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is rather to be expected that we should long ago have put the
question； how the understanding can arrive at these a priori
cognitions； and what is the extent； validity； and worth which they may
possess？ We say； 〃This is natural enough；〃 meaning by the word
natural； that which is consistent with a just and reasonable way of
thinking； but if we understand by the term； that。 which usually
happens； nothing indeed could be more natural and more
comprehensible than that this investigation should be left long
unattempted。 For one part of our pure knowledge； the science of
mathematics； has been long firmly established； and thus leads us to
form flattering expectations with regard to others； though these may
be of quite a different nature。 Besides； when we get beyond the bounds
of experience； we are of course safe from opposition in that
quarter； and the charm of widening the range of our knowledge is so
great that； unless we are brought to a standstill by some evident
contradiction； we hurry on undoubtingly in our course。 This；
however； may be avoided； if we are sufficiently cautious in the
construction of our fictions； which are not the less fictions on
that account。
Mathematical science affords us a brilliant example； how far；
independently of all experience； we may carry our a priori
knowledge。 It is true that the mathematician occupies himself with
objects and cognitions only in so far as they can be represented by
means of intuition。 But this circumstance is easily overlooked；
because the said intuition can itself be given a priori； and therefore
is hardly to be distinguished from a mere pure conception。 Deceived by
such a proof of the power of reason； we can perceive no limits to
the extension of our knowledge。 The light dove cleaving in free flight
the thin air； whose resistance it feels； might imagine that her
movements would be far more free and rapid in airless space。 just in
the same way did Plato； abandoning the world of sense because of the
narrow limits it sets to the understanding； venture upon the wings
of ideas beyond it； into the void space of pure intellect。 He did
not reflect that he made no real progress by all his efforts； for he
met with no resistance which might serve him for a support； as it
were； whereon to rest； and on which he might apply his powers； in
order to let the intellect acquire momentum for its progress。 It is；
indeed； the common fate of human reason in speculation； to finish
the imposing edifice of thought as rapidly as possible； and then for
the first time to begin to examine whether the foundation is a solid
one or no。 Arrived at this point； all sorts of excuses are sought
after； in order to console us for its want of stability； or rather；
indeed； to enable Us to dispense altogether with so late and dangerous
an investigation。 But what frees us during the process of building
from all apprehension or suspicion； and flatters us into the belief of
its solidity； is this。 A great part； perhaps the greatest part； of the
business of our reason consists in the analysation of the
conceptions which we already possess of objects。 By this means we gain
a multitude of cognitions； which although really nothing more than
elucidations or explanations of that which （though in a confused
manner） was already thought in our conceptions； are； at least in
respect of their form； prized as new introspections； whilst； so far as
regards their matter or content； we have really made no addition to
our conceptions； but only disinvolved them。 But as this process does
furnish a real priori knowledge； which has a sure progress and
useful results； reason； deceived by this； slips in； without being
itself aware of it； assertions of a quite different kind； in which； to
given conceptions it adds others； a priori indeed； but entirely
foreign to them； without our knowing how it arrives at these； and；
indeed； without such a question ever suggesting itself。 I shall
therefore at once proceed to examine the difference between these
two modes of knowledge。
IV。 Of the Difference Between Analytical and Synthetical Judgements。
In all judgements wherein the relation of a subject to the predicate
is cogitated （I mention affirmative judgements only here； the
application to negative will be very easy）； this relation is
possible in two different ways。 Either the predicate B belongs to
the subject A； as somewhat which is contained （though covertly） in the
conception A； or the predicate B lies completely out of the conception
A； although it stands in connection with it。 In the first instance；
I term the judgement analytical； in the second； synthetical。
Analytical judgements （affirmative） are therefore those in which the
connection of the predicate with the subject is cogitated through
identity； those in which this connection is cogitated without
identity； are called synthetical judgements。 The former may be
called explicative； the latter augmentative judgements； because the
former add in the predicate nothing to the conception of the
subject； but only analyse it into its constituent conceptions； which
were thought already in the subject； although in a confused manner；
the latter add to our conceptions of the subject a predicate which was
not contained in it； and which no analysis could ever have
discovered therein。 For example； when I say； 〃All bodies are
extended；〃 this is an analytical judgement。 For I need not go beyond
the conception of body in order to find extension connected with it；
but merely analyse the conception； that is； become conscious of the
manifold properties which I think in that conception； in order to
discover this predicate in it： it is therefore an analytical
judgement。 On the other hand； when I say； 〃All bodies are heavy；〃
the predicate is something totally different from that which I think
in the mere conception of a body。 By the addition of such a predicate；
therefore； it becomes a synthetical judgement。
Judgements of experience； as such； are always synthetical。 For it
would be absurd to think of grounding an analytical judgement on
experience； because in forming such a judgement I need not go out of
the sphere of my conceptions； and therefore recourse to the
testimony of experience is quite unnecessary。 That 〃bodies are
extended〃 is not an empirical judgement； but a proposition which
stands firm a priori。 For before addressing myself to experience； I
already have in my conception all the requisite conditions for the
judgement； and I have only to extract the predicate from the
conception； according to the principle of contradiction； and thereby
at the same time become conscious of the necessity of the judgement； a
necessity which I could never learn from experience。 On the other
hand； though at first I do not at all include the predicate of
weight in my conception of body in general； that conception still
indicates an object of experience； a part of the totality of
experience； to which I can stil