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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]<

Now that Many Ones have been posited out of their Repulsion from the One, their original Oneness reasserts itself and their Repulsion passes over to (b) Attraction. Attraction presupposes Repulsion: for the Many to be Attracted by the One, they must have at first been Repulsed by it.[46]

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]

C. Quantitative InfinityAlthough 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]

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]

C. Quantitative Infinity

Although a particular Quantum, of its own inner necessity, points beyond itself, this beyond is necessarily an Other Quantum. This fact, that Quantum eternally repulses itself, yet equally eternally remains Quantum, demonstrates the (a) Notion of Quantitative Infinity, which is the self-related, affirmative opposition between Finitude and Infinity that lies within it.[62] This irresolvable self-contradiction within Quantum yields (b) the Quantitative Infinite Progress. This progress can take place in one of two directions, the greater or the smaller, giving us the so-called "infinitely great" or "infinitely small." That these "infinites" are each the Spurious

Although a particular Quantum, of its own inner necessity, points beyond itself, this beyond is necessarily an Other Quantum. This fact, that Quantum eternally repulses itself, yet equally eternally remains Quantum, demonstrates the (a) Notion of Quantitative Infinity, which is the self-related, affirmative opposition between Finitude and Infinity that lies within it.[62] This irresolvable self-contradiction within Quantum yields (b) the Quantitative Infinite Progress. This progress can take place in one of two directions, the greater or the smaller, giving us the so-called "infinitely great" or "infinitely small." That these "infinites" are each the Spurious Quantitative Infinite is evident in the fact that "great" and "small" designate Quanta, whereas the Infinite by definition is not a Quantum.[63]

EXAMPLE: Hegel here gives several examples of the appearance of the Spurious Quantitative Infinite in philosophy, namely in Kant’s notion of the sublime and his categorical imperative, as well as Ficht

The Quantitative Infinite negates Quantum, and Quantum in turn negates Infinity. As occurs so often in The Science of Logic, a negation that is itself negated produces a new affirmative standpoint, the formerly negated terms having become the unified moments thereof. This standpoint is (c) the Infinity of Quantum from where it is seen that Infinity, initially the absolute Other of Quantum, essentially belongs to it and in fact determines it as a particular Quality alongside all the other Determinate Beings that had long since been sublated. This particular Quality which distinguishes Quantum from any other Qualitatively Determined Being is in fact the total lack of explicit self-determinateness that differentiated Quantity from Quality in the first place. The repulsion of Quantum from itself out into the beyond of Infinity, is actually a gesture back towards the world of Qualitative Determination, thus bridging once again the two worlds. This gesture is made explicit in the Quantitative Ratio, where two Quanta are brought into relationship with one another in such a way that neither one in itself is self-determined, but in relating to each other, they Qualitatively determine something beyond themselves, e.g., a line or a curve.[65]

EXAMPLE: Hegel here engages in a lengthy survey of the history and development of the Differential and Integral Calculus, citing the works of Cavalieri, Descartes, Fermat, Barrow, Newton, Leibniz, Euler, Lagrange, Landen, and Carnot. His main point of concern is the compulsion of mathematicians to neglect the infinitesimal differences that result from calculus equations in order to arrive at a coherent result. The inexactitude of this method of procedure results, says Hegel, prim

A. The Direct Ratio

A ratio, such as x:y, is a Direct Ratio if both terms of the ratio are delimited by a single Quantum, a constant, k (what Hegel calls in the language of his day the "exponent" of the ratio),

In the Direct Ratio, the previously sublated Quantitative moments of Amount and Unit are retrieved and brought into immediate relation with each other. One side of the ratio, y, is a certain Amount relative to the other side, x, which serves as the Unit whereby this Amount is measured. If the constant is given, then the Quantum on any one side of the ratio could be any Number, and the Number on the other side will automatically be determined. Therefore, the first Number of the ratio completely loses its independent significance and only functions as a determinate Quantum in relation to an other. Formerly, any single Number could simultaneously denote either an Amount or a Unit; now, it must serve exclusively as the one or the other in relation to another Number serving as the opposite. The constant would seem to bring these moments back into unity with each other, but in actuality, it too can serve only as either Amount or Unit. If x is Unit and y Amount, then k is the Amount of such Units,

