第 17 节
作者:
匆匆 更新:2021-02-27 02:11 字数:9315
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;
therefore; also quantum in its complete determinateness; for its principle the one; the absolutely
determinate。 Continuity; in which the one is present only in principle; as a sublated moment —
posited as a unity — is the form of indeterminateness。
Quantum; merely as such; is limited generally; its limit is an abstract simple determinateness of it。
But in quantum as number; this limit is posited as manifold within itself。 It contains the many ones
which constitute its determinate being; but does not contain them in an indeterminate manner; for
the determinateness of the limit falls in them; the limit excludes other determinate being; that is;
other pluralities and the ones it encloses are a specific aggregate; the amount — which is the form
taken by discreteness in number — the other to which is the unit; the continuity of the amount。
Amount and unit constitute the moments of number。
As regards amount; we must see more closely how the many ones of which it consists are present
in the limit; it is correct to say of amount that it consists of the many; for the ones are in it not as
sublated but as affirmatively present; only posited with the excluding limit to which they are
indifferent。 This; however; is not indifferent to them。 In the sphere of determinate being; the relation
of the limit to it was primarily such that the determinate being persisted as the affirmative on this
side of its limit; while the limit; the negation; was found outside on the border of the determinate
being; similarly; the breaking…off 'in the counting' of the many ones and the exclusion of other ones
appears as a determination falling outside the enclosed ones。 But in the qualitative sphere it was
found that the limit pervades the determinate being; is coextensive with it; and consequently that it
lies in the nature of something to be limited; that is; finite。 In the quantitative sphere a number; say a
hundred; is conceived in such a manner that the hundredth one alone limits the many to make them
a hundred。 In one sense this is correct; but on the other hand none of the hundred ones has
precedence over any other for they are only equal — each is equally the hundredth; thus they all
belong to the limit which makes the number a hundred and the number cannot dispense with any of
them for its determinateness。 Hence; relatively to the hundredth one; the others do not constitute a
determinate being that is in any way different from the limit; whether they are outside or inside it。
Consequently; the number is not a plurality over against the enclosing; limiting one; but itself
constitutes this limitation which is a specific quantum; the many constitute a number; a two; a ten; a
hundred; and so on。
Now the limiting one is the number as determined relatively to other numbers; as distinguished
from them。 But this distinguishing does not become a qualitative determinateness but remains
quantitative; falling only within the comparing external reflection; the number; as a one; remains
returned into itself and indiffe