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discover analytical propositions; which may be produced merely by
analysing our conceptions… for in this the philosopher would have
the advantage over his rival; we aim at the discovery of synthetical
propositions… such synthetical propositions; moreover; as can be
cognized a priori。 I must not confine myself to that which I
actually cogitate in my conception of a triangle; for this is
nothing more than the mere definition; I must try to go beyond that;
and to arrive at properties which are not contained in; although
they belong to; the conception。 Now; this is impossible; unless I
determine the object present to my mind according to the conditions;
either of empirical; or of pure; intuition。 In the former case; I
should have an empirical proposition (arrived at by actual measurement
of the angles of the triangle); which would possess neither
universality nor necessity; but that would be of no value。 In the
latter; I proceed by geometrical construction; by means of which I
collect; in a pure intuition; just as I would in an empirical
intuition; all the various properties which belong to the schema of
a triangle in general; and consequently to its conception; and thus
construct synthetical propositions which possess the attribute of
universality。
  It would be vain to philosophize upon the triangle; that is; to
reflect on it discursively; I should get no further than the
definition with which I had been obliged to set out。 There are
certainly transcendental synthetical propositions which are framed
by means of pure conceptions; and which form the peculiar
distinction of philosophy; but these do not relate to any particular
thing; but to a thing in general; and enounce the conditions under
which the perception of it may bee a part of possible experience。
But the science of mathematics has nothing to do with such
questions; nor with the question of existence in any fashion; it is
concerned merely with the properties of objects in themselves; only in
so far as these are connected with the conception of the objects。
  In the above example; we merely attempted to show the great
difference which exists between the discursive employment of reason in
the sphere of conceptions; and its intuitive exercise by means of
the construction of conceptions。 The question naturally arises: What
is the cause which necessitates this twofold exercise of reason; and
how are we to discover whether it is the philosophical or the
mathematical method which reason is pursuing in an argument?
  All our knowledge relates; finally; to possible intuitions; for it
is these alone that present objects to the mind。 An a priori or
non…empirical conception contains either a pure intuition… and in this
case it can be constructed; or it contains nothing but the synthesis
of possible intuitions; which are not given a priori。 In this latter
case; it may help us to form synthetical a priori judgements; but only
in the discursive method; by conceptions; not in the intuitive; by
means of the construction of conceptions。
  The only a priori intuition is that of the pure form of phenomena…
space and time。 A conception of space and time as quanta may be
presented a priori in intuition; that is; constructed; either alone
with their quality (figure); or as pure quantity (the mere synthesis
of the homogeneous); by means of number。 But the matter of
phenomena; by which things are given in space and time; can be
presented only in perception; a posteriori。 The only conception
which represents a priori this empirical content of phenomena is the
conception of a thing in general; and the a priori synthetical
cognition of this conception can give us nothing more than the rule
for the synthesis of that which may be contained in the
corresponding a posteriori perception; it is utterly inadequate to
present an a priori intuition of the real object; which must
necessarily be empirical。
  Synthetical propositions; which relate to things in general; an a
priori intuition of which is impossible; are transcendental。 For
this reason transcendental propositions cannot be framed by means of
the construction of conceptions; they are a priori; and based entirely
on conceptions themselves。 They contain merely the rule; by which we
are to seek in the world of perception or experience the synthetical
unity of that which cannot be intuited a priori。 But they are
inpetent to present any of the conceptions which appear in them
in an a priori intuition; these can be given only a posteriori; in
experience; which; however; is itself possible only through these
synthetical principles。
  If we are to form a synthetical judgement regarding a conception; we
must go beyond it; to the intuition in which it is given。 If we keep
to what is contained in the conception; the judgement is merely
analytical… it is merely an explanation of what we have cogitated in
the conception。 But I can pass from the conception to the pure or
empirical intuition which corresponds to it。 I can proceed to
examine my conception in concreto; and to cognize; either a priori
or a posterio; what I find in the object of the conception。 The
former… a priori cognition… is rational…mathematical cognition by
means of the construction of the conception; the latter… a
posteriori cognition… is purely empirical cognition; which does not
possess the attributes of necessity and universality。 Thus I may
analyse the conception I have of gold; but I gain no new information
from this analysis; I merely enumerate the different properties
which I had connected with the notion indicated by the word。 My
knowledge has gained in logical clearness and arrangement; but no
addition has been made to it。 But if I take the matter which is
indicated by this name; and submit it to the examination of my senses;
I am enabled to form several synthetical… although still empirical…
propositions。 The mathematical conception of a triangle I should
construct; that is; present a priori in intuition; and in this way
attain to rational…synthetical cognition。 But when the
transcendental conception of reality; or substance; or power is
presented to my mind; I find that it does not relate to or indicate
either an empirical or pure intuition; but that it indicates merely
the synthesis of empirical intuitions; which cannot of course be given
a priori。 The synthesis in such a conception cannot proceed a
priori… without the aid of experience… to the intuition which
corresponds to the conception; and; for this reason; none of these
conceptions can produce a determinative synthetical proposition;
they can never present more than a principle of the synthesis* of
possible empirical intuitions。 A transcendental proposition is;
therefore; a synthetical cognition of reason by means of pure
conceptions and the discursive method; and it renders possible all
synthetical unity in empirical cognition; though it cannot present
us with any intuition a priori。

  *In the case of the conception of cause; I do really go beyond the
empirical conception of an event… but not to the intuition which
presents this conception in concreto; but only to the time…conditions;
which may be found in experience to correspond to the conception。 My
procedure is; therefore; strictly according to conceptions; I cannot
in a case of this kind employ the construction of conceptions; because
the conception is merely a rule for the synthesis of perceptions;
which are not pure intuitions; and which; therefore; cannot be given a
priori。

  There is thus a twofold exercise of reason。 Both modes have the
properties of universality and an a priori origin in mon; but
are; in their procedure; of widely different character。 The reason
of this is that in the world of phenomena; in which alone objects
are presented to our minds; there are two main elements… the form of
intuition (space and time); which can be cognized and determined
pletely a priori; and the matter or content… that which is
presented in space and time; and which; consequently; contains a
something… an existence corresponding to our powers of sensation。 As
regards the latter; which can never be given in a determinate mode
except by experience; there ar

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