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Science of Logic (SL; German: Wissenschaft der Logik, WdL), first published between 1812 and 1816, is the work in which Georg Wilhelm Friedrich Hegel outlined his vision of logic. Hegel's logic is a system of dialectics, i.e., a dialectical metaphysics: it is a development of the principle that thought and being constitute a single and active unity. Science of Logic also incorporates the traditional Aristotelian syllogism: It is conceived as a phase of the "original unity of thought and being" rather than as a detached, formal instrument of inference.

For Hegel, the most important achievement of German idealism, starting with Immanuel Kant and culminating in his own philosophy, was the argument that reality (being) is shaped through and through by thought and is, in a strong sense, identical to thought. Thus ultimately the structures of thought and being, subject and object, are identical. Since for Hegel the underlying structure of all of reality is ultimately rational, logic is not merely about reasoning or argument but rather is also the rational, structural core of all of reality and every dimension of it. Thus Hegel's Science of Logic includes among other things analyses of being, nothingness, becoming, existence, reality, essence, reflection, concept, and method. As developed, it included the fullest description of his dialectic.

Hegel considered it one of his major works and therefore kept it up to date through revision.

Science of Logic is sometimes referred to as the Greater Logic to distinguish it from the Lesser Logic, the moniker given to the condensed version Hegel presented as the "Logic" section of his Encyclopedia of the Philosophical Sciences.

## Publication history

Hegel wrote Science of Logic after he had completed his Phenomenology of Spirit and while he was in Nuremberg working at a secondary school and courting his fiancée. It was published in two volumes. The first, ‘The Objective Logic’, has two parts (the Doctrines of Being and Essence) and each part was published in 1812 and 1813 respectively. The second volume, ‘The Subjective Logic’, was published in 1816 the same year he became a professor of philosophy at Heidelberg. Science of Logic is too advanced for undergraduate students so Hegel wrote an Encyclopaedic version of the logic which was published in 1817.

In 1826, the book went out of stock. Instead of reprinting, as requested, Hegel undertook some revisions. By 1831, Hegel completed a greatly revised and expanded version of the ‘Doctrine of Being’, but had no time to revise the rest of the book. The Preface to the second edition is dated 7 November 1831, just before his death on 14 November 1831. This edition appeared in 1832, and again in 1834–5 in the posthumous Works. Only the second edition of Science of Logic is translated into English.

## Introduction

### Hegel's general concept of logic

According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been practiced, this science demanded a total and radical reformulation "from a higher standpoint." At the end of the preface he wrote that "Logic is the thinking of God." His stated goal with The Science of Logic was to overcome what he perceived to be a common flaw running through all other former systems of logic, namely that they all presupposed a complete separation between the content of cognition (the world of objects, held to be entirely independent of thought for their existence), and the form of cognition (the thoughts about these objects, which by themselves are pliable, indeterminate and entirely dependent upon their conformity to the world of objects to be thought of as in any way true). This unbridgeable gap found within the science of reason was, in his view, a carryover from everyday, phenomenal, unphilosophical consciousness.[1]

The task of extinguishing this opposition within consciousness Hegel believed he had already accomplished in his book German idealism, starting with Immanuel Kant and culminating in his own philosophy, was the argument that reality (being) is shaped through and through by thought and is, in a strong sense, identical to thought. Thus ultimately the structures of thought and being, subject and object, are identical. Since for Hegel the underlying structure of all of reality is ultimately rational, logic is not merely about reasoning or argument but rather is also the rational, structural core of all of reality and every dimension of it. Thus Hegel's Science of Logic includes among other things analyses of being, nothingness, becoming, existence, reality, essence, reflection, concept, and method. As developed, it included the fullest description of his dialectic.

Hegel considered it one of his major works and therefore kept it up to date through revision.

Science of Logic is sometimes referred to as the Greater Logic to distinguish it from the Lesser Logic, the moniker given to the condensed version Hegel presented as the "Logic" section of his Encyclopedia of the Philosophical Sciences.

