but a playing with a mere figment
of the brain, were it not that space has to be regarded as a condition
of the appearances which constitute the material for outer experi-
ence. . . ." 3

In the first part of the last sentence, as in the page which
precedes it, Kant would seem to be inculcating his doctrine
of a pure a priori manifold, but the latter part of the state-
ment would not be affected by the admission that space is
not an independent intuition but only the form of outer sense.

Third Section. Systematic Representation of all the Synthetic
Principles of Understanding. Kant is not concerned in this

1 A 148=6 188. 2 A 156=6 195. 3 A 157 =B 196.



THE PRINCIPLES OF UNDERSTANDING 345

section with the fundamental propositions of mathematical
science, since, on his view, they rest upon the evidence of
intuition. He claims, however, that their objective validity
depends upon two principles, which, though not themselves
mathematical in the strict sense, may conveniently be so
described from the transcendental standpoint the principle
of the " axioms of intuition," and the principle of the " anti-
cipations of experience." The physicist, who takes the legiti-
macy of applied mathematics for granted, has no occasion to
formulate these principles. That he none the less presupposes
them is shown, however, by his unquestioning assumption
that nature conforms to the strict requirements of pure mathe-
matics. And since the principles involve pure concepts, the one
embodying the schema of number, and the other the schema
of quality, they fall outside the scope of the Transcendental
Aesthetic, and call for a deduction similar to that of the other
categories.

As already indicated, Kant's procedure is extremely
arbitrary, and is due to the perverting influence of his archi-
tectonic. Proof of the validity of applied mathematics has
already been given in the Aesthetic^- of the first edition a
proof which is further developed in the Prolegomena? and
recast in the second edition so as to constitute a separate
" transcendental exposition." 3 As Kant teaches in these
passages, the objective validity of applied mathematics rests
upon proof that space and time are the a priori forms of
outer and inner sense. The new deductions of the schemata
of number and quality, which he now proceeds to formulate,
are quite unnecessary, and also are by no means conclusive
in the manner of their proof. This, however, is more than
compensated by the extremely valuable proofs of the
schematised categories of relation which he gives in the
section on the Analogies of Experience. The section on
the Postulates of Empirical Experience, which deals with the
principles of modality, also contains matter of very real im-
portance.

The principles with which this chapter has to deal can
thus be arranged according to the fourfold division of the
table of categories : (i) Axioms of Intuition, (2) Anticipations
of Perception, (3) Analogies of Experience, (4) Postulates of
Empirical Thought. And following the distinction already
drawn in the Analytic of Concepts f Kant distinguishes be-
tween the Axioms and Anticipations on the one hand, and
the Analogies and Postulates on the other. The former
determine the conditions of intuition in space and time, and

1 A 24. 2 13, Anmerkung'\. 3 B 40-1. 4 B no.



346 THE ANALYTIC OF PRINCIPLES

may therefore be called mathematical and constitutive. They
express what is necessarily involved in every intuition a<
such. The latter are dynamical. They are principles accord-
ing to which we must think the existence of an object
determined in its relation to others. While, therefore, th(
first set of principles can be intuitively verified, the secom
set have only an indirect relation to the objects experienced.
Whereas a relation of causality can never be intuited as
holding between two events, but only thought into them,
spatial and temporal relations are direct objects of the mind.
Similarly, the relation of substance and attribute cannot be
intuited ; it can only be thought into what is intuited. The
mathematical principles thus acquire an immediate (though,
be it remembered, merely de facto) evidence ; the a priori
certainty, equally complete, of the dynamical principles can
be verified only through the circuitous channel of transcend-
ental proof.

The composite constitution of these sections finds strik-
ing illustration in the duplicated account of this distinction
which precedes and follows the table of principles. The
two accounts can hardly have been written in immediate
succession to one another. The earlier in location 1 is
probably the later in date. It would seem to rest upon some
such uncritical distinction as that drawn in the Prolegomena
between judgments of perception and judgments of experi-
ence. 2 The second and briefer account 3 is not open to this
objection.

In A 178-80=6 220-3 Kant develops a further point
of difference between the mathematical and the dynamical
principles, or rather explains what he means by his all too
brief and consequently ambiguous reference in the first of the
above accounts to " existence " (Dasein). The mathematical
principles are constitutive ; the dynamical are regulative.
That is to say, the mathematical principles lay down the
conditions for the generation or construction of appearances.
The dynamical only specify rules whereby we can define the
relation in which existences contingently given are connected.
As existence can never be constructed a priori, we are limited
to the determination of the interrelations between existences
all of which must be given. Thus the principle of causality
enables us to predict a priori that for every event there must
exist some antecedent cause ; but only through empirical in-
vestigation can we determine which of the particular given
antecedents may be so described. That is to say, the principle
defines conditions to which experience must conform, but does

