determinateness and an equally external something; such a limit; the indifference of the limit within
itself and of the something to the limit; constitutes the quantitative determinateness of the
something。
In the first place; pure quantity is to be distinguished from itself as a determinate quantity; from
quantum。 As the former; it is in the first place real being…for…self which has returned into itself and
which as yet contains no determinateness: a compact; infinite unity which continues itself into itself。
Secondly; this develops a determinateness which is posited in it as one which is at the same time
no determinateness; as only an external one。 It becomes quantum。 Quantum is indifferent
determinateness; that is; a self…transcending; self…negating determinateness; as this otherness of
otherness it relapses into the infinite progress。 But the infinite quantum is the indifferent
determinateness sublated; it is the restoration of quality。
Thirdly; quantum in a qualitative form is quantitative ratio。 Quantum transcends itself only generally:
in ratio; however; its transition into its otherness is such that this otherness in which it has its
determination is at the same time posited; is another quantum。 Thus quantum has returned into
itself and in its otherness is related to itself。
At the base of this ratio there is still the externality of quantum; the quanta which are related to
each other are indifferent; that is; they have their self…relation in such self…externality。 The ratio is
thus only a formal unity of quality and quantity。 Its dialectic is its transition into their absolute unity;
into Measure。
Remark: Something's Limit as Quality
Chapter 1 Quantity
Quantity is sublated being…for…self; the repelling one which related itself only negatively to the
excluded one; having passed over into relation to it; treats the other as identical with itself; and in
doing so has lost its determination: being…for…self has passed over into attraction。 The absolute
brittleness of the repelling one has melted away into this unity which; however; as containing this
one; is at the same time determined by the immanent repulsion; and as unity of the self…externality
is unity with itself。 Attraction is in this way the moment of continuity in quantity。
Continuity is; therefore; simple; self…same self…relation; which is not interrupted by any limit or
exclusion; it is not; however; an immediate unity; but a unity of ones which possess being…for…self。
The asunderness of the plurality is still contained in this unity; but at the same time as not
differentiating or interrupting it。 In continuity; the plurality is posited as it is in itself; the many are
all alike; each is the same as the other and the plurality is; consequently; a simple; undifferentiated
sameness。 Continuity is this moment of self…sameness of the asunderness; the self…continuation of
the different ones into those from which they are distinguished。
In continuity; therefore; magnitude immediately possesses the moment of discreteness…repulsion;
as now a moment in quantity。 Continuity is self…sameness; but of the Many which; however; do not
become exclusive; it is repulsion which expands the selfsameness to continuity。 Hence
discreteness; on its side; is a coalescent discreteness; where the ones are not connected by the
void; by the negative; but by their own continuity and do not interrupt this self…sameness in the
many。
Quantity is the unity of these moments of continuity and discreteness; but at first it is so in the form
of one of them; continuity; as a result of the dialectic of being…for…self; which has collapsed into
the form of self…identical immediacy。 Quantity is; as such; this simple result in so far as
being…for…self has not yet developed its moments and posited them within itself。 It contains them
to begin with as being…for…self posited as it is in truth。 The determination of being…for…self was to
be a self…sublating relation…to…self; a perpetual coming…out…of…itself。 But what is repelled is itself;
repulsion is; therefore; the creative flowing away of itself。 On account of the self…sameness of what
is repelled; this distinguishing or differentiation is an uninterrupted continuity; and because of the
coming…out…of…itself this continuity; without being interrupted; is at the same time a plurality; which
no less immediately remains in its self…identicalness。
Remark 1: The Conception of Pure Quantity
Remark 2: The Kantian Antinomy of the Indivisibility and the Infinite Divisibility
B Continuous and Discrete Magnitude
Remark: The Usual Separation of These Magnitudes
In the usual ideas of continuous and discrete magnitude; it is overlooked that each of these
magnitudes contains both moments; continuity and discreteness; and that the distinction between
them consists only in this; that in one of the moments the determinateness is posited and in the
other it is only implicit。 Space; time; matter; and so forth are continuous magnitudes in that they
are repulsions from themselves; a streaming forth out of themselves which at the same time is not