Hegel wrote Science of Logic after he had completed his Phenomenology of Spirit and while he was in Nuremberg working at a secondary school and courting his fiancée. It was published in two volumes. The first, ‘The Objective Logic’, has two parts (the Doctrines of Being and Essence) and each part was published in 1812 and 1813 respectively. The second volume, ‘The Subjective Logic’, was published in 1816 the same year he became a professor of philosophy at Heidelberg. Science of Logic is too advanced for undergraduate students so Hegel wrote an Encyclopaedic version of the logic which was published in 1817.

In 1826, the book went out of stock. Instead of reprinting, as requested, Hegel undertook some revisions. By 1831, Hegel completed a greatly revised and expanded version of the ‘Doctrine of Being’, but had no time to revise the rest of the book. The Preface to the second edition is dated 7 November 1831, just before his death on 14 November 1831. This edition appeared in 1832, and again in 1834–5 in the posthumous Works. Only the second edition of Science of Logic is translated into English.

## Introduction

### Hegel's general concept of logic

According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been practiced, this science demanded a total and radical reformulation "from a higher standpoint." At the end of the preface he wrote that "Logic is the thinking of God." His stated goal with The Science of Logic was to overcome what he perceived to be a common flaw running through all other former systems of logic, namely that they all presupposed a complete separation between the content of cognition (the world of objects, held to be entirely independent of thought for their existence), and the form of cognition (the thoughts about these objects, which by themselves are pliable, indeterminate and entirely dependent upon their conformity to the world of objects to be thought of as in any way true). This unbridgeable gap found within the science of reason was, in his view, a carryover from everyday, phenomenal, unphilosophical consciousness.[1]

The task of extinguishing this opposition within consciousness Hegel believed he had already accomplished in his book Phänomenologie des Geistes (1807) with the final attainment of Absolute Knowing: "Absolute knowing is the truth of every mode of consciousness because ... it is only in absolute knowing that the separation of the object from the certainty of itself is completely eliminated: truth is now equated with certainty and certainty with truth."[2] Once thus liberated from duality, the science of thinking no longer requires an object or a matter outside of itself to act as a touchstone for its truth, but rather takes the form of its own self-mediated exposition and development which eventually comprises within itself every possible mode of rational thinking. "It can therefore be said," says Hegel, "that this content is the exposition of God as he is in his eternal essence before the creation of nature and a finite mind."[3] The German word Hegel employed to denote this post-dualist form of consciousness was Begriff (traditionally translated either as Concept or Notion).

### General division of the Logic

The self-exposition of this unified consciousness, or Notion, follows a series of necessary, self-determined stages in an inherently logical, dialectical progression. Its course is from the objective to the subjective "sides" (or judgements as Hegel calls them) of the Notion. The objective side, its Being, is the Notion as it is in itself [an sich], its reflection in nature being found in anything inorganic such as water or a rock. This is the subject of Book One: The Doctrine of Being. Book Three: The Doctrine of the Notion outlines the subjective side of the Notion as Notion, or, the Notion as it is for itself [für sich]; human beings, animals and plants being some of the shapes it takes in nature. The process of Being's transition to the Notion as fully aware of itself is outlined in Book Two: The Doctrine of Essence, which is included in the Objective division of the Logic.[4] The Science of Logic is thus divided like this:

Volume One: The Objective Logic
Book One: The Doctrine of Being
Book Two: The Doctrine of Essence
Volume Two: The Subjective Logic
Book Three: The Doctrine of the Notion

This division, however, does not represent a strictly linear progression. At the end of the book Hegel wraps all of the preceding logical development into a single Absolute Idea. Hegel then links this final absolute idea with the simple concept of Being which he introduced at the start of the book. Hence the Science of Logic is actually a circle and there is no starting point or end, but rather a totality. This totality is itself, however, but a link in the chain of the three sciences of Logic, Nature and Spirit, as developed by Hegel in his Encyclopedia of the Philosophical Sciences (1817), that, when taken as a whole, comprise a "circle of circles."[5]