1 A i6o = B 199-200. 2 Cf. above, pp. 288-9, 3 A i6i-2 = B 201-2.



I



THE AXIOMS OF INTUITION 347

not enable us to construct it in advance. This distinction is
inspired by the contrast between mathematical and physical
science, and is valuable as defining the empirically regulative
function of the a priori dynamical principles; but its somewhat
forced character 1 becomes apparent when we bear in mind
Kant's previous distinction between the principles of pure
mathematical science and the transcendental principles which
justify their application to experience. Those latter principles
concern existence as apprehended through schematised cate-
gories, and are consequently, as regards certainty and method
of proof, in exactly the same position as the dynamical prin-
ciples. This is sufficiently evident from his own illustration
of sunlight. 2 There is as little possibility of " constructing "
its intensity as of determining a priori the cause of an effect.

i. THE AXIOMS OF INTUITION

All appearances are in their intuition extensive magnitudes.
Or as in the second edition : All intuitions are extensive
magnitudes.

( Extensive ' is here used in a very wide sense to include
temporal as well as spatial magnitude. Kant bases this
principle upon the schema of number, and the proof which
he propounds in its support is therefore designed to show
that apprehension of an object of perception, whether spatial
or temporal, is only possible in so far as we bring that schema
into play. But though this is the professed purpose of the
argument, number is itself never even mentioned ; and the
reason for the omission is doubtless Kant's consciousness of
the obvious objections to any such position. That aspect
of the argument is therefore, no doubt without explicit inten-
tion, kept in the background. But even as thus given, the
argument must have left Kant with some feeling of dissatis-
faction. Loyalty to his architectonic scheme prevents such
doubt and disquietude from finding further expression.

The argument, in its first-edition statement, starts from
the formulation of a view of space and time directly opposed
to that of the Aesthetic : 3

" I entitle a magnitude extensive when the representation of
the parts makes possible, and therefore necessarily precedes, the
representation of the whole. I cannot represent to myself a line,
however small, without drawing it in thought, i.e. generating from a
point all its parts one after another, and thus for the first time
recording this intuition."

1 Cf. below, pp. 510-11. 2 A 178-9 = 6 221. 3 Cf. above, pp. 94-5.



348 THE ANALYTIC OF PRINCIPLES

Similarly with even the smallest time. And as all appear-
ances are intuited in space or time, every appearance, so far
as intuited, is an extensive magnitude, that is to say, can be
apprehended only through successive generation of its parts.
All appearances are " aggregates, i.e. manifolds of antecedently
given parts."

This definition of extensive magnitude involves an assump-
tion which Kant also employs elsewhere in the Critique, 1 but
which he nowhere attempts to establish by argument ; namely,
that it is impossible to apprehend a manifold save in succes-
sion. This assumption is, of course, entirely false (at least as
applied to our empirical consciousness), as has since been amply
demonstrated by experimental investigation. Kant adopted
it in the earlier subjectivist stage of his teaching, before he
had come to recognise that consciousness of space is involved
in consciousness of time. But even after he had done so, the
earlier view still tended to gain the upper hand whenever the
doctrines of inner sense and of productive imagination were
under consideration. For in regard to the transcendental
activities of productive imagination, which are essentially
synthetic, Kant continued to treat time as more fundamental
than space. But, as already noted, 2 a directly opposite
view of the interrelations of space and time is expounded in
passages added in the second edition.

The two central paragraphs are very externally connected
with the main argument, and are probably later interpolations. 3
In the first of these two paragraphs Kant ascribes the
synthetic activity involved in the " generation of figures " to
the productive imagination, and maintains that geometry is
rendered possible by this faculty. In the other paragraph
Kant deals with arithmetic, but makes no reference to the
productive imagination. Its argument is limited to the con-
tention that propositions expressive of numerical relation,
though synthetic, are not universal. They are not axioms,
but numerical formulae. This distinction has no very obvious
bearing on the present argument, and serves only to indicate
Kant's recognition that no rigid parallelism can be estab-
lished between geometry and arithmetic. There are, it would
seem, no arithmetical axioms corresponding to the axioms
of Euclid. 4

The concluding paragraph is a restatement of the argu-
ment of the Aesthetic and of 13, Note i. of the Pro-
legomena. Appearances are not things in themselves.
They are conditioned by the pure intuitional forms, and are

1 Cf. below, pp. 358-9, 367-8, 371-2, 381-2. 2 Above, p. 309 ff.

3 Cf. Adickes, K. p. 190 . 4 Cf. above, p. 127 ff.






THE ANTICIPATIONS OF PERCEPTION 349



therefore subject to pure mathematics " in all its precision."
Were we compelled to regard the objects of the senses as
things in themselves, an applied science of geometry (again
taken, in Kant's habitual manner, as typically representing
the mathematical disciplines) would not be possible. The only
new element in the argument is the reference to synthesis as
presupposed in all apprehension.

