the very reason that their content is greater than that which is
cogitated in the general conception。 And yet the whole intellectual
system of Leibnitz is based upon this false principle； and with it
must necessarily fall to the ground； together with all the ambiguous
principles in reference to the employment of the understanding which
have thence originated。
Leibnitz's principle of the identity of indiscernibles or
indistinguishables is really based on the presupposition that； if in
the conception of a thing a certain distinction is not to be found； it
is also not to be met with in things themselves； that； consequently；
all things are pletely identical （numero eadem） which are not
distinguishable from each other （as to quality or quantity） in our
conceptions of them。 But； as in the mere conception of anything
abstraction has been made of many necessary conditions of intuition；
that of which abstraction has been made is rashly held to be
non…existent； and nothing is attributed to the thing but what is
contained in its conception。
The conception of a cubic foot of space； however I may think it；
is in itself pletely identical。 But two cubic feet in space are
nevertheless distinct from each other from the sole fact of their
being in different places （they are numero diversa）； and these
places are conditions of intuition； wherein the object of this
conception is given； and which do not belong to the conception； but to
the faculty of sensibility。 In like manner； there is in the conception
of a thing no contradiction when a negative is not connected with an
affirmative； and merely affirmative conceptions cannot； in
conjunction； produce any negation。 But in sensuous intuition；
wherein reality （take for example； motion） is given； we find
conditions （opposite directions）… of which abstraction has been made
in the conception of motion in general… which render possible a
contradiction or opposition （not indeed of a logical kind）… and
which from pure positives produce zero = 0。 We are therefore not
justified in saying that all reality is in perfect agreement and
harmony； because no contradiction is discoverable among its
conceptions。* According to mere conceptions； that which is internal is
the substratum of all relations or external determinations。 When；
therefore； I abstract all conditions of intuition； and confine
myself solely to the conception of a thing in general； I can make
abstraction of all external relations； and there must nevertheless
remain a conception of that which indicates no relation； but merely
internal determinations。 Now it seems to follow that in everything
（substance） there is something which is absolutely internal and
which antecedes all external determinations； inasmuch as it renders
them possible； and that therefore this substratum is something which
does not contain any external relations and is consequently simple
（for corporeal things are never anything but relations； at least of
their parts external to each other）； and； inasmuch as we know of no
other absolutely internal determinations than those of the internal
sense； this substratum is not only simple； but also； analogously
with our internal sense； determined through representations； that is
to say； all things are properly monads； or simple beings endowed
with the power of representation。 Now all this would be perfectly
correct； if the conception of a thing were the only necessary
condition of the presentation of objects of external intuition。 It is；
on the contrary； manifest that a permanent phenomenon in space
（impenetrable extension） can contain mere relations； and nothing
that is absolutely internal； and yet be the primary substratum of
all external perception。 By mere conceptions I cannot think anything
external； without； at the same time； thinking something internal；
for the reason that conceptions of relations presuppose given
things； and without these are impossible。 But； as an intuition there
is something （that is； space； which； with all it contains； consists of
purely formal； or； indeed； real relations） which is not found in the
mere conception of a thing in general； and this presents to us the
substratum which could not be cognized through conceptions alone； I
cannot say： because a thing cannot be represented by mere
conceptions without something absolutely internal； there is also； in
the things themselves which are contained under these conceptions； and
in their intuition nothing external to which something absolutely
internal does not serve as the foundation。 For； when we have made
abstraction of all the conditions of intuition； there certainly
remains in the mere conception nothing but the internal in general；
through which alone the external is possible。 But this necessity；
which is grounded upon abstraction alone； does not obtain in the
case of things themselves； in so far as they are given in intuition
with such determinations as express mere relations； without having
anything internal as their foundation； for they are not things of a
thing of which we can neither for they are not things in themselves；
but only phenomena。 What we cognize in matter is nothing but relations
（what we call its internal determinations are but paratively
internal）。 But there are some self…subsistent and permanent； through
which a determined object is given。 That I； when abstraction is made
of these relations； have nothing more to think； does not destroy the
conception of a thing as phenomenon； nor the conception of an object
in abstracto； but it does away with the possibility of an object
that is determinable according to mere conceptions； that is； of a
noumenon。 It is certainly startling to hear that a thing consists
solely of relations； but this thing is simply a phenomenon； and cannot
be cogitated by means of the mere categories： it does itself consist
in the mere relation of something in general to the senses。 In the
same way； we cannot cogitate relations of things in abstracto； if we
mence with conceptions alone； in any other manner than that one
is the cause of determinations in the other； for that is itself the
conception of the understanding or category of relation。 But； as in
this case we make abstraction of all intuition； we lose altogether the
mode in which the manifold determines to each of its parts its
place； that is； the form of sensibility （space）； and yet this mode
antecedes all empirical causality。
*If any one wishes here to have recourse to the usual subterfuge；
and to say； that at least realitates noumena cannot be in opposition
to each other； it will be requisite for him to adduce an example of
this pure and non…sensuous reality； that it may be understood
whether the notion represents something or nothing。 But an example
cannot be found except in experience； which never presents to us
anything more than phenomena； and thus the proposition means nothing
more than that the conception which contains only affirmatives does
not contain anything negative… a proposition nobody ever doubted。
If by intelligible objects we understand things which can be thought
by means of the pure categories； without the need of the schemata of
sensibility； such objects are impossible。 For the condition of the
objective use of all our conceptions of understanding is the mode of
our sensuous intuition； whereby objects are given； and； if we make
abstraction of the latter； the former can have no relation to an
object。 And even if we should suppose a different kind of intuition
from our own； still our functions of thought would have no use or
signification in respect thereof。 But if we understand by the term；
objects of a non…sensuous intuition； in respect of which our
categories are not valid； and of which we can accordingly have no
knowledge （neither intuition nor conception）； in this merely
negative sense noumena must be admitted。 For this is no more than
saying that our mode of intuition is not applicable to all things； but
only to objects of our senses； that consequently its objective
validity is limited； and that room is therefore left for another
kind of intuition； and thus also for things that may be objects of it。
But in this sense the conception of a noumenon is problematical；
that is to say； it is the notion of that it that it is possible； nor
that it is impossible； inasmuch as we do not know of any mode of
intuition besides the sensuous； or of any other sort of conceptions
than the categories… a mode of intuition and a kind of conception
neither of which is applicable to a non…sensuous object。 We are on
this account inpetent to extend the sphere of our objects of
thought beyond the conditions of our sensibility； and to assume the
existence of objects of pure thought； that is； of noumena； inasmuch as
these have no true positive signification。 For it must be confessed of
the categories that they are not of themselves sufficient for the
cognition of things in themselves and； without the data of
sensibility； are mere subjective forms of the unity of the
understanding。 Thought is certainly not a product of the senses； and
in so far is not limited by them； but it does not therefore follow
that it may be employed purely and without the intervention of
sensibility； for it would then be without reference to an object。
And we cannot call a noumenon an object of pure thought； for the
representation thereof is but the problematical conception of an
object for a perfectly different intuition and a perfectly different
understanding from ours； both of which are consequently themselves
problematical。 The conception of a noumenon is therefore not the
conception of an object； but merely a problematical conception
inseparably connected with the limitation of our sensibility。 That
is to say； this conception contains the answer to the question： 〃Are
there objects quite unconnected with； and independent of； our
intuition？〃… a question to which only an indeterminate answer can be
given。 That answer is： 〃Inasmuch as sensuous intuition does not
apply to all things without distinction； there remains room for
other and different objects。〃 The existence of these problematical
objects is therefore not absolutely denied； in the absence of a