## Objective Logic: Doctrine of Being

### Determinate Being (Quality)

#### Being

A. Being

Being, specifically Pure Being, is the first step taken in the scientific development of Pure Knowing, which itself is the final state achieved in the historical self-manifestation of Geist (Spirit/Mind) as described in detail by Hegel in Phänomenologie des Geistes (1807).[6] This Pure Knowing is simply Knowing as Such, and as such, has for its first thought product Being as Such, i.e., the purest abstraction from all that is (although, importantly, not distinct from, or alongside, all that is), having "no diversity within itself nor with any reference outwards. ... It is pure indeterminateness and emptiness."[7]

EXAMPLE: Hegel claims that the Eleatic philosopher Parmenides was the person who "first enunciated the simple thought of pure being as the absolute and sole truth."[8]

B. Nothing

Nothing, specifically Pure Nothing, "is simply equality with itself, complete emptiness, absence of all determination and content." It is therefore identical with Being, except that it is thought of as its very opposite. This distinction is therefore meaningful as posited by thought.[9]

EXAMPLE: in Hegel's estimation, Pure Nothing is the absolute principle "in the oriental systems, princip

In 1826, the book went out of stock. Instead of reprinting, as requested, Hegel undertook some revisions. By 1831, Hegel completed a greatly revised and expanded version of the ‘Doctrine of Being’, but had no time to revise the rest of the book. The Preface to the second edition is dated 7 November 1831, just before his death on 14 November 1831. This edition appeared in 1832, and again in 1834–5 in the posthumous Works. Only the second edition of Science of Logic is translated into English.

According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been practiced, this science demanded a total and radical reformulation "from a higher standpoint." At the end of the preface he wrote that "Logic is the thinking of God." His stated goal with The Science of Logic was to overcome what he perceived to be a common flaw running through all other former systems of logic, namely that they all presupposed a complete separation between the content of cognition (the world of objects, held to be entirely independent of thought for their existence), and the form of cognition (the thoughts about these objects, which by themselves are pliable, indeterminate and entirely dependent upon their conformity to the world of objects to be thought of as in any way true). This unbridgeable gap found within the science of reason was, in his view, a carryover from everyday, phenomenal, unphilosophical consciousness.[1]

The task of extinguishing this opposition within consciousness Hegel believed he had already accomplished in his book Phänomenologie des Geistes (1807) with the final attainment of Absolute Knowing: "Absolute knowing is the truth of every mode of consciousness because ... it is only in absolute knowing that the separation of the object from the certainty of itself is completely eliminated: truth is now equated with certainty and certainty with truth."[2] Once thus liberated from duality, the science of thinking no longer requires an o

The task of extinguishing this opposition within consciousness Hegel believed he had already accomplished in his book Phänomenologie des Geistes (1807) with the final attainment of Absolute Knowing: "Absolute knowing is the truth of every mode of consciousness because ... it is only in absolute knowing that the separation of the object from the certainty of itself is completely eliminated: truth is now equated with certainty and certainty with truth."[2] Once thus liberated from duality, the science of thinking no longer requires an object or a matter outside of itself to act as a touchstone for its truth, but rather takes the form of its own self-mediated exposition and development which eventually comprises within itself every possible mode of rational thinking. "It can therefore be said," says Hegel, "that this content is the exposition of God as he is in his eternal essence before the creation of nature and a finite mind."[3] The German word Hegel employed to denote this post-dualist form of consciousness was Begriff (traditionally translated either as Concept or Notion).

The self-exposition of this unified consciousness, or Notion, follows a series of necessary, self-determined stages in an inherently logical, dialectical progression. Its course is from the objective to the subjective "sides" (or judgements as Hegel calls them) of the Notion. The objective side, its Being, is the Notion as it is in itself [an sich], its reflection in nature being found in anything inorganic such as water or a rock. This is the subject of Book One: The Doctrine of Being. Book Three: The Doctrine of the Notion outlines the subjective side of the Notion as Notion, or, the Notion as it is for itself [für sich]; human beings, animals and plants being some of the shapes it takes in nature. The process of Being's transition to the Notion as fully aware of itself is outlined in Book Two: The Doctrine of Essence, which is included in the Objective division of the Logic.[4] The Science of Logic is thus divided like this:

Volume One: The Objective Logic
Book One: The Doctrine of Being
Book Two: The Doctrine of Essence
Volume Two: The Subjective Logic
Book Three: The Doctrine of the Notion

This division, however, does not represent a strictly linear progression. At the end of the book

This division, however, does not represent a strictly linear progression. At the end of the book Hegel wraps all of the preceding logical development into a single Absolute Idea. Hegel then links this final absolute idea with the simple concept of Being which he introduced at the start of the book. Hence the Science of Logic is actually a circle and there is no starting point or end, but rather a totality. This totality is itself, however, but a link in the chain of the three sciences of Logic, Nature and Spirit, as developed by Hegel in his Encyclopedia of the Philosophical Sciences (1817), that, when taken as a whole, comprise a "circle of circles."[5]

## Objective Logic: Doctrine of Being

(a) Something and Other are separate from each other, but each still contains within itself, as moments, their former unity in Determinate Being. These moments now re-emerge as Being-in-Itself, i.e., Something as Something only insofar as it is in opposition to the Other; and Being-for-Other, i.e., Something as Something only insofar as it is in relation to the Other.[17] (Hegel's view is in this way contrasted with Kant's noumenon, the unknowable "thing in itself": Being-in-itself taken in isolation from Being-for-Other is nothing but an empty abstraction and

(a) Something and Other are separate from each other, but each still contains within itself, as moments, their former unity in Determinate Being. These moments now re-emerge as Being-in-Itself, i.e., Something as Something only insofar as it is in opposition to the Other; and Being-for-Other, i.e., Something as Something only insofar as it is in relation to the Other.[17] (Hegel's view is in this way contrasted with Kant's noumenon, the unknowable "thing in itself": Being-in-itself taken in isolation from Being-for-Other is nothing but an empty abstraction and to ask "what it is" is to ask a question made impossible to answer.)[18]

Something is now no longer only an isolated something, but is in both positive and negative relationship to the Other. This relationship, however, is then reflected back into the Something as isolated, i.e., in-itself, and bestows upon it further determinations. What a Something is in

Something is now no longer only an isolated something, but is in both positive and negative relationship to the Other. This relationship, however, is then reflected back into the Something as isolated, i.e., in-itself, and bestows upon it further determinations. What a Something is in opposition to an Other is its (b) Determination;[19] what it is in relation to an Other is its Constitution.[20]

The point at which Something ceases to be itself and becomes an Other is that Something's Limit. This Limit is also shared by its Other which is itself an other Something only insofar as it is on the far side of this Limit. It is therefore by their common Limits that Somethings and Others are mediated with one another and mutually define each other's inner Qualities.[22]

EXAMPLE: The point at which a point ceases to be a point and becomes a line constitutes the Limit between them. However, a line is not only something other than a point, i.e., only a Determinate Being, but its very principle is at the same time defined by it, just as a plane is defined by the line and the solid by the plane, etc.[23]

From the perspective of the Limit, a Something is only a particular Something insofar as

From the perspective of the Limit, a Something is only a particular Something insofar as it is not something else. This means that the Something's self-determination (inherited from Determined Being as Such) is only relative, entirely dependent on what it isn't to be what it is, and entirely dependent on Something posited as the contradiction of itself, of its own Limit.[24] Something is thus only temporary, contains its own Ceasing-to-Be within itself and so is (c) Finite, i.e., doomed to eventually cease to be. For Finite things, "the hour of their birth is the hour of their death."[25] At this point the Limit ceases to play its mediating role between Something and Other, i.e., is negated, and is taken back into the self-identity―the Being-Within-Self―of the Something to become that Something’s Limitation, the point beyond which that Something will cease to be.[26] The flip side of this, though, is that the Limit also takes its negative along with it back into the Something, this (the result of negating the Limit) being the Other yet now as posited in the Something as that Something’s very own Determination. What this means is that, in the face of its own Limitation, the very Quality that defined the Something in the first place ceases to be in any opposition to the Other, which is to say that it no longer strictly is this Quality but now Ought to be this Quality. Limitation and the Ought are the twin, self-contradictory moments of the Finite.[27]