A ratio, such as x:y, is a Direct Ratio if both terms of the ratio are delimited by a single Quantum, a constant, k (what Hegel calls in the language of his day the "exponent" of the ratio),

In the Direct Ratio, the previously sublated Quantitative moments of Amount and Unit are retrieved and brought into immediate relation with each other. One side of the ratio, y, is a certain Amount relative to the other side, x, which serves as the Unit whereby this Amount is measured. If the constant is given, then the Quantum on any one side of the ratio could be any Number, and the Number on the other side will automatically be determined. Therefore, the first Number of the ratio completely loses its independent significance and only functions as a determinate Quantum in relation to an other. Formerly, any single Number could simultaneously denote either an Amount or a Unit; now, it must serve exclusively as the one or the other in relation to another Number serving as the opposite. The constant would seem to bring these moments back into unity with each other, but in actuality, it too can serve only as either Amount or Unit. If x is Unit and y Amount, then k is the Amount of such Units,

if x is Amount, then k is the Unit, the amount of which, y<

if x is Amount, then k is the Unit, the amount of which, y, determines it,

[67]

B. Inverse Ratio

The Inverse Ratio is a ratio, x:y, in which the relation between both sides is expressed in a constant which is their product, i.e.,

B. Inverse Ratio

The Inverse Ratio is a ratio, x:y, in which the relation between both sides is expressed in a constant which is their product, i.e.,

or

Whereas formerly with the Direct Ratio, the quotient between the two terms was fixed, in the Inverse Ratio it becomes alterable. Because the Inverse Ratio confines within itself many Direct Ratios, the constant of the former displays itself not merely as a Quantitative, but also as a Qualitative Limit. It is therefore a Qualitative Quantum. The Spurious Infinity/True Infinity dialectic again makes an appearance here as either term of the ratio is only capable of infinitely approximating the ratio's constant, the one increasing in proportion to a decrease in the other, but never actually reaching it (neither x nor y may equal zero). The constant is nonetheless present as a simple Quantum, and is not an eternal beyond, making its self-mediation through the two terms of the ratio an example of True Infinity.[68]

C. The Ratio of Powers

The Ratio of Powers takes the following form:

C. The Ratio of Powers

The Ratio of Powers takes the following form:

It is in this form of the Ratio, says Hegel, that "quantum has reached its Notion and has completely realized it." In the Direct and Inverse Ratios, the relation between the constant and its variables was not continuous, the former only being a fixed proportionality between them, and the latter relating itself to them only negatively. With the Ratio of Powers, however, this relationship is not simply one of external limitation, but, as a Quantum brought into relationship with itself through the power, it is self-determining Limit. This self-determination constitutes the Quality of the Quantum, and finally demonstrates the full significance of the essential identity of Quality and Quantity. Originally, Quantity differentiated itself from Quality in that it was indifferent to what was external to it, that which it quantified. Now however, in the Ratio of Powers, what it relates itself to externally is determined by its own self, and that which relates externally to its own self has long since been defined as Quality. "But quantity is not only a quality; it is the truth of quality itself." Quantum, having sublated the moment of Quantity that originally defined it and returned to Quality, is now what it is in its truth: Measure.[69]

Measure

Specific Quantity

A. The Specific Quantum
A. The Relation of Self-Subsistent Measures

Real Measure gives us a new standpoint external to the different Measures being brought into relation with each other, this relation now designating the independent existence of an actual physical Something. This Something gains its Qualitative determination from the Quantitative (a) combination between two Measures immanent in it, i.e., volume and weight. One designates an inner Quality, in this case weight; the other designates an external Quality, in this case volume, the amount of space it takes up. Their combination gives us the ratio of weight to volume which is its specific gravity. The constant that results from this ratio is the inner characteristic Real Measure of the thing in question, but, taking the form as it does of a mere number, a Quantum, this constant is likewise subject to alteration, i.e., addition, subtraction, etc. Unlike mere Quantum, however, the Real Measure of a thing is inwardly determined, and so preserves itself somewhat in alteration. If two material things are combined, the dual Measures of the one are added to those of the other. The degree to which they exhibit self-preservation is registered in the internal Measure—weight in this case—which ends up being equal, after combination, to the sum of the original two Measures; the degree to which they exhibit Qualitative alteration is registered in the external Measure—space in this case—which does not necessarily result in a sum equal to its parts, but often in the case of material substances exhibits a diminution in overall volume.[77]

