rather, How is pure geometry possible ? for it is practically
to geometry that Kant limits the inquiry there can be little
doubt that it was through this question that he first got
beyond Hume, when already by the year 1770 he is seen
with his doctrine of space wrought out. It took a much
longer time before he was equally sure of having surmounted
Hume's doctrine of physical experience. The reason for
this was not only because the second question was one more
difficult in itself: Hume did not grapple with the first in that
portion of his work known to Kant 2 . Neither had Locke
done much more to explain the true import of mathematical
science, though to attempt it lay still more in his way than in
Hume's, bent as he was on giving a positive account of the
variety of human knowledge from the ground of experience.
Before Kant's time the Rationalists also had failed to
1 The student should here refer to supra, Lect. XIII, and study
the 'Transcendental Aesthetic' in the Kritik. ED.
2 Hume's Inquiry concerning Human Understanding was translated
into German in 1765; the Treatise ^in which he does deal with the
question of mathematical truth) was not translated till 1793. Kant,
when he wrote the Kritik, knew the former work only.
324 Elements of General Philosophy. [LECT.
account for the nature of the science of mathematics.
Splendid mathematician as Leibniz was, he did not in his
philosophy distinguish between the logical necessity of
analytic judgment and the necessity that might be claimed,
which he was foremost to claim, for judgments that were
really synthetic. Kant just did that, and so put the question
as to mathematical truth in train for settlement ! It may be
said that on all hands before Kant the necessity of geometry
was saved at the expense of its character as a real objective
science.
The answer of the Prolegomena to the question, How
can geometry be at once a science of pure intuition and*
objectively valid ? if not in these words, may be thus stated:
Geometry can make universal and necessary determinations,
if it makes them concerning that which is not got by way of
experience, but is furnished forth from within the mind ; and
these determinations are objectively valid of sensible things,
if sense-experience cannot be had by the mind except under
conditions of that which is thus supplied by the mind.
Geometry deals with space and is valid for objects as filling
space. If space is not got through sense, but is given with
the sensibility is presupposed before sensations then what-
ever is determined regarding it is necessarily determined for
all that cannot be received except as falling within it.
But this is only half the battle. We are not told how the
determination of space is made. Granted that, being made,
it is made also necessarily for all that in any case it may
enfold, the real difficulty is as to the making of it. Space
taken merely as a Form of Sensibility a sort of indispensable
frame within which sensations are received is something
inert and barren, explaining nothing. That the mind should
be so constituted as to receive sense-impressions only in
XXVIIL] Elements of General Philosophy. 325
a fixed way is one thing : it is another that the mind should
be able, as regards this fixed way of receiving, to make all
kinds of a priori determination of it to make it the subject
of an endless variety of pure intuitions. Or let the difficulty
be put thus : Geometry in its intuitive judgments brings to-
gether into synthetic unity different aspects of space. Where
does the combining power come in ?
The Kriiik, within its wide scope, does not fail to meet and
resolve this difficulty. It draws a distinction, which we shall
dwell upon more fully at a later stage, between receptivity
of sense and spontaneity of knowledge through under-
standing. The mind is not only liable to be affected, but
is capable of acting in the one case, as in the other, in
a determinate manner prescribed by its constitution. Its
action is what is called thinking, and how Thought must
operate to become Knowledge proper may be called the
central question in the whole critical inquiry. Geometrical
science, being knowledge knowledge indeed of the most
perfect sort involves thinking or the spontaneous activity
of mind; but, as its judgments were said to be intuitive,
depending upon no generalised expeiience nay, for that
matter, upon no experience at all the mental action takes
place in a manner peculiar. What the mind spontaneously
brings before itself to be regarded intuitively, for example
a line, is something singular, as much singular as in the
empirical intuition of sensation. Without having an object
actually before the senses it is as if an object were there.
