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 indifferent to others。 This indifference of a number to others is an essential
determination of it and constitutes the implicit determinedness of the number； but also the number's
own externality。 Number is thus a numerical one as the absolutely determinate one； which at the
same time has the form of simple immediacy and for which； therefore； the relation to other is
completely external。 Further； one as a number possesses determinateness （in so far as this is a
relation to other） as the moments of itself contained within it； in its difference of unit and amount；
and amount is itself a plurality of ones； that is； this absolute externality is in the one itself。 This
contradiction of number or of quantum as such within itself is the quality of quantum； in the further
determinations of which this contradiction is developed。
Remark 1： The Species of Calculation in Arithmetic； Kant's Synthetic Propositions a priori
Remark 2： The Employment of Numerical Distinctions for Expressing Philosophical
Notions
B Extensive and Intensive Quantum
（a） Their Difference
（b） Identity of Extensive and Intensive Magnitude
Remark 1： Examples of This Identity
Remark 2： The determination of degree as applied by Kant to the soul
（c） Alteration of Quantum
C Quantitative Infinity
（a） Its Notion
（b） The Quantitative Infinite Progress
Remark 1： The High Repute of the Progress to Infinity
Remark 2： The Kantian Antinomy of the Limitation and Nonlimitation of the World
（c） The Infinity of Quantum
Remark 1： The Specific Nature of the Notion of the Mathematical Infinite
Remark 2： The Purpose of the Differential Calculus Deduced from its Application
Remark 3： Further Forms Connected With the Qualitative Determinateness of Magnitude
Chapter 3 The Quantitative Relation or Quantitative Ratio
A The Direct Ratio
B Inverse Ratio
C The Ratio of Powers
Remark
In the Remarks above on the quantitative infinite； it was shown that this infinite and also the
difficulties associated with it have their origin in the qualitative moment which makes its
appearance in the sphere of quantity； and also how the qualitative moment of the ratio of powers
in particular is the source of various developments and complexities。 It was shown that the chief
obstacle to a grasp of the Notion of this infinite is the stopping short at its merely negative
determination as the negation of quantum； instead of advancing to the simple affirmative
determination which is the qualitative moment。 The only further remark to be made here concerns
the intrusion of quantitative forms into the pure qualitative forms of powers in of thought in
philosophy。 It is the relationship particular which has been applied recently to the determinations of
the Notion。 The Notion in its immediacy was called the first power or potence； in its otherness
or difference； in the determinate being of its moments； the second power； and in its return into
itself or as a totality； the third power。 It is at once evident that power as used thus is a category
which essentially belongs to quantum … these powers do not bear the meaning of the potentia； the
dynamis of Aristotle。 Thus； the relationship of powers expresses determinateness in the form or
difference which has reached its truth； but difference as it is in the particular Notion of quantum；
not as it is in the Notion as such。 In quantum； the negativity which belongs to the nature of the
Notion is still far from being posited in the determination proper to the Notion； differences which
are proper to quantum are superficial determinations for the Notion itself and are still far from
being determined as they are in the Notion。 It was in the infancy of philosophic thinking that
numbers were used； as by Pythagoras； to designate universal； essential distinctions…and first and
second power； and so on are in this respect not a whit better than numbers。 This was a preliminary
stage to comprehension in the element of pure thought； it was not until after Pythagoras that
thought determinations themselves were discovered； i。e。； became on their own account objects
for consciousness。 But to retrogress from such determinations to those of number is the action of a
thinking which feels its own incapacity； a thinking which； in Opposition to current philosophical
culture which is accustomed to thought determinations； now also makes itself ridiculous by
pretending that this impotence is something new； superior； and an advance。
There is as little to be said against the expression power when it is used only as a symbol； as there
is against the use of numbers or any other kind of symbols for Notions…but also there is just as
much to be said against them as against all symbolism whatever in which pure determinations of
the Notion or of philosophy are supposed to be represented。
Philosophy needs no such help either from the world of sense or from the products of the
imagination； or from subordinate spheres in its own peculiar province； for the determinations of
such spheres are unfitted for higher spheres and for the whole。 This unfitness is manifest whenever
categories of the finite are applied to the infinite； the current determinations of force； or
substantiality； cause and effect； and so on； are likewise only symbols for expressing； for example；
vital or spiritual relationships； i。e。 they are untrue determinations for such relationships； and still
more so are the powers of quantum and degrees of powers； both for such and for speculative
relationships generally。
If numbers； powers； the mathematical infinite； and suchlike are to be used not as symbols but as
forms for philosophical determinations and hence themselves as philosophical forms； then it would
be necessary first of all to demonstrate their philosophical meaning； i。e。 the specific nature of their
Notion。 If this is done； then they themselves are superfluous designations； the determinateness of
the Notion specifies its own self and its specification alone is the correct and fitting designation。
The use of those forms is； therefore； nothing more than a convenient means of evading the task of
grasping the determinations of the Notion； of specifying and of justifying them。
Section Three： Measure
Abstractly expressed； in measure quality and quantity are united。 Being as such is an immediate
identity of the determinateness with itself。 This immediacy of the determinateness has sublated
itself。 Quantity is being which has returned into itself in such a manner that it is a simple
self…identity as indifference to the determinateness。
But this indifference is only the externality of having the determinateness not in its own self but in an
other。 Thirdly； we now have self…related externality； as self…related it is also a sublated externality
and has within itself the difference from itself…the difference which； as an externality is the
quantitative； and as taken back into itself is the qualitative； moment。
In transcendental idealism the categories of quantity and quality