EXAMPLE: "The sentient creature, in the limitation of hunger, thirst, etc., is the urge to overcome this limitation and it does overcome it. It feels pain, and it is the privilege of the sentient nature to feel pain; it is a negation in its self, and the negation is determined as a limitation in its feeling, just because the sentient creature has the feeling of its self, which is the totality that transcends this determinateness [i.e., it feels

Once again, sublation occurs. Both Limitation and the Ought point beyond the Finite something, the one negatively and the other positively. This beyond, in which they are unified, is the Infinite.[29]

##### C. Infinity

The negation that Being-in-Itself experienced in the Limitation, the negation that made it Finite, is again negated resulting in the affirmative determination of (a) the Infinite in General which now reveals itself, not as something distinct from, but as the true nature of the Finite. "At the name of the infinite, t

The negation that Being-in-Itself experienced in the Limitation, the negation that made it Finite, is again negated resulting in the affirmative determination of (a) the Infinite in General which now reveals itself, not as something distinct from, but as the true nature of the Finite. "At the name of the infinite, the heart and the mind light up, for in the infinite the spirit is not merely abstractly present to itself, but rises to its own self, to the light of thinking, of its universality, of its freedom."[30]

This affirmation of the Infinite, however, carries with it a negative relation to an other, the Finite. Because of this, it falls back into the determination of the Something with a Limit peculiar to itself. This In-finite, then, is not the pure Infinite, but merely the non-Finite. Hegel calls this the

This affirmation of the Infinite, however, carries with it a negative relation to an other, the Finite. Because of this, it falls back into the determination of the Something with a Limit peculiar to itself. This In-finite, then, is not the pure Infinite, but merely the non-Finite. Hegel calls this the Spurious Infinite and it is this that is spoken of whenever the Infinite is held to be over and above―separated from―the Finite. This separateness is in itself false since the Finite naturally engenders the Infinite through Limitation and the Ought, while the Infinite, thus produced, is bounded by its Other, the Finite, and is therefore itself Finite. Yet they are held to be separate by this stage of thought and so the two terms are eternally stuck in an empty oscillation back and forth from one another. This Hegel calls (b) the Infinite Progress.[31]

This impasse can only be overcome, as usual, via sublation. From the standpoint of the Finite, the Infinite cannot break free into independence, but must always be bounded, and therefore finitized, by its Other, the Finite. For further logical development to be possible, this standpoint must shift to a new one where the Infinite is no longer simply a derivation of the Finite, but where the Finite, as well as the Infinite in General, are but moments of (c) the True Infinite. The True infinite bears the same relation of mediation to these moments as Becoming did to Being and Nothing and as Alteration did to Something and Other.[32]

This move is highly significative of Hegel's philosophy because it means that, for him, "[it] is not the finite which is the real but the infinite." The reality of the True Infinite is in fact "more real" than the Reality of Determinate Being. This higher, and yet more concrete, reality is the Ideal [das Ideell]: "The idealism of philosophy consists in nothing else than in recognizing that the finite has no veritable being."[34]

As having been sublated, the mediation which was performed by the True Infinite between the Finite and the Infinite now has resulted in their immediate unity. This unity is called Being-for-Self.[35]

#### Being-for-Self

This (a) One in its Own Self, standing in negative relation to all its preceding moments, is entirely differentiated from each of them. It is neither a Determinate Being, nor a Something, nor a Constitution, etc. It is therefore indeterminate and unalterable. There is Nothing in it.[40] Just as there is no criterion to distinguish Be

This (a) One in its Own Self, standing in negative relation to all its preceding moments, is entirely differentiated from each of them. It is neither a Determinate Being, nor a Something, nor a Constitution, etc. It is therefore indeterminate and unalterable. There is Nothing in it.[40] Just as there is no criterion to distinguish Being and Nothing despite the fact that they are opposites, the One is also identical with its opposite, (b) the Void. The Void can be said to be the Quality of the One.[41]