That condition, with reference to anything that we have had
sensible experience of, is called Representative or Reproductive
Imagination. The geometrical figure is also had in Imagi-
nation, but not representatively, because there never was any
experience of it. The mental act by which it is called into
326 Elements of General Philosophy. [LECT.
being is an act of Productive Imagination. When we think
of a line or circle we draw it in thought by a motion which,
says Kant, is an act of pure subject. Drawing it so, we in
the very act or fact accomplish a synthesis of the successive
stages. Such is the agency through which it comes to pass
that within space, as the pure Form of Sensibility, particular
determinations can be made and particular conjunctions
be established. The space of the geometer, had by pure
intuition, is therefore something very different from space
as the mere form of Sensibility. Were space not such
a form, no pure intuition would be possible, or at least
none having any reference or application to sensible objects.*
But for the pure intuition to take place, constructive action
is necessary, and this, according to Kant, is the work of the
faculty called Productive Imagination.
Between Kant and modern Experientialism the question
as to geometry still remains under dispute. I say geometry,
because that is the particular exact science as regards which
Kant fully defined his position ; but, of course, it is not only
geometry that is involved. Modern Experientialism has
generalised the inquiry, and has found its profit in so doing.
But what is this Experientialism ? Under that common ban-
ner are ranged inquiries of very different kinds. When Kant,
defining the exact character of the pure science of geometry
upon the side where its demonstrative certainty had been
confounded with mere logical necessity, declared that it could
never be explained if its subject were held to be given in or
through any experience, he was reckoning only with psycho-
logists like Locke and Berkeley, and with these when they
had implied rather than asserted certainly not when they
had ever tried to show that the science had an experiential
XXVIIL] Elements of General Philosophy. 327
origin. Professional mathematicians except Leibniz, and
he rather in his other capacity as a speculative philosopher
had not reflected upon the theory of their practice. But,
since the time of Kant, and more or less in the light of his
Criticism, mathematicians have been forward to probe
the secret of their methods and sound the foundations of
their science. Logicians also, or generaL theorists upon
Method, have considered the case of mathematics in
relation to that of the positive sciences generally. And
psychologists, concerned to trace the development of human
knowledge, have brought to light sources of experience and
determined the character of intellectual processes of special
import to the theory of mathematics. As regards the pro-
fessional mathematicians, I take it to be a mere statement of
fact to say that their late researches and their present outlook
do not tend to make them rest content with Kant's resolution
of his first problem. I refrain, however, from the presump-
tion of offering a lay opinion upon the attitude now taken by
the leaders on this line of special inquiry. Neither is the
opportunity suitable for resuming and estimating such
a general theory of science, inclusive of mathematics, as,
in this country, J. S. Mill especially has wrought out from
the ground of Experience. But as Kant based his theory of
geometry upon a doctrine of Sense his Transcendental
doctrine, devised to explain what he denied was or could be
explicable through psychological experience there is forced
upon us the consideration whether psychology can better
now than then meet the requirements of the case.
In investigating the conditions of geometry Kant laid
stress on the two facts that it dealt with a subject of which
there was direct intuition, and that it accomplished its
synthesis by actual construction. In both respects he must
328 Elements of General Philosophy. [LECT.
be held to have judged rightly, and shown great insight
beyond his predecessors. The psychology of that day
whether that of Berkeley, which was the most advanced as
regards sense-perception, or any that Kant himself wrought
out before he entered upon the line of critical inquiry which
raised him, as he thought, above the field of psychological
research took no account of any intuition but that of
sensation in which the mind remained wholly passive.
Hence it became necessary for Kant, as we shall see, to
ascribe all mental activity to the faculty of understanding or
intellect ; and having to provide for the construction of figures
a priori, he did, as we have already seen, call into play the
intellectual faculty working as Productive Imagination.