The additional proof with which in the second edition
Kant prefaces the entire argument calls for no special
comment. It may, however, be noted that though in the
argument of the first edition the need of synthesis in all
apprehension is clearly taught, the term synthesis is not itself
employed except in the central and final paragraphs. In the
proof given in the second edition both the term and what it
stands for are allowed due prominence.

2. THE ANTICIPATIONS OF PERCEPTION

In all appearances sensation and the real which corresponds
to it in the object (realitas phaenomenon] has an intensive
magnitude or degree. Or as in the second edition : In all
appearances the real, which is an object of sensation, has
intensive magnitude or degree.

We may first analyse the total section. The first para-
graph * explains the term anticipation. The second and
third paragraphs give a first proof of the principle. Para-
graphs four to ten treat of continuity in space, time and
change, and of the impossibility of empty space, and also
afford Kant the opportunity to develop his dynamical theory
of matter, and so to indicate the contribution which transcend-
ental philosophy is able to make towards a more adequate
understanding of the principles of physical science. The
eleventh and twelfth paragraphs, evidently later interpola-
tions, give a second proof of the principle which in one im-
portant respect varies from the first proof. In the second
edition a third proof akin to this second proof, but carrying it
a stage further, is added in the form of a new first paragraph.

Kant's reason for changing the formulation of the prin-
ciple in the second edition is evidently the unsatisfactoriness
of the phrase "sensation and the real." 2 The principle, properly
interpreted, applies not, as the first edition title and also the
second proof would lead us to expect, to sensation itself, but
to its object, realitas phaenomenon. It is phenomenalist in its
teaching. The emphatic term " anticipation " is adopted by

1 That is to say, in the first edition.
2 The phrase is followed, it may be observed, by a verb in the irregular.



350 THE ANALYTIC OF PRINCIPLES

Kant to mark that in this principle we are able in a priori
fashion to determine something in regard to what in itself is
purely empirical. Sensation as such, being the matter of
experience, can never be known a priori. Its quality, as
being a colour or a taste, depends upon factors which are for us,
owing to the limitations of our knowledge, wholly contingent.
None the less in one particular respect we can predetermine
the object of all sensation, and so can anticipate experience,
even in its material aspect.

The first proof is as follows. Apprehension, so far as
it takes place through a sensation, occupies only a single
moment ; it does not involve any successive synthesis proceed-
ing from parts to the complete representation. That which is
apprehended cannot, therefore, possess extensive magnitude.
But, as already stated in the chapter on Schematism, reality is
that in appearance which corresponds to a sensation. It is
realitas phaenomenon. The absence of it is negation = o.
Now every sensation is capable of diminution ; between
reality in the appearance and negation there is a continuous
series of many possible intermediate sensations, the difference
between any two of which is always smaller than the differ-
ence between the given sensation and zero. That is to say,
the real in appearance has intensive magnitude or degree.
The argument is from capability of variation in the intensity
of sensation to existence of degree in its object or cause. For
the most part this reality is spoken of as that which is appre-
hended in sensation, but Kant adds that if it be

"... viewed as cause either of sensation or of other reality in appear-
ance, such as change, the degree of its reality ... is then entitled
a moment, as for instance the moment of gravity."

The obscurity of what in itself is a very simple and direct
argument would seem to be traceable to the lack of clearness
in Kant's own mind as to what is to be signified by reality.
The implied distinction between sensation and its object has
not been clearly formulated. Definitions have, indeed, been
given of reality in the chapter on Schematism ; x but they are
extremely difficult to decipher. Kant never varies from the
assertion that reality is " that which corresponds to sensation
in general." Our difficulty is with the additional qualifications.
This reality, he further declares, is

"... that, the concept of which in itself points to an existence [.&/]
in time." 2

1 A 143= B 182.
2 Loc. cit. in the chapter on Schematism.



THE ANTICIPATIONS OF PERCEPTION 351

The words 'in time' would seem to show that what is
referred to is reality in the realm of appearance, the realitas
phaenomenon of the Anticipations. But immediately below
we find the following sentence :

" As time is only the form of intuition, and consequently of objects
as appearances, what corresponds in them to sensation is the tran-
scendental matter of all objects as things in themselves, thinghood
[SaMeitl reality." *

The teaching of the first sentence is phenomenalist ; that
of the other is subjectivist.

Now in the section on Anticipations of Perception the
phenomenalist tendencies of Kant's thought are decidedly
the more prominent. The implied distinction is threefold,
between sensation as subjective state possessing intensive
magnitude, spatial realities that possess both intensive and
extensive magnitude, and the thing in itself. Objects as
appearances are regarded as causes of sensation and as pro-
ducing changes in one another.

The explanation of the phenomenalist character of this
section is not far to seek. Kant's chief purpose in it, as we
shall find, is to develop the dynamical theory of matter to
which he had long held, and which, as he was convinced,
would ultimately be substituted for the mechanistic view to
which almost all physicists then adhered. We can easily
understand how in this endeavour the realist tendencies of
his thinking should at once come to the surface, and why he



Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 43 of 72)