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real acquisition。
V。 In all Theoretical Sciences of Reason； Synthetical Judgements
〃a priori〃 are contained as Principles。
1。 Mathematical judgements are always synthetical。 Hitherto this
fact； though incontestably true and very important in its
consequences； seems to have escaped the analysts of the human mind；
nay； to be in plete opposition to all their conjectures。 For as
it was found that mathematical conclusions all proceed according to
the principle of contradiction （which the nature of every apodeictic
certainty requires）； people became persuaded that the fundamental
principles of the science also were recognized and admitted in the
same way。 But the notion is fallacious； for although a synthetical
proposition can certainly be discerned by means of the principle of
contradiction； this is possible only when another synthetical
proposition precedes； from which the latter is deduced； but never of
itself which
Before all； be it observed； that proper mathematical propositions
are always judgements a priori； and not empirical； because they
carry along with them the conception of necessity； which cannot be
given by experience。 If this be demurred to； it matters not； I will
then limit my assertion to pure mathematics； the very conception of
which implies that it consists of knowledge altogether non…empirical
and a priori。
We might； indeed at first suppose that the proposition 7 ＋ 5 = 12 is
a merely analytical proposition； following （according to the principle
of contradiction） from the conception of a sum of seven and five。
But if we regard it more narrowly； we find that our conception of
the sum of seven and five contains nothing more than the uniting of
both sums into one； whereby it cannot at all be cogitated what this
single number is which embraces both。 The conception of twelve is by
no means obtained by merely cogitating the union of seven and five；
and we may analyse our conception of such a possible sum as long as we
will； still we shall never discover in it the notion of twelve。 We
must go beyond these conceptions； and have recourse to an intuition
which corresponds to one of the two… our five fingers； for example； or
like Segner in his Arithmetic five points； and so by degrees； add
the units contained in the five given in the intuition； to the
conception of seven。 For I first take the number 7； and； for the
conception of 5 calling in the aid of the fingers of my hand as
objects of intuition； I add the units； which I before took together to
make up the number 5； gradually now by means of the material image
my hand； to the number 7； and by this process； I at length see the
number 12 arise。 That 7 should be added to 5； I have certainly
cogitated in my conception of a sum = 7 ＋ 5； but not that this sum was
equal to 12。 Arithmetical propositions are therefore always
synthetical； of which we may bee more clearly convinced by trying
large numbers。 For it will thus bee quite evident that； turn and
twist our conceptions as we may； it is impossible； without having
recourse to intuition； to arrive at the sum total or product by
means of the mere analysis of our conceptions。 just as little is any
principle of pure geometry analytical。 〃A straight line between two
points is the shortest；〃 is a synthetical proposition。 For my
conception of straight contains no notion of quantity； but is merely
qualitative。 The conception of the shortest is therefore fore wholly
an addition； and by no analysis can it be extracted from our
conception of a straight line。 Intuition must therefore here lend
its aid； by means of which； and thus only； our synthesis is possible。
Some few principles preposited by geometricians are； indeed；
really analytical； and depend on the principle of contradiction。
They serve； however； like identical propositions； as links in the
chain of method； not as principles… for example； a = a； the whole is
equal to itself； or （a＋b） 》 a； the whole is greater than its part。 And
yet even these principles themselves； though they derive their
validity from pure conceptions； are only admitted in mathematics
because they can be presented in intuition。 What causes us here
monly to believe that the predicate of such apodeictic judgements
is already contained in our conception； and that the judgement is
therefore analytical； is merely the equivocal nature of the
expression。 We must join in thought a certain predicate to a given
conception； and this necessity cleaves already to the conception。
But the question is； not what we must join in thought to the given
conception； but what we really think therein； though only obscurely；
and then it bees manifest that the predicate pertains to these
conceptions； necessarily indeed； yet not as thought in the
conception itself； but by virtue of an intuition； which must be
added to the conception。
2。 The science of natural philosophy （physics） contains in itself
synthetical judgements a priori； as principles。 I shall adduce two
propositions。 For instance； the proposition； 〃In all changes of the
material world； the quantity of matter remains unchanged〃； or； that；
〃In all munication of motion； action and reaction must always be
equal。〃 In both of these； not only is the necessity； and therefore
their origin a priori clear； but also that they are synthetical
propositions。 For in the conception of matter； I do not cogitate its
permanency； but merely its presence in space； which it fills。 I
therefore really go out of and beyond the conception of matter； in
order to think on to it something a priori； which I did not think in
it。 The proposition is therefore not analytical； but synthetical；
and nevertheless conceived a priori； and so it is with regard to the
other propositions of the pure part of natural philosophy。
3。 As to metaphysics； even if we look upon it merely as an attempted
science； yet； from the nature of human reason； an indispensable one；
we find that it must contain synthetical propositions a priori。 It
is not merely the duty of metaphysics to dissect； and thereby
analytically to illustrate the conceptions which we form a priori of
