priori concepts, he seeks to show, are in all cases purely
logical functions without content, and accordingly are as
little capable as are empirical concepts of carrying us over
to the supersensible. This is an objection which holds
quite independently of that already noted, namely, that
their objective validity would involve a pre-established
What, then, is the nature and what are the generating
conditions of synthetic judgments that are also a priori^
In all judgments there is a relation between subject and
predicate, and that can be of two kinds. Either the predicate
B belongs to the subject A, or B lies outside the sphere of
the concept A though somehow connected with it. In the
former case the judgment is analytic ; in the latter it is
synthetic. The one simply unfolds what has all along been
conceived in the subject concept ; the other ascribes to the
concept of the subject a predicate which cannot be found in it
by any process of analysis. Thus the judgment * all bodies
are extended' is analytic. The concept of body already
contains that of extension, and is impossible save through it.
On the other hand, the judgment ' all bodies are heavy ' is
synthetic. For not body as such, but only bodies which are
in interaction with other bodies, are found to develop this
1 A 6 = B 10. I here follow the wording of the second edition.
property. Bodies can very well be conceived as not influencing
one another in any such manner.
There is no difficulty in accounting for analytic judgments.
They can all be justified by the principle of contradiction.
Being analytic, they can be established a priori. Nor,
Kant here claims, is there any difficulty in regard to synthetic
judgments that are empirical. Though the predicate is not
contained in the subject concept, they belong to each other
(though accidentally) as parts of a given empirical whole.
Experience is the x which lies beyond the concept A, and
on which rests the possibility of the synthesis of B with A.
In regard, however, to synthetic judgments which are likewise
a priori^ the matter is very different. Hitherto, both by the
sensationalists and by the rationalists, all synthetic judgments
have been regarded as empirical, and all a priori judgments as
analytic. The only difference between the opposed schools
lies in the relative value which they ascribe to the two types
of judgment. For Hume the only really fruitful judgments
are the synthetic judgments a posteriori ; analytic judgments
are of quite secondary value ; they can never extend our
knowledge, but only clarify its existing content. For Leibniz,
on the other hand, true knowledge consists only in the analysis
of our a priori concepts, which he regards as possessing an
intrinsic and fruitful content ; synthetic judgments are always
empirical, and as such are purely contingent. 1
Thus for pre-Kantian philosophy analytic is interchange-
able with a priori^ and synthetic with a posteriori. Kant's
Critical problem arose from the startling discovery that the
a priori and the synthetic do not exclude one another. A
judgment may be synthetic and yet also a priori. He appears
to have made this discovery under the influence of Hume,
through study of the general principle of causality every
event must have a cause. 2 In that judgment there seems to
be no connection of any kind discoverable between the subject
(the conception of an event as something happening in time)
and the predicate (the conception of another event preceding
it as an originating cause); and yet we not merely ascribe the
one to the other but assert that they are necessarily connected.
We can conceive an event as sequent upon a preceding
empty time ; none the less, in physical enquiry, the causal
principle is accepted as an established truth. Here, then, is
a new and altogether unique type of judgment, of thoroughly
1 Kant's view of the a priori differs from that of Leibniz in two respects. For
Kant a priori concepts are merely logical functions, i.e. empty ; and secondly, ar
always synthetic. Cf. above, pp. xxxiii-vi, 186, 195-6, 257-8, 290-1, 404 ff.
2 Cf. above, pp. xxv-vii; below, pp. 61 ff., 593 ff.
THREE CLASSES OF A PRIORI JUDGMENT 31
paradoxical nature. So entirely is it without apparent basis,
that Hume, who first deciphered its strange character, felt
constrained to ascribe our belief in it to an unreasoning and
merely instinctive, ' natural ' habit or custom.