If we adopt the constant of one specific Real Measure as our Unit, the constants of other Real Measures can be brought into relation to it as Amounts in a (b) series of Measure relations. Since it is arbitrary which one Real Measure in such a series will serve as the Unit, there are as many incommensurable series of Measure relations as there are individual Real Measures. However, when two Real Measures, which are themselves ratios, are combined, the result is a new ratio of those ratios, itself designated by a constant in the form of a Quantum. If this constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator. Since each Real Measure within a series forms such a constant with every other member in that series, any individual series in which a particular Real Measure serves as the Unit can be made commensurable with any other series with a different Real Measure as Unit. Since it is a thing’s Real Measure that determines its specific Quality, and since that Real Measure is in turn derived from the Quantitative relation it has with other Real Measures in the form of a series of constants, it would appear that, as in Determinate Being above, Quality is only relative and externally determined. However, as we have seen, a Real Measure also has an internal relation that gives it a self-subsistence that is indifferent to any external relation. Therefore, the series of Quantitative relationships between these Real Measures only determines the (c) Elective Affinity between their different Qualities, but not these Qualities themselves.[78]Real Measure gives us a new standpoint external to the different Measures being brought into relation with each other, this relation now designating the independent existence of an actual physical Something. This Something gains its Qualitative determination from the Quantitative (a) combination between two Measures immanent in it, i.e., volume and weight. One designates an inner Quality, in this case weight; the other designates an external Quality, in this case volume, the amount of space it takes up. Their combination gives us the ratio of weight to volume which is its specific gravity. The constant that results from this ratio is the inner characteristic Real Measure of the thing in question, but, taking the form as it does of a mere number, a Quantum, this constant is likewise subject to alteration, i.e., addition, subtraction, etc. Unlike mere Quantum, however, the Real Measure of a thing is inwardly determined, and so preserves itself somewhat in alteration. If two material things are combined, the dual Measures of the one are added to those of the other. The degree to which they exhibit self-preservation is registered in the internal Measure—weight in this case—which ends up being equal, after combination, to the sum of the original two Measures; the degree to which they exhibit Qualitative alteration is registered in the external Measure—space in this case—which does not necessarily result in a sum equal to its parts, but often in the case of material substances exhibits a diminution in overall volume.[77]

If we adopt the constant of one specific Real Measure as our Unit, the constants of other Real Measures can be brought into relation to it as Amounts in a (b) series of Measure relations. Since it is arbitrary which one Real Measure in such a series will serve as the Unit, there are as many incommensurable series of Measure relations as there are individual Real Measures. However, when two Real Measures, which are themselves ratios, are combined, the result is a new ratio of those ratios, itself designated by a constant in the form of a Quantum. If this constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with ea

If we adopt the constant of one specific Real Measure as our Unit, the constants of other Real Measures can be brought into relation to it as Amounts in a (b) series of Measure relations. Since it is arbitrary which one Real Measure in such a series will serve as the Unit, there are as many incommensurable series of Measure relations as there are individual Real Measures. However, when two Real Measures, which are themselves ratios, are combined, the result is a new ratio of those ratios, itself designated by a constant in the form of a Quantum. If this constant is adopted as the Unit, instead of an individual Real Measure, then what were two incommensurable series are now made commensurable with each other in a common denominator. Since each Real Measure within a series forms such a constant with every other member in that series, any individual series in which a particular Real Measure serves as the Unit can be made commensurable with any other series with a different Real Measure as Unit. Since it is a thing’s Real Measure that determines its specific Quality, and since that Real Measure is in turn derived from the Quantitative relation it has with other Real Measures in the form of a series of constants, it would appear that, as in Determinate Being above, Quality is only relative and externally determined. However, as we have seen, a Real Measure also has an internal relation that gives it a self-subsistence that is indifferent to any external relation. Therefore, the series of Quantitative relationships between these Real Measures only determines the (c) Elective Affinity between their different Qualities, but not these Qualities themselves.[78]