their transition or relating of themselves to a qualitative other。 They possess the absolute possibility
that the one may be posited in them at any point…not the empty possibility of a mere otherness (as
when it is said; it is possible that a tree might stand in the place of this stone); but they contain the
principle of the one within themselves; it is one of the determinations which constitute them。
Conversely; in discrete magnitude continuity is not to be overlooked; this moment is; as has been
shown; the one as unity。
Continuous and discrete magnitude can be regarded as species of quantity; provided that
magnitude is posited; not under any external determinateness; but under the determinatenesses of
its own moments; the ordinary transition from genus to species allows external characteristics to
be attributed to the former according to some external basis of classification。 And besides;
continuous and discrete magnitude are not yet quanta; they are only quantity itself in each of its
two forms。 They are perhaps; called magnitudes in so far as they have in common with quantum
simply this…to be a determinateness in quantity。
C。 LIMITATION OF QUANTITY
Discrete magnitude has first the one for its principle; secondly; it is a plurality of ones; and thirdly;
it is essentially continuous; it is the one as at the same time sublated; as unity; the continuation of
itself as such in the discreteness of the ones。 Consequently; it is posited as one magnitude; the
determinateness of which is the one which; in this posited and determinate being is the excluding
one; a limit in the unity。 Discrete magnitude as such is immediately not limited; but as distinguished
from continuous magnitude it is a determinate being; a something; with the one as its
determinateness and also as its first negation and limit。
This limit; which is related to the unity and is the negation in it; is also; as the one; self…related; it is
thus the enclosing; encompassing limit。 Limit here is not at first distinguished from its determinate
being as something; but; as the one; is immediately this negative point itself。 But the being which
here is limited is essentially a continuity; by virtue of which it passes beyond the limit; beyond this
one; to which it is indifferent。 Real discrete quantity is thus a quantity; or quantum…quantity as a
determinate being and a something。
Since the one which is a limit includes within itself the many ones of discrete quantity; it equally
posits them as sublated within it; and because it is a limit of continuity simply as such; the
distinction between continuous and discrete magnitude is here of no significance; or; more
correctly; it is a limit to the continuity of the one as much as of the other; both undergo transition
into quanta。
Chapter 2 Quantum
Quantum; which to begin with is quantity with a determinateness or limit in general is; in its
complete determinateness; number。 Quantum differentiates itself secondly; into (a) extensive
quantum; in which the limit is a limitation of the determinately existent plurality; and (b) intensive
quantum or degree; the determinate being having made the transition into being…for…self。 Intensive
quantum as both for itself and at the same time immediately outside itself — since it is an
indifferent limit — has its determinateness in an other。 As this manifest contradiction of being
determined simply within itself yet having its determinateness outside it; pointing outside itself for it;
quantum posited as being in its own self external to itself; passes over thirdly; into quantitative
infinity。
A。 NUMBER
Quantity is quantum; or has a limit; both as continuous and as discrete magnitude。 The difference
between these two kinds has here; in the first instance; no immediate significance。
The very nature of quantity as sublated being…for…self is ipso facto to be indifferent to its limit。 But
equally; too; quantity is not unaffected by the limit or by being; a quantum; for it contains within
itself as its own moment the one; which is absolutely determined and which; therefore; as posited
in the continuity or unity of quantity; is its limit; but a limit which remains what it has become;
simply a one。
This one is thus the principle of quantum; but as the one of quantity。 Hence; first; it is continuous;
it is a unity; secondly; it is discrete; a plurality of ones; which is implicit in continuous; or explicit in
discrete magnitude; the ones having equality with one another; possessing the said continuity; the
same unity。 Thirdly; this one is also a negation of the many ones as a simple limit; an excluding of
its otherness from itself; a determination of itself in opposition to other quanta。 Thus the one is 'a'
self…relating; 'b' enclosing and 'c' other…excluding limit。
Quantum completely posited in these determinations is number。 The complete positedness lies in
the existence of the limit as a plurality and so in its distinction from the unity。 Consequently;
number appears as a discrete magnitude; but in the unity it equally possesses continuity。 It is;
ther