Kant found, however, that the paradoxical characteristics
of the causal principle also belong to mathematical and
physical judgments. This fact makes it impossible to accept
Hume's sceptical conclusion. If even the assertion 7+5 = 12
is both synthetic and a priori, it is obviously impossible to
question the validity of judgments that possess these
characteristics. But they do not for that reason any the
less urgently press for explanation. Such an enquiry might
not, indeed, be necessary were we concerned only with
scientific knowledge. For the natural sciences justify them-
selves by their practical successes and by their steady
unbroken development. But metaphysical judgments are
also of this type ; and until the conditions which make a
priori synthetic judgment possible have been discovered, the
question as to the legitimacy of metaphysical speculation
cannot be decided. Such judgments are plainly mysterious,
and urgently call for further enquiry.
The problem to be solved concerns the ground of our
ascription to the subject concept, as necessarily belonging to
it, a predicate which seems to have no discoverable relation to
it. What is the unknown x on which the understanding
Crests. Jn^siSeTtfng the connection ? It cannot be repeated
experience~]~lor the judgments in question claim necessity.
Nor can such judgments be proved by means of a logical test,
such as the inconceivability of the opposite. The absence
of all apparent connection between subject and predicate
removes that possibility. These, however, are the only two
methods of proof hitherto recognised in science and philo-
sophy. The problem demands for its solution nothing less
than the discovery and formulation of an entirely novel method
The three main classes of a priori synthetic judgments are,
Kant proceeds, the mathematical, the physical, and the meta-
physical. The synthetic character of mathematical judgments
has hitherto escaped observation owing to their being proved
(as is required of all apodictic certainty) according to the
principle of contradiction. It is therefrom inferred that
they rest on the authority of that principle, and are there-
fore analytic. That, however, is an illegitimate inference ;
for though the truth of a synthetic proposition can be thus
demonstrated, that can only be if another synthetic principle
is first presupposed. It can never be proved that its truth, as
a separate judgment, is demanded by the principle of con-
tradiction. That 7 + 5 must equal 12 does not follow analytic-
ally from the conception of the sum of seven and five. This
conception contains nothing beyond the union of both numbers
into one ; it does not tell us what is the single number that
combines both. That five should be added to seven is no
doubt implied in the conception, but not that the sum
should be twelve. To discover that, we must, Kant main-
tains, go beyond the concepts and appeal to intuition. This
is more easily recognised when we take large numbers. We
then clearly perceive that, turn and twist our concepts as we
may, we can never, by means of mere analysis of them,
and without the help of intuition, arrive at the sum that is
wanted. The fundamental propositions of geometry, the
so-called axioms, are similarly synthetic, e.g. that the
straight line between two 'points is the shortest. The con-
cept 'straight' only defines direction; it says nothing as
As an instance of a synthetic a priori judgment in
physical science Kant cites the principle : the quantity of
matter remains constant throughout all changes. In the
conception of matter we do not conceive its permanency, but
only its presence in the space which it fills. The opposite of
the principle is thoroughly conceivable.
Metaphysics is meant to contain a priori knowledge. For
it seeks to determine that of which, we can have no ex-
perience, as e.g. that the world must have a first beginning.
And if, as will be proved, our a priori concepts have no
content, which through analysis might yield such judgments,
these judgments also must be synthetic.
Here, then, we find the essential problem of pure reason.
Expressed in a single formula, it runs : How are synthetic
a priori judgments possible? To ask this question is to
enquire, first, how pure mathematics is possible ; secondly,
how pure natural science is possible ; and thirdly, how meta-
physics is possible. That philosophy has hitherto remained
in so vacillating a state of ignorance and contradiction is
entirely due to the neglect of this problem of a priori synthesis.
" Its solution is the question of life and death to metaphysics."
Hume came nearest to realising the problem, but he discovered
it in too narrow a form to appreciate its full significance an<
its revolutionary consequences.
" Greater firmness will be required if we are not to be deterred b)
inward difficulties and outward opposition from endeavouring, through
application of a method entirely different from any hitherto employee
IMMANENT & TRANSCENDENT METAPHYSICS 33
to further the growth and fruitfulness of a science indispensable to
human reason a science whose every branch may be cut away but
whose root cannot be destroyed." 1
These statements are decidedly ambiguous, owing to
Kant's failure to distinguish in any uniform and definite
manner between immanent and transcendent metaphysics. 2
The term metaphysics is used to cover both. Sometimes it
signifies the one, sometimes the other ; while in still other
passages its meaning is neutral. But if we draw the distinc-
tion, Kant's answer is that a genuine and valid immanent
metaphysics is for the first time rendered possible by his
Critique-, its positive content is expounded in the Analytic.