EXAMPLE: At this stage, the Logic has incorporated the ancient atomism of Leucippus and Democritus. Hegel actually held the ancient philosophical notion of atomism in higher esteem than the [43]

##### C. Repulsion and Attraction

Once these many Ones have been posited, the nature of their relationship begins to unfold. Because it is the nature of the One to be purely self-related, their relation to one another is in fact a non-relation, i.e., takes place externally in the Void. From the standpoint of the one One, then, there are no other Ones, that is, its relation to them is one of (a) Exclusion. Seen from within the One there is only one One, but at th

Once these many Ones have been posited, the nature of their relationship begins to unfold. Because it is the nature of the One to be purely self-related, their relation to one another is in fact a non-relation, i.e., takes place externally in the Void. From the standpoint of the one One, then, there are no other Ones, that is, its relation to them is one of (a) Exclusion. Seen from within the One there is only one One, but at the same time the One only exists in the first place through its negative external relation to other Ones, i.e., for there to be the one One there must be Many Ones that mutually Exclude one another.[44]

EXAMPLE: The idea that the One is entirely self-subsistent and can exist without the Many is, according to Hegel, "the supreme, most stubborn error, which takes itself for the highest truth, manifesting in more concrete forms as abstract freedom, pure ego and, further, as Evil."[45]<

The One having been restored to unity by Attraction now contains Repulsion and Attraction within it as moments. It is the Ideal One of Infinite Being, which, for Hegel, actually makes it more "real" than the merely Real Many. From the standpoint of this Ideal One, both Repulsion and Attraction now presuppose each other, and, taken one step further, each presu

The One having been restored to unity by Attraction now contains Repulsion and Attraction within it as moments. It is the Ideal One of Infinite Being, which, for Hegel, actually makes it more "real" than the merely Real Many. From the standpoint of this Ideal One, both Repulsion and Attraction now presuppose each other, and, taken one step further, each presupposes itself as mediated by the other. The One is only a One with reference to another One―Repulsion; but this "other" One is in itself identical to, is in fact, the original One―Attraction: each is the moment of the other. This is the (c) Relation of Repulsion and Attraction, which at this point is only relative.[47]

Repulsion and Attraction are relative to one another insofar as the One is taken either as the beginning or result of their mediation with one another. Imparted with continuous, Infinite motion, the One, Repulsion and Attraction become the sublated moments of Quantity.[49]

### Magnitude (Quantity)

#### Quantity

A. Pure Quantity

The previous determinations of Being-for-Self have now become the sublated moments of Pure Quantity. Pure Quantity is a One, but a One made up of the Many having been Attracted back into each other out of their initial Repulsion. It therefore contains Many identical Ones, but

A. Pure Quantity

The previous determinations of Being-for-Self have now become the sublated moments of Pure Quantity. Pure Quantity is a One, but a One made up of the Many having been Attracted back into each other out of their initial Repulsion. It therefore contains Many identical Ones, but in their coalescence, they have lost their mutual Exclusion, giving us a simple, undifferentiated sameness. This sameness is Continuity, the moment of Attraction within Quantity. The other moment, that of Repulsion, is also retained in Quantity as Discreteness. Discreteness is the expansion of the self-sameness of the Ones into Continuity. What the unity of Continuity and Discreteness, i.e.

The previous determinations of Being-for-Self have now become the sublated moments of Pure Quantity. Pure Quantity is a One, but a One made up of the Many having been Attracted back into each other out of their initial Repulsion. It therefore contains Many identical Ones, but in their coalescence, they have lost their mutual Exclusion, giving us a simple, undifferentiated sameness. This sameness is Continuity, the moment of Attraction within Quantity. The other moment, that of Repulsion, is also retained in Quantity as Discreteness. Discreteness is the expansion of the self-sameness of the Ones into Continuity. What the unity of Continuity and Discreteness, i.e., Quantity, results in is a continual outpouring of something out of itself, a perennial self-production.[50]

