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It follows； as an immediate inference； that the things in the
world are all； without exception； simple beings… that position is
merely an external condition pertaining to them… and that； although we
never can separate and isolate the elementary substances from the
state of position； reason must cogitate these as the primary
subjects of all position； and consequently； as prior thereto… and
as simple substances。
ANTITHESIS。
No posite thing in the world consists of simple parts； and
there does not exist in the world any simple substance。
PROOF。
Let it be supposed that a posite thing （as substance） consists of
simple parts。 Inasmuch as all external relation； consequently all
position of substances； is possible only in space； the space；
occupied by that which is posite； must consist of the same number
of parts as is contained in the posite。 But space does not
consist of simple parts； but of spaces。 Therefore； every part of the
posite must occupy a space。 But the absolutely primary parts of
what is posite are simple。 It follows that what is simple
occupies a space。 Now； as everything real that occupies a space；
contains a manifold the parts of which are external to each other； and
is consequently posite… and a real posite； not of accidents （for
these cannot exist external to each other apart from substance）； but
of substances… it follows that the simple must be a substantial
posite； which is self…contradictory。
The second proposition of the antithesis… that there exists in the
world nothing that is simple… is here equivalent to the following： The
existence of the absolutely simple cannot be demonstrated from any
experience or perception either external or internal； and the
absolutely simple is a mere idea； the objective reality of which
cannot be demonstrated in any possible experience； it is consequently；
in the exposition of phenomena； without application and object。 For；
let us take for granted that an object may be found in experience
for this transcendental idea； the empirical intuition of such an
object must then be recognized to contain absolutely no manifold
with its parts external to each other； and connected into unity。
Now； as we cannot reason from the non…consciousness of such a manifold
to the impossibility of its existence in the intuition of an object；
and as the proof of this impossibility is necessary for the
establishment and proof of absolute simplicity； it follows that this
simplicity cannot be inferred from any perception whatever。 As；
therefore； an absolutely simple object cannot be given in any
experience； and the world of sense must be considered as the sum total
of all possible experiences： nothing simple exists in the world。
This second proposition in the antithesis has a more extended aim
than the first。 The first merely banishes the simple from the
intuition of the posite； while the second drives it entirely out of
nature。 Hence we were unable to demonstrate it from the conception
of a given object of external intuition （of the posite）； but we
were obliged to prove it from the relation of a given object to a
possible experience in general。
OBSERVATIONS ON THE SECOND ANTINOMY。
THESIS。
When I speak of a whole； which necessarily consists of simple parts；
I understand thereby only a substantial whole； as the true
posite； that is to say； I understand that contingent unity of the
manifold which is given as perfectly isolated （at least in thought）；
placed in reciprocal connection； and thus constituted a unity。 Space
ought not to be called a positum but a totum； for its parts are
possible in the whole； and not the whole by means of the parts。 It
might perhaps be called a positum ideale； but not a positum
reale。 But this is of no importance。 As space is not a posite of
substances （and not even of real accidents）； if I abstract all
position therein… nothing； not even a point； remains； for a point
is possible only as the limit of a space… consequently of a posite。
Space and time； therefore； do not consist of simple parts。 That
which belongs only to the condition or state of a substance； even
although it possesses a quantity （motion or change； for example）；
likewise does not consist of simple parts。 That is to say； a certain
degree of change does not originate from the addition of many simple
changes。 Our inference of the simple from the posite is valid
only of self…subsisting things。 But the accidents of a state are not
self…subsistent。 The proof； then； for the necessity of the simple；
as the ponent part of all that is substantial and posite； may
prove a failure； and the whole case of this thesis be lost； if we
carry the proposition too far； and wish to make it valid of everything
that is posite without distinction… as indeed has really now and
then happened。 Besides； I am here speaking only of the simple； in so
far as it is necessarily given in the posite… the latter being
capable of solution into the former as its ponent parts。 The proper
signification of the word monas （as employed by Leibnitz） ought to
relate to the simple； given immediately as simple substance （for
example； in consciousness）； and not as an element of the posite。 As
an clement； the term atomus would be more appropriate。 And as I wish
to prove the existence of simple substances； only in relation to；
and as the elements of； the posite； I might term the antithesis
of the second Antinomy； transcendental Atomistic。 But as this word has
long been employed to designate a particular theory of corporeal
phenomena （moleculae）； and thus presupposes a basis of empirical
conceptions； I prefer calling it the dialectical principle of
Monadology。
ANTITHESIS。
Against the assertion of the infinite subdivisibility of matter
whose ground of proof is purely mathematical； objections have been
alleged by the Monadists。 These objections lay themselves open； at
first sight； to suspicion； from the fact that they do not recognize
the clearest mathematical proofs as propositions relating to the
constitution of space； in so far as it is really the formal
condition of the possibility of all matter； but regard them merely
as inferences from abstract but arbitrary conceptions； which cannot
have any application to real things。 just as if it were possible to
imagine another mode of intuition than that given in the primitive
intuition of space； and just as if its a priori determinations did not
apply to everything； the existence of which is possible； from the fact
alone of its filling space。 If we listen to them； we shall find
ourselves required to cogitate； in addition to the mathematical point；
which is simple… not； however； a part； but a mere limit of space…
physical points； which are indeed likewise simple； but possess the
peculiar property； as parts of space； of filling it merely by their
aggregation。 I shall not repeat here the mon and clear
refutations of this absurdity； which are to be found everywhere in
numbers： every one knows that it is impossible to undermine the
evidence of mathematics by mere discursive conceptions