Transcendent metaphysics, on the other hand, is criticised in
the Dialectic ; it is never possible. The existing speculative
sciences transgress the limits of experience and yield only a
pretence of knowledge. This determination of the limits of
our possible a priori knowledge is the second great achieve-
ment of the Critique. Thus the Critique serves a twofold
purpose. It establishes a new a priori system of meta-
physics, and also determines on principles equally a priori
the ultimate limits beyond which metaphysics can never
advance. The two results, positive and negative, are in-
separable and complementary. Neither should be emphasised
to the neglect of the other.
COMMENT ON THE ARGUMENT OF KANT'S
This Introduction, though a document of great historical
importance as being the first definite formulation of the
generating problem of Kant's new philosophy, is extremely
unsatisfactory as a statement of Critical teaching. The
argument is developed in terms of distinctions which are
borrowed from the traditional logic, and which are not in
accordance v/ith the transcendental principles that Kant is
professing to establish. This is, indeed, a criticism which
may be passed upon the Critique as a whole. Though
Kant was conscious of opening a new era in the history of
philosophy, and compares his task with that of Thales,
Copernicus, Bacon and Galileo, it may still be said that he
lever fully appreciated the greatness of his own achievement.
He invariably assumes that the revolutionary consequences
}f his teaching will not extend to the sphere of pure logic.
They concern, as he believed, only our metaphysical theories
1 B 24. 2 Cf. above, pp. xliv-xlv, 22 ; below, pp. 52-3, 55-6, 66 ff.
regarding the nature of reality and the determining condi-
tions of our human experience. As formal logic prescribes
the axiomatic principles according to which all thinking must
proceed, its validity is not affected by the other philosophical
disciplines, and is superior to the considerations that deter-
mine their truth or falsity. Its distinctions may be securely
relied upon in the pioneer labours of Critical investigation.
This was, of course, a very natural assumption for Kant to
make ; and many present-day thinkers will maintain that it
is entirely justified. Should that be our attitude, we may
approve of Kant's general method of procedure, but shall be
compelled to dissent from much in his argument and from
many of his chief conclusions. If, on the other hand, we
regard formal logic as in any degree adequate only as a
theory of the thought processes involved in the formation
and application of the generic or class concept, 1 we shall be
prepared to find that the equating of this highly specialised
logic with logic in general has resulted in the adoption of
distinctions which may be fairly adequate for the purposes
in view of which they have been formulated, but which must
break down when tested over a wider field. So far from
condemning Kant for departing in his later teaching from
these hard and fast distinctions, we shall welcome every sign
of his increasing independence.
Kant was not, of course, so blind to the real bearing of his
principles as to fail to recognise that they have logical implica-
tions. 2 He speaks of the new metaphysics which he has created
as being a transcendental logic. It is very clear, however,
that even while so doing he does not regard it as in any way
alternative to the older logic, but as moving upon a different
plane, and as yielding results which in no way conflict with any-
thing that formal logic may teach. Indeed Kant ascribes to
the traditional logic an almost sacrosanct validity. Both the
general framework of the Critique and the arrangement of
the minor subdivisions are derived from it. It is supposed to
afford an adequate account of discursive thinking, and such
supplement as it may receive is regarded as simply an ex-
tension of its carefully delimited field. There are two logics,
that of discursive or analytic reasoning, and that of synthetic
interpretation. The one is formal ; the other is transcendental.
The one was created by Aristotle, complete at a stroke ; Kant
professes to have formulated the other in an equally complete
and final manner.
1 Needless to say, this "Aristotelian" logic, in the traditional form in which
alone Kant was acquainted with it, diverges very widely from Aristotle's actu
teaching. 2 Cf. above, pp. xxxvi-ix ; below, pp. 36, 181, 184-6.