But modern psychology has shown that empirical intuition
is by no means confined to sensation in which the mind's
state is to be described, with Kant, as receptivity, and in
which the bodily organs of sense are also passively affected
or acted upon. There is a direct intuitive consciousness
when the muscular organs are thrown into action from the
brain outwards, and in such circumstances the mental state
can only be described as spontaneity or activity. Intellectual
action there is as little in this latter as in the former mode of
intuition, or, if the view be so taken, it is present as much in
the first as in the second.
Why then, for the sake of the construction necessary in
geometry, resort to the recondite agency of Productive
Imagination? When we think of a line, says Kant, we
draw it in thought by a motion which is an act of pure subject.
Be it so ; but to have intuition of a line we can also draw it,
and do first draw it, by a motion which is an act of muscle
with a peculiar slate of consciousness attached.
Mere empirical intuition this, it will be said, and incapable
XXVIIL] Elements of General Philosophy. 329
of being made the ground of judgments holding necessarily
and universally. True, it is empirical ; but that it is incapable
of being made the ground of all that geometry in fact is, is
not so clear. It is empirical after a fashion of its own
a fashion very different from that of sensation proper. Sen-
sations, as it were, come or happen to us; are had under
certain circumstances over which we may not have the least
control, and in the ab:ence of those circumstances are not
had. That is the true note of what Experience, in the
despised sense of the word, is. How different our expe-
rience of muscular activity ! We can have it when we like,
for as long as we like, as varied as we like ; and when we
like, we can cease to have it. What more does Kant get
from the Productive Imagination in the way of intuition
a priori ?
Then it is an experience which enfolds and circumscribes
our experiences of sensation proper. When Kant declares
Space to be the Form of all External Sense he says more
than the truth ; for there are sensations received by some of
the external senses without any reference to space ; or, at all
events, there are among the so-called external sensations
great differences in this respect, some being referred altogether
away into objects as qualities thereof, others being referred
not beyond our own organs, and so forth. But precisely in
as far as any sensations have a reference to space, in so far
are they subject to modification through muscular move-
ments of which we are conscious ; and if they have a definite
setting in space, they are sensations which movements of
ours may bring on, and which movements of ours may
limit.
It is now a psychological commonplace to say that we
apprehend objects as spread out in space through conscious
33 Elements of General Philosophy. [LECT.
movements of our members, and such experience renders
account of their extension as much as our sensation renders
account of their sensible qualities. We may think away,
says Kant, all the sensible qualities of a body, but not ex-
tension. If he means its determinate extension of which
we had experience by particular conscious muscular move-
ments, the statement is not true : we can think that away as
well as the rest. If he means space generally or space
altogether, the statement is irrelevant; no Experientialist
would pretend to think that away, in thinking away any-
thing belonging to a particular body. Space in general or
space altogether, supposing it developed by experience, was
assuredly not got with the experience of any particular body.
Upon what varied and protracted experience it may be
supposed to be developed, there is no time now to consider.
Suffice it only to say or to repeat that the experience is such,
in comparison with the experience had through the senses
proper, that the difference of result I mean between the
appearance of space and appearance in space is not at all
surprising. And scientific determinations made of it, though
they need not have that absolute character ascribed to them
which Kant claims for geometrical propositions, must still be
allowed a character of relative generality and priority in com-
parison with the propositions of physical science.
It is enough if the remarks just made have indicated that
Kant's theory of Space and Geometry, however it rose high
above any that had been thought out before, is now put on
its defence and has a hard task to maintain itself. Yet no
theory that may take its place can do so without well regard-
ing all that it involves. Of such importance the part of
Kant's critical doctrine which we have now considered can
never be robbed.