The Quantity/Quality dialectic manifests itself in the realm of Elective Affinity in that a Real Measure within in a series will not necessarily resonate Qualitatively with those in another series even if they bear a proportional Quantitative relationship. In fact, the specific Quality of a particular Real Measure is in part registered by the other Real Measures it has a special Affinity for, that is, how it responds to Quantitative Alteration. It is the Intensive side of Quantity (see above) such as it relates to specific Real Measures that determines its Qualitative behaviour when subject to changes in Extensive Quantity.[79]

The relation of Elective Affinity is an external relation between two Real Measures that is determined by their Quantitative aspects. In and of themselves, each Real Measure retains its Qualitative indifference to all others, even those it has Affinity for. Real Measures, however, are also subject to internal alteration akin to what has already been discussed in "Measure" above, i.e., that its Quality can be maintained only within a certain Quantitative range beyond which it undergoes a sudden "leap" into another Quality. These different Qualities form Nodes on a line of gradual Quantitative increase or decrease.[81]

EXAMPLE: Natural numbers consist of a series of numbers that gradually increase by one in perpetual succession. However, some of these numbers relate in specific ways to others, being their multiple, power or root, etc., and thus constitute "Nodes." Transition from the liquid to the frozen state in water does not occur gradually with a diminution of temperature, but all of a sudden at 0°C. Finally, the "state has its own measure of magnitude and when this is exceeded this mere change in size renders it liable to instability and disruption under that same constitution which was its good fortune and its strength before its expansion." Thus, contrary to Aristotle’s doctrine that natura non facit saltum, according to Hegel nature does make leaps.[82]
C. The Measureless

A. Absolute Indifference

This Substrate, as what persists through the succession of States, is in a relation of Absolute Indifference to every particular determination—be it of quality, quantity or measure—that it contains. It is merely the abstract expression of the unity that underlies their totality.[84]

B. Indifference as Inverse Ratio of its Factors

Taken in its immediacy, this Indifference is simply the result of all the different determinatenesses that emerge within it. It itself does not determine its own inner fluctuations, i.e., is not self-determining. However, in accordance with the measure relations developed so far, each of its moments are in reciprocal, quantitatively determined ratios with one another. Formerly, from the standpoint of Quality, a sufficient Quantitative increase or decrease would result in a sudden transition from one Quality to another. Now, with Absolute Indifference as our standpoint, every possible Qualitative determination is already implicitly related to every other by means of a Quantitative ratio. Every Quality is connected to, and in equilibrium with, its corresponding other. It is therefore no

A. Absolute Indifference

This Substrate, as what persists through the succession of States, is in a relation of Absolute Indifference to every particular determination—be it of quality, quantity or measure—that it contains. It is merely the abstract expression of the unity that underlies their totality.[84]

B. Indifference as Inverse Ratio of its Factors

Taken in its immediacy, this Indifference is simply the result of all the different determinatenesses that emerge within it. It itself does not determine its own inner fluctuations, i.e., is not self-determining. However, in accordance with the measure relations developed so far, each of its moments are in reciprocal, quantitatively determined ratios with one another. Formerly, from the standpoint of Quality, a sufficient Quantitative increase or decrease would result in a sudden transition from one Quality to another. Now, with Absolute Indifference as our standpoint, every possible Qualitative determination is already implicitly related to every other by means of a Quantitative ratio. Every Quality is connected to, and in equilibrium with, its corresponding other. It is therefore no longer meaningful to say that something can have "more" or "less" of one Quality than another as if each Quality were absolutely distinct from each other. Whatever Quality there is "more" of in one thing than another can be equally said to be a "less" of whatever Quality exists in its stead in the other, i.e., there is an Inverse Ratio of their Factors. So, with a so-called "Quantitative" change, "one factor becomes preponderant as the other diminishes with accelerated velocity and is overpowered by the first, which therefore constitutes itself the sole self-subsistent Quality." The two Qualities are no longer distinct, mutually exclusive determinations, but together comprise a single whole.[85]