KANT'S SANGUINE EXPECTATIONS 35
This latter claim, which is expressed in the most un-
qualified terms in the Prefaces to the first and second editions,
is somewhat startling to a modern reader, and would seem to
imply the adoption of an ultra-rationalistic attitude, closely
akin to that of Wolff.
"In this work I have made completeness my chief aim, and I
venture to assert that there is not a single metaphysical problem
which has not been solved, or for the solution of which the key at
least has not been supplied. Reason is, indeed, so perfect a unity
that if its principle were insufficient for the solution of even a single
one of all the questions to which it itself gives birth, we should be
justified in forthwith rejecting it as incompetent to answer, with
perfect certainty, any one of the other questions." 1 " Metaphysics has
this singular advantage, such as falls to the lot of no other science
which deals with objects (for logic is concerned only with the form of
thought in general), that should it, through this Critique, be set
upon the secure path of science, it is capable of acquiring exhaustive
knowledge of its entire field. It can finish its work and bequeath it
to posterity as a capital that can never be added to. For metaphysics
has to deal only with principles, and with the limits of their employ-
ment as determined by these principles themselves. Since it is a
fundamental science, it is under obligation to achieve this complete-
ness. We must be able to say of it : nil actum reputans, si quid
super es set agendum" 2
These sanguine expectations by no means supported by
the after-history of Kant's system are not really due to
Kant's immodest over-estimate of the importance of his work.
They would rather seem to be traceable, on the one hand to
his continuing acceptance of rationalistic assumptions proper
only to the philosophy which he is displacing, and on the
other to his failure to appreciate the full extent of the revolu-
tionary consequences which his teaching was destined to
produce in the then existing philosophical disciplines. Kant,
like all the greatest reformers, left his work in the making.
Both his results and his methods call for modification and
extension in the light of the insight which they have them-
selves rendered possible. Indeed, Kant was himself constantly
occupied in criticising and correcting his own acquired views ;
and this is nowhere more evident than in the contrast
between the teaching of this Introduction and that of the
central portions of the Analytic. But even the later ex-
pressions of his maturer views reveal the persisting conflict.
They betray the need for further reconstruction, even in the
very act of disavowing it. Not an additional logic, but the
1 A vii. - B xxiii-iv.
demonstration of the imperative need for a complete revisal
of the whole body of logical science, is the first, and in many
respects the chief, outcome of his Critical enquiries.
The broader bearings of the situation may perhaps be
indicated as follows. If our account of Kant's awakening
from his dogmatic slumber 1 be correct, it consisted in his
recognition that self-evidence will not suffice to guarantee any
general principle. The fundamental principles of our ex-
perience are synthetic. That is to say, their opposite is in
all cases conceivable. Combining this conclusion with his
previous conviction that they can never be proved by induc-
tion from observed facts, he was faced with the task of estab-
lishing rationalism upon a new and altogether novel basis.
If neither empirical facts nor intuitive self-evidence may be
appealed to, in what manner can proof proceed ? And how
can we make even a beginning of demonstration, if our very
principles have themselves to be established ? Principles are
never self-evident, and yet principles are indispensable. Such
was Kant's unwavering conviction as regards the fundamental
postulates alike of knowledge and of conduct.
This is only another way of stating that Kant is the real
founder of the Coherence theory of truth. 2 He never himself
employs the term Coherence, and he constantly adopts
positions which are more in harmony with a Correspondence
view of the nature and conditions of knowledge. But all
that is most vital in his teaching, and has proved really
fruitful in its after-history, would seem to be in line with the
positions which have since been more explicitly developed by
such writers as Lotze, Sigwart, Green, Bradley, Bosanquet,
Jones and Dewey, and which in their tenets all derive from
Hegel's restatement of Kant's logical doctrines. From this
point of view principles and facts mutually establish one
another, the former proving themselves by their capacity to
account for the relevant phenomena, and the latter dis-
tinguishing themselves from irrelevant accompaniments by
their conformity to the principles which make insight possible.