XXVIIL] Elements of General Philosophy. 331
IV. On the Nature and Conditions of Intellectual Synthesis.
WE now come to the most difficult part of Kant's critical
doctrine the part at least that has commonly been found
most difficult, and of which even the general import has mostly
remained sealed to the English thinkers who have touched it
in going about their own business. In the Kritik it is the
subject of a very long and crooked exposition, enough to
daunt the resolution of many who are not weak. Kant
himself found it the hardest part of all his task to think out,
and was after all so little satisfied with his first exposition of
it, that he must needs, at the most important stage, make
another attempt in his second edition an attempt ending in
a result which not the most devoted adherent can pronounce
a uniform improvement. It is the part of his doctrine
where we seem to have most reason to be thankful for
having the Prolegomena to bring out into relief the points of
greatest importance from the surrounding mass of subsidiary
argument ; and we shall accordingly begin with the questions
as there put and answered. But here, even more than before, it
is impossible to confine the view to the minor work. Unless
resort is had to the Kritik itself, the strength of Kant's
position, with its elaborate system of defences, must remain
unknown. Its weak points also, if we can discover such,
must then become more apparent when he is seen wrestling
with the difficulties which he was too acute not to apprehend,
and too honest to glide over.
The general question as put in the Prolegomena is in this
form: flow is pure Science of Nature possible? which, as
we must now understand, is the same as asking, How is it
possible for the mind to determine anything necessarily about
Nature ? The mind does so, for example, when it declares
332 Elements of General Philosophy. [LECT.
that every event must have a cause ; also in mathematical
physics, or the application of mathematics to nature, the
determinations made are necessary. About the fact, in
Kant's opinion, there can be no doubt, and we may at
once have before us his general answer to the question.
Nature could never become the subject of synthetic judgment
a priori if for our knowledge we were dependent on mere
experience that comes to us ; in other words, if Nature had
an existence quite independent of the mind. It can be
known as it is known only if the mind, which so judges
a priori, itself constitutes or makes Nature.
The strain of this answer is manifestly similar to that of
the solution given to the question about pure Geometry.
But it is not less clear that the circumstances of the two
questions are very different. The mind in making determi-
nations of space by intuition a priori is, in Kant's view, in no
respect dependent on experience. True, the determinations
when made are valid for sensible objects; but this fact,
which makes geometry a real objective science and has to
be explained, does nothing to impair its purity as regards
experience. On the other hand, Nature is the world of
Experience the complex of all the objects of Experience,
as Kant himself calls it. How then can the mind make or
constitute that which confessedly it has to acquire ? Or how
can that be experience which the mind, in order to know
anything about it a priori, must constitute ?
Kant meets this difficulty also by a further application of
the distinction of Form and Matter before employed to
account for Intuition a priori of Space and Time. Such
intuition was possible because it bore altogether upon the
mere form of sensibility, which is innate, to the exclusion
of the matter of sensation, which is received or acquired.
xxvui.] Elements of General Philosophy. 333
In like manner a priori determination of experience will
be possible, if it bears altogether upon the mere form
of experience to the exclusion of its matter. The matter
of experience is the variety of phenomena constituted of
sensations received in Space and Time, and this matter
cannot but be empirically got ; but Nature is more than
a variety of phenomena. We have just spoken of Nature
as a complex of objects, meaning that the objects are in
fixed relations with one another are connected bound up
together. Otherwise expressed, Nature is the complex of
the objects of experience constituted through or according
to fixed laws. Formally, it is the system of laws. These
laws in so far as necessary which is to say, the form of
experience cannot be acquired as matter of experience is.
The only alternative is that the form must be innate that
the necessary laws of experience spring from the mind ;
and that experience, in the full and effective sense that is
meant when we speak of Nature, is constituted by the mind
imposing laws upon phenomena.
Now the Prolegomena says shortly that judgments of
perception or merely subjective associations (e. g. ' when the
sun shines on the stone it grows warm') are turned into
judgments of experience or objective conjunctions holding
necessarily for all (e.g. 'the sun warms the stone') by the
addition of concepts having their origin a priori in the
understanding. This is fully explained only in the Kritik 1 .
The truly fundamental question at this stage wiih Kant
is as to the nature and conditions of intellectual synthes.s
1 Read Transcendental Logic, first division ; especially Book I of
Transcendental Analytic. Cf supra, Lect XIII. ED.