C. Transition into Essence

Strictly within the realm of Being, the underlying unity behind all its determinations necessarily stands externally, and in contradiction, to those determinations themselves. The transition to Essence occurs when these determinations reabsorb this unity back into themselves, i.e., they sublate it. The inherent contradiction between difference and unity is resolved when the latter is posited as the negative of the former. So, from henceforth it cannot be said that they simply emerge within the Substrate of Indifference, but that this "substrate" itself is their very own living self-relation. In other words, the differences between all the determinations of Being, namely the Quantitative difference and the inverse ratio of factors, are no longer self-subsistent, but in fact are mere moments in the expression of the implicit unity that rules them and, themselves, "are only through their repulsion from themselves." Being has finally determined itself to no longer be simply affirmative Being, i.e., that which characterized Being as Being in the first place, but as a relation with itself, as Being-With-Self, or Essence.[87]

Objective Logic: Doctrine of Essence

So in its relation to Essence, Being has lost its being, has become Illusory. All the determinations of Being covered in the first third of the Science of Logic are no longer self-subsistent, but only "are" at all as negations of Essence. This total dependence on Essence means that there is nothing any longer in Being itself upon which any of its own determinations can be based, i.e., there is no longer any mediation within Being. This role is entirely taken up by Essence which is pure mediation relative to Illusory Being's pure immediacy. Hegel claims this is the mode of thought that corresponds to ancient skepticism as well as the "modern" idealism of Leibniz, Kant, and Fichte. Illusory Being, though not Essence itself, nevertheless belongs enti

So in its relation to Essence, Being has lost its being, has become Illusory. All the determinations of Being covered in the first third of the Science of Logic are no longer self-subsistent, but only "are" at all as negations of Essence. This total dependence on Essence means that there is nothing any longer in Being itself upon which any of its own determinations can be based, i.e., there is no longer any mediation within Being. This role is entirely taken up by Essence which is pure mediation relative to Illusory Being's pure immediacy. Hegel claims this is the mode of thought that corresponds to ancient skepticism as well as the "modern" idealism of Leibniz, Kant, and Fichte. Illusory Being, though not Essence itself, nevertheless belongs entirely to Essence. It is that through which Essence generates itself as what it is, namely, the purely negative as regards Being. The constant appearance and disappearance of the empty manifestations of Illusory Being can now be seen as Essence's own self-generating movement, its own Reflection.[89]

C. Reflection

Reflectio

Reflection in the sphere of Essence corresponds to Becoming in the sphere of Being. However, in Being, this movement was between a positive—pure Being—and a negative—pure Nothingness. Here however, the two terms are Illusory Being and Essence. Illusory Being, as has already been established, is a nullity, nothingness. Essence, by definition, is non-being, absolute negativity. So Reflection, the movement between them, is the movement of nothing to nothing and so back to itself. Both these terms, in being absolutely negative, are identical to one another: Essence is Illusory Being and Illusory Being is Essence. They are, however, also relatively negative, in that the one is, by definition, not what the other is. This contradiction manifests in Essence in that it presupposes or posits, on its own, that which it immediately differentiates itself from: Illusory Being. This absolute recoil upon itself is Essence as a) Positing Reflection.[90]

The next determination of Reflection, b) External Reflection, shifts the emphasis from the absolute negativity, or nothingness, in which the posited Illusory Being and its positing Essence find their identity, to the relative negativity upon which their opposition is based. Although it "know

The next determination of Reflection, b) External Reflection, shifts the emphasis from the absolute negativity, or nothingness, in which the posited Illusory Being and its positing Essence find their identity, to the relative negativity upon which their opposition is based. Although it "knows" that the Illusory Being it finds immediately before it has been posited by none other than itself, External Reflection nevertheless regards this Being as something external to it from which it returns to itself. What concerns it, therefore, is no longer the act of positing itself, but the specific determinateness of that which is posited, since it is this and nothing else that establishes its externality in the first place.[91]

With Positing Reflection, the Illusory Being that was posited was only a means for Essence's mediation with itself. Now, with c) Determining Reflection, not only is the moment of Illusory Being foregrounded again, but the specific determinations of this Being come into play as well. The absolute nothingness of Essence forms the background to any and all of the determinations it chooses to Reflect itself off of. These Determinations of Reflection—formerly known as Determinate Beings when they were in the realm of Quality (see above)—therefore share in the nullity that undergirds them. This nullity actually serves to fix them eternally in their specific determination and preserve them from Alteration, because they no longer relate to each other externally as Others to one another, but internally as equals in Essence's nothingness. All the possible determinations of Being are thus preserved negatively in Essence as free Essentialities "floating in the void without attracting or repelling one another."[93]