things； but we seek to widen the range of our a priori knowledge。
For this purpose； we must avail ourselves of such principles as add
something to the original conception… something not identical with；
nor contained in it； and by means of synthetical judgements a
priori； leave far behind us the limits of experience； for example；
in the proposition； 〃the world must have a beginning；〃 and such
like。 Thus metaphysics； according to the proper aim of the science；
consists merely of synthetical propositions a priori。
VI。 The Universal Problem of Pure Reason。
It is extremely advantageous to be able to bring a number of
investigations under the formula of a single problem。 For in this
manner； we not only facilitate our own labour； inasmuch as we define
it clearly to ourselves； but also render it more easy for others to
decide whether we have done justice to our undertaking。 The proper
problem of pure reason； then； is contained in the question： 〃How are
synthetical judgements a priori possible？〃
That metaphysical science has hitherto remained in so vacillating
a state of uncertainty and contradiction； is only to be attributed
to the fact that this great problem； and perhaps even the difference
between analytical and synthetical judgements； did not sooner
suggest itself to philosophers。 Upon the solution of this problem；
or upon sufficient proof of the impossibility of synthetical knowledge
a priori； depends the existence or downfall of the science of
metaphysics。 Among philosophers； David Hume came the nearest of all to
this problem； yet it never acquired in his mind sufficient
precision； nor did he regard the question in its universality。 On
the contrary； he stopped short at the synthetical proposition of the
connection of an effect with its cause （principium causalitatis）；
insisting that such proposition a priori was impossible。 According
to his conclusions； then； all that we term metaphysical science is a
mere delusion； arising from the fancied insight of reason into that
which is in truth borrowed from experience； and to which habit has
given the appearance of necessity。 Against this assertion； destructive
to all pure philosophy； he would have been guarded； had he had our
problem before his eyes in its universality。 For he would then have
perceived that； according to his own argument； there likewise could
not be any pure mathematical science； which assuredly cannot exist
without synthetical propositions a priori… an absurdity from which his
good understanding must have saved him。
In the solution of the above problem is at the same time
prehended the possibility of the use of pure reason in the
foundation and construction of all sciences which contain
theoretical knowledge a priori of objects； that is to say； the
answer to the following questions：
How is pure mathematical science possible？
How is pure natural science possible？
Respecting these sciences； as they do certainly exist； it may with
propriety be asked； how they are possible？… for that they must be
possible is shown by the fact of their really existing。* But as to
metaphysics； the miserable progress it has hitherto made； and the fact
that of no one system yet brought forward； far as regards its true
aim； can it be said that this science really exists； leaves any one at
liberty to doubt with reason the very possibility of its existence。
*As to the existence of pure natural science； or physics； perhaps
many may still express doubts。 But we have only to look at the
different propositions which are monly treated of at the
mencement of proper （empirical） physical science… those； for
example； relating to the permanence of the same quantity of matter；
the vis inertiae； the equality of action and reaction； etc。… to be
soon convinced that they form a science of pure physics （physica pura；
or rationalis）； which well deserves to be separately exposed as a
special science； in its whole extent； whether that be great or
confined。
Yet； in a certain sense； this kind of knowledge must
unquestionably be looked upon as given； in other words； metaphysics
must be considered as really existing； if not as a science；
nevertheless as a natural disposition of the human mind （metaphysica
naturalis）。 For human reason； without any instigations imputable to
the mere vanity of great knowledge； unceasingly progresses； urged on
by its own feeling of need； towards such questions as cannot be
answered by any empirical application of reason； or principles derived
therefrom； and so there has ever really existed in every man some
system of metaphysics。 It will always exist； so soon as reason
awakes to the exercise of its power of speculation。 And now the
question arises： 〃How is metaphysics； as a natural disposition；
possible？〃 In other words； how； from the nature of universal human
reason； do those questions arise which pure reason proposes to itself；
and which it is impelled by its own feeling of need to answer as
well as it can？
But as in all the attempts hitherto made to answer the questions
which reason is prompted by its very nature to propose to itself；
for example； whether the world had a beginning； or has existed from
eternity； it has always met with unavoidable contradictions； we must
not rest satisfied with the mere natural disposition of the mind to
metaphysics； that is； with the existence of the faculty of pure
reason； whence； indeed； some sort of metaphysical system always
arises； but it must be possible to arrive at certainty in regard to
the question whether we know or do not know the things of which
metaphysics treats。 We must be able to arrive at a decision on the
subjects of its questions； or on the ability or inability of reason to
form any judgement respecting them； and therefore either to extend
with confidence the bounds of our pure reason； or to set strictly
defined and safe limits to its action。 This last question； which
arises out of the above universal problem； would properly run thus：
〃How is metaphysics possible as a science？〃
Thus； the critique of reason leads at last； naturally and
necessarily； to science；