science of logic-第18节
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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 are followed； after the insertion of
relation； by modality； which may therefore be mentioned here。 This category has there the
meaning of being the relation of the object to thought。 According to that idealism thought generally
is essentially external to the thing…in…itself。 In so far as the other categories have only the
transcendental character of belonging to consciousness； but to the objective element of it； so
modality as the category of relation to the subject； to this extent contains relatively the
determination of reflection…into…self； i。e。 the objectivity which belongs to the other categories is
lacking in the categories of modality； these； according to Kant； do not in the least add to the
concept as a determination of the object but only express the relation to the faculty of cognition。
The categories which Kant groups under modality … namely； possibility； actuality and necessity will
occur later in their proper place； Kant did not apply the infinitely important form of triplicity … with
him it manifested itself at first only as a formal spark of light … to the genera of his categories
（quantity； quality； etc。）； but only to their species which； too； alone he called categories。
Consequently he was unable to hit on the third to quality and quantity。
With Spinoza； the mode is likewise the third after substance and attribute； he explains it to be the
affections of substance； or that element which is in an other through which it is comprehended。
According to this concept； this third is only externality as such； as has already been mentioned；
with。 Spinoza generally； the rigid nature of substance lacks the return into itself。
The observation here made extends generally to those systems of pantheism which have been
partially developed by thought。 The first is being； the one； substance； the infinite； essence； in
contrast to this abstraction the second； namely； all determinateness in general； what is only finite；
accidental； perishable； non…essential； etc。 can equally abstractly be grouped together； and this is
what usually happens as the next step in qui