B. Continuous and Discrete Magnitude

Although unified in Quantity, Continuity and Discreteness still retain their distinction from one another. They cannot be cut off from each other, but either one can be foregrounded leaving the other present only implicitly. Quantity is a Continuous Magnitude when seen as a coherent whole; as a collection of identical Ones, it is a Discrete Magnitude.[53]

C. Limitation of Quantity

Quantity is the One, but containing within it the moments of the Many, Repulsion, Attraction, etc. At this point the negative, Excluding nature of the One is reasserted within Quantity. The Discrete Ones within Quantity now become Limited, isolated Somethings: Quanta.Although unified in Quantity, Continuity and Discreteness still retain their distinction from one another. They cannot be cut off from each other, but either one can be foregrounded leaving the other present only implicitly. Quantity is a Continuous Magnitude when seen as a coherent whole; as a collection of identical Ones, it is a Discrete Magnitude.[53]

C. Limitation of Quantity

Quantity is the One, but containing within it the moments of the Many, Repulsion, Attraction, etc. At this point the negative, Excluding nature of the One is reasserted within Quantity. The Discrete Ones within Quantity now become Limited, isolated Somethings: Quanta.[54]

The first determination of quantum is Number. Number is made up of a One or Many Ones—which, as quanta, are called Units—each of which is identical to the other. This identity in the Unit constitutes the Continuity of Number. However, a Number is also a specific Determinate Being that encloses an aggregate of Units while excluding from itself other such aggregates. This, the Amount, is the moment of Discreteness within Number. Both Qualitative and Quantitative Determinate Being have Limits that demarcate the boundary between their affirmative presence and their negation, but in the former the Limit determines its Being to be of a specific Quality unique to itself, whereas in the latter, made up as it is of homogeneous Units that remain identical to each other no matter which side of the Limit they fall upon, the Limit serves only to enclose a specific Amount of Units, e.g., a hundred, and to distinguish it from other such aggregates.[55]

EXAMPLE: The species of calculationcounting, addition/subtraction, multiplication/division, powers/roots—are the different modes of bringing Numbers into relation with e

Taken in its immediacy, a Number is an Extensive Magnitude, that is, a collection of a certain Amount of self-same Units. These Units, say ten or twenty of them, are the sublated moments of the Extensive Magnitudes ten or twenty. However, the Number ten or twenty, though made up of Many, is also a self-determining One, independent of other Numbers for its determination. Taken in this way, ten or twenty (a) differentiates itself from Extensive Magnitude and becomes an Intensive Magnitude, which is expressed as the tenth or twentieth Degree. Just as the One was completely indifferent to the other Ones of the Many yet depended on them for its existence, each Degree is indifferent to every other Degree, yet they are externally related to one another in ascending or descending flow through a scale of Degrees.[58]

Although thus differentiated from each other, Extensive and Intensive magnitude are essentially (b) the same. "[T]hey are only distinguished by the one having amount within itself and the other having amount outside itself." It is at this point that the moment of the Something reasserts itself having remained implicit over the course of the development of Quantity. This Something, which reappears when the negation between Extensive and Intensive Magnitude is itself negated, is the re-emergence of Quality within the dialectic of Quantity.[59]

EXAMPLE: Weight exerts a certain pressure which is its Intensive Magnitude. This pressure, however, can be measured Extensively, in pounds, kilograms, etc. Heat or cold can be Qualitatively experienced as different Degrees of temperature, but can also be Extensively measured in a thermometer. High and low Intensities of notes are the results of a greater or smaller Amount of vibrations per unit of time. Finally, "in the spiritual sphere, high intensity of character, of talent or genius, is bound up with a correspondingly far-reaching reality in the outer world, is of widespread influence, touching the real world at many points."[60]

In the realm of Quantity, the relationship between Something and Other lacked any mutual Qualitative Determinateness. A One could only relate to another One identical to itself. Now, however, that Qualitative Determinateness has returned, the Quantum loses its simple self-relation and can relate to itself only through a Qualitative Other that is beyond itself. This Other is another Quantum, of a greater or lesser Amount, which, in turn, immediately points beyond itself to yet an Other Quantum ad infinitum. This is what constitutes the self-propelled (c) Alteration of Quantum.[61]