334 Elements of General Philosophy. [LECT.
at all stages indeed, but more especially now at this. The
general problem of the Critical Philosophy, How are
synthetic judgments a priori possible ? showed it to be so
everywhere. In the Prolegomena the first special inquiry,
How is pure mathematics possible? raised a question of
synthesis. The second special inquiry, as to Science of
Nature, raises it again. In the first part of the Kritik (the
Transcendental Aesthetic) the question was submerged, only
to come forth expressly now. What was the result of the
Transcendental Aesthetic ? That all sensations are received
by the mind in the form of Time, and external sensations
J
farther in the form of Space. In Sense the mind is passively
affected, and not less so, because the affection takes place
under conditions that are fixed in its nature. There is, in
Kant's view, no synthesis in the faculty, or, as we should
more properly call it, the capacity, of Sense. Synthesis
means activity Spontaneity as opposed to Receptivity and
in Sense the mind is not active at all. But the mind can
act can combine ; manifests another faculty truly to be
called such the faculty, namely, of Thought or Understand-
ing. That faculty also will have its fixed conditions, as the
other had. The mind will think in a determinate way, as
it was shown to be in a determinate way liable to be sensibly
affected, and by reason of its native constitution in the one
case as in the other. To discover the a priori conditions
under which the mind thinks or performs synthesis that is
the second part of the critical task.
Kant wrought out the theory with infinite pains in revul-
sion from the scepticism of Hume. The force of all that
Hume had urged as to the impossibility of finding outside
the mind a ground of order and connexion among things he
XXVIIL] Elements of General Philosophy. 335
was constrained to allow; but while Hume was content to
rest all upon mere subjective custom a tendency to imagine
upon the strength of past experience Kant's interest in
science of nature, if nothing else, impelled him to find some
surer foundation. Nothing besides was more obvious than
that Hume, in his dialectical handling of Cause in Nature,
was touching but one side of a much greater question the
question of objective knowledge generally ; and no less a
question than this, in all its aspects, could Kant stop short of
raising and trying to settle. The world had never seen the
attempt made with such consciousness of its full import
before.
It was made by Kant upon assumptions both as to fact
and principle that drew a clear line of separation between
him and Experientialism, which had spent itself for the time
in the scepticism of Hume. But Experientialism girt itself
again to the task of positive explanation, and stands now in
a very different position from where it stood when Kant
sought to take away the very ground from beneath its feet.
What is known as the Associationist school in psychology
which connects itself, doubtless, through Hume with Berkeley
and Locke, but which made, as it were, a new start after
Hume in Hartley and the elder Mill has expressly aimed
in this generation at rendering an account of Objective
Experience. And in particular the theory of scientific know-
ledge of nature, which was Kant's first care, has found
among Experientialists in the younger Mill one who made
it his chief object of philosophic concern. Mill's System of
Logic indeed, however different its aspect first and last, does
attempt from its own point of view a task corresponding with
that of Kant's Transcendental Logic. Through Mill the
conception of a Real or Material Logic as opposed to one
336 Elements of General Philosophy. [LECT.
purely Formal, has become familiar to English minds ; and
a Real or Material Logic is what, from his own principles,
Kant gave in his Transcendental Analytic. Let this be well
understood, that with its own lights, and in the light more-
over of advancing science, the present English school has
made it its object to give all that satisfaction which Kant
failed to find in the thought of the English school before his
day, and set himself to supply upon a different line of inves-
tigation. With what present success, and yet with what
remaining obligation to ponder now, since it did not ponder
earlier, Kant's extraordinary work, I have already tried to
suggest. I have greatly failed if I have not conveyed such a
notion of the reach and profundity of that work as to make the
obligation apparent. Quite apart from the validity of Kant's
principles or assumptions, there is, in his appreciation of the
problems to be grappled with for the explanation of objective