The Essentialities

A. Identity

In the sphere of Being, above, Qualities were determined only relatively. What something was, was determined entirely by that which differentiated it from what it wasn't, i.e., it was negatively determined by its Other. Here in Essence however, the negativity nece

In the sphere of Being, above, Qualities were determined only relatively. What something was, was determined entirely by that which differentiated it from what it wasn't, i.e., it was negatively determined by its Other. Here in Essence however, the negativity necessary to establish determination is no longer directed outward, towards an Other, but inward. This is because Essence is in itself absolute negativity, nothingness, and it follows that any determination made therein will share in this negativity and itself be essentially nothing. Therefore, an Essentiality, as opposed to a Quality, is essentially the same as its other—they are both essentially nothing. As self-determining, whatever determination Essence takes on is freely self-generated, it "is what it is," and so is simple Identity-with-self. This absolute Identity rests on the absolute negativity that unites Essence with its Essentialities. However, if we recall from "Reflection" above, Essence is also negative relative to its Essentialities. The Essentialities are determined Essence and, as we know, determination by definition involves negation. Therefore, while the Essentialities are absolutely Identical in their shared nothingness, their absolute negativity, they are equally absolutely Different in their determinations, their relative negativity.[88]

EXAMPLE: Here Hegel embarks on a critique on one of the most basic assumptions of classical logic, the Law of Identity, usually expressed as A=A. Although superficially the immediate truth of this proposition cannot be denied, further reflection reveals that nothing absolute can be derived from it. For it can only hold true provisionally insofar as A is different from not-A. The Law of Identity, the purpose of which is to draw an absolute distinction between identity and difference, therefore contains difference as a necessary moment implicitly within

The Difference of Reflection must be distinguished from the Otherness of Determinate Being. The latter is a relative relation between two Determinate Beings whereby they distinguish themselves one from another and in turn determine themselves as specific Beings based on this distinction. In the sphere of Reflection, however, any determination posited by Essence is, as a determination, necessarily Different from the absolute negativity that is its Essence. The Difference of Reflection, therefore, is different in relation to its own self, and so it is not relative but a) Absolute Difference.[95]

Absolute Difference contains both Difference and Identity within it as moments just as, conversely, Identity contains itself and Difference as its moments. The relation between Identity and Difference takes the form of one term reflecting off the other back into itself: Difference off of Identity back into itself or Identity off of Difference back into itself. "This is to be considered as the essential nature of reflection and as the specific, original ground of all activity and self-movement." Because each of these two moments are self-related in this way, they do not mutually determine one another. Instead, they are indifferent to one another. Therefore, Difference is b) Diversity.[96]

Yet another duality emerges at this point. As moments, Identity and Difference require each other and are bound up with one another: one term could not exist without the other. But at the same time, they absolutely negate one another and only are at all by virtue of their mutual negation of each other. So if we are an external party concerned with a specific determination of Identity, the moment of Difference, though intrinsic to the fact of this Identity, is very far from our minds. That it is Different from other things does not concern us or it at the moment: it is implicit. The cat

Absolute Difference contains both Difference and Identity within it as moments just as, conversely, Identity contains itself and Difference as its moments. The relation between Identity and Difference takes the form of one term reflecting off the other back into itself: Difference off of Identity back into itself or Identity off of Difference back into itself. "This is to be considered as the essential nature of reflection and as the specific, original ground of all activity and self-movement." Because each of these two moments are self-related in this way, they do not mutually determine one another. Instead, they are indifferent to one another. Therefore, Difference is b) Diversity.[96]