In other words, all proof conforms in general type to the
hypothetical method of the natural sciences. Kant's so-
called transcendental method, the method by which he
establishes the validity of the categories, is itself, as we have
already observed, 3 of this character. Secondly, the distinction
between the empirical and the a priori must not be taken (a
Kant himself takes it in his earlier, and occasionally even ii
his later utterances) as marking a distinction between \.\
1 Above, pp. xxv- vii, 26; below, p. 593 ff. 2 Cf. above, p. xxxvi ff.
8 Cf. above, pp. xxxvii-viii ; below, pp. 238-42.
KANT'S ATTRIBUTIVE VIEW OF JUDGMENT 37
kinds of knowledge. They are elements inseparably involved
in all knowledge. And lastly, the contrast between analysis
and synthesis becomes a difference not of kind but of degree.
Nothing can exist or be conceived save as fitted into a system
which gives it meaning and decides as to its truth. In the
degree to which it can be studied in relative independence
of the supporting system analysis will suffice ; in the degree
to which it refers us to this system it calls for synthetic
interpretation. But ultimately the needs of adequate under-
standing must constrain us to the employment of both
methods of enquiry. Nothing can be known save in terms
of the wider whole to which it belongs.
There is, however, one important respect in which Kant
diverges in very radical fashion from the position of Hegel.
The final whole to which all things must be referred is
represented to us only through an " Idea," for which no
corresponding reality can ever be found. The system which
decides what is to be regarded as empirically real is the
mechanical system of natural science. We have no sufficient
theoretical criterion of absolute reality.
These somewhat general considerations may be made
more definite if we now endeavour to determine in what
specific respects the distinctions employed in the Introduction
fail to harmonise with the central doctrines of the Analytic.
In the first place, Kant states his problem in reference
only to the attributive judgment. The other types of rela-
tional judgment are entirely ignored. For even when he cites
judgments of other relational types, such as the propositions
of arithmetic and geometry, or that which gives expression
to the causal axiom, he interprets them on the lines of the
traditional theory of the categorical proposition. As we
shall find, 1 it is with the relational categories, and consequently
with the various types of relational judgment to which they
give rise, that the Critique is alone directly concerned. Even
the attributive judgment is found on examination to be of
this nature. What it expresses is not the inclusion of an
attribute within a given group of attributes, but the organisa-
tion of a complex manifold in terms of the dual category of
substance and attribute.
Secondly, this exclusively attributive interpretation of the
judgment leads Kant to draw, in his Introduction^ a hard and
fast distinction between the analytic and the synthetic pro-
position a distinction which, when stated in such extreme
fashion, obscures the real implications of the argument of the
Analytic. For Kant here propounds 2 as an exhaustive
1 Cf. below, pp. 176 ff., 181, 191, 257. 2 A 6 = B 10.
3 8 INTRODUCTION
division the two alternatives : (a) inclusion of the predicate
concept within the subject concept, and (b) the falling of
the predicate concept entirely outside it. He adds, indeed,
that in the latter case the two concepts may still be in some
way connected with one another ; but this is a concession of
which he takes no account in his subsequent argument. He
leaves unconsidered the third possibility, that every judgment
is both analytic and synthetic. If concepts are not inde-
pendent entities, 1 as Kant, in agreement with Leibniz, still
continues to maintain, but can function only as members of
an articulated system, concepts will be distinguishable from
one another, and yet will none the less involve one another.
In so far as the distinguishable elements in a judgment are
directly related, the judgment may seem purely analytic ; in
so far as they are related only in an indirect manner through
a number of intermediaries, they may seem to be purely syn-
thetic. But in every case there is an internal articulation
which is describable as synthesis, and an underlying unity
that in subordinating all differences realises more adequately
than any mere identity the demand for connection between
subject and predicate. In other words, all judgments will, on
this view, be of the relational type. Even the attributive
judgment, as above noted, is no mere assertion of identity.
It is always expressed in terms of the dual category of sub-
stance and attribute, connecting by a relation contents that as
contents may be extremely diverse.
This would seem to be the view to which Kant's Critical