Yet another duality emerges at this point. As moments, Identity and Difference require each other and are bound up with one another: one term could not exist without the other. But at the same time, they absolutely negate one another and only are at all by virtue of their mutual negation of each other. So if we are an external party concerned with a specific determination of Identity, the moment of Difference, though intrinsic to the fact of this Identity, is very far from our minds. That it is Different from other things does not concern us or it at the moment: it is implicit. The category of Identity itself, however, is not determined by whatever it is that it is applied to, but by its reflection off of Difference back into itself. So if, from our external standpoint, that which comprises the Identity of something cannot be established without a Comparison of Likeness with something else. What specifically is Different about something can similarly only be determined by a Comparison of Unlikeness between it and something else. Like and Unlike, being external to the things they refer to, can each be equally applied to one and the same Determination. Things are Like each other insofar as they are not Unlike each other and vice versa: the two terms are mutually exclusive insofar as they refer to the same thing, but in themselves, apart from the things they refer to, there is no difference between them. Since any aspect may be externally selected to demonstrate the Likeness and Unlikeness of any two things, these terms really only refer, not intrinsically to their objects, but to themselves only and, as likewise self-referred, are indistinguishable from each other independent of their objects. Likeness and Unlikeness are both in fact only Likeness. The internal union that existed between Identity and Difference which is merely implicit to the outside observer, therefore emerges again in external reflection between Likeness and Unlikeness, and thus overcomes the external Diversity that held Identity and Difference indifferently apart from each other. This reconstituted unity that thus comes out of Diversity is c) Opposition.

The hidden, internal unity that bound the two moments of Identity and Difference together despite their apparent mutual indifference becomes explicit once they are mediated from the outside by Likeness and Unlikeness. They are no longer indifferent to one another but relate to each other intrinsically as Opposites. A given determination, as seen from its Positive aspect, is Likeness reflected back onto itself off of Unlikeness. Seen from its Negative aspect, it is Unlikeness reflected back onto itself off of Likeness. These two aspects, however, are the constitutive moments of one and the same overall determination. Although as a whole, the Positive and Negative comprise a unity, the Positive on its own is also a self-subsistent being, as is the Negative on its own. Because of this, the Negative can equally well be regarded as positive and vice versa. They are not Positive and Negative merely in comparison with one another, but each contains within itself the other as an essential element of its own determination.[97]

Both the Positive and the Negative are self-subsistent determinations: each side can stand on its own without explicit reference to the other. At the same time, however, they completely exclude one another and in fact rely on this exclusion for their self-subsistence. In that sense, the Positive itself is constituted by the very Negative that it excludes; it is based on this exclusion and thus contains what it excludes it within itself. Ditto the Negative. This inclusion of what is excluded is what constitutes the Positive and the Negative as what they are. This is Contradiction. (In the Negative, this self- contradiction is explicit, but it is no less the nature of the Positive.)

So, similar to Becoming above, the Positive and the Negative immediately transition the one into the other: the Positive includes the Negative which immediately excludes the Positive; the resulting Negative however also includes the Positive which in turn excludes the Negative and so on ad infinitum. This mutual inclusion and exclusion cancels out the both of them. This results in nullity. Out of this nullity, the unity of the two sides is restored in the following way. As stated above, both the Positive and the Negative are each self-subsistent on their own, but it is a self-subsistence that is immediately obliterated by the other's. Now, however, arising out of their mutual destruction comes a self-subsistence that is common to the both of them. Instead of merely excluding each other, each side sublates the other, meaning that whatever is posited as Positive is at the same time equally the Negative of its Negative, and whatever is Negative is So, similar to Becoming above, the Positive and the Negative immediately transition the one into the other: the Positive includes the Negative which immediately excludes the Positive; the resulting Negative however also includes the Positive which in turn excludes the Negative and so on ad infinitum. This mutual inclusion and exclusion cancels out the both of them. This results in nullity. Out of this nullity, the unity of the two sides is restored in the following way. As stated above, both the Positive and the Negative are each self-subsistent on their own, but it is a self-subsistence that is immediately obliterated by the other's. Now, however, arising out of their mutual destruction comes a self-subsistence that is common to the both of them. Instead of merely excluding each other, each side sublates the other, meaning that whatever is posited as Positive is at the same time equally the Negative of its Negative, and whatever is Negative is at the same time equally a Positive. The two sides posit and negate each other simultaneously, and in doing so they no longer destroy each other, but preserve one another. Therefore, the Positive and Negative are in fact the same and this, their sameness—which nevertheless includes their Contradiction—is their Essence as Ground.[99]

Simply put ground is the "essence of essence," which for Hegel arguably means the lowest, broadest rung in his ontology because ground appears to fundamentally support his system. Hegel says, for example, that ground is "that from which phenomena is understood." Within ground Hegel brings together such basic constituents of reality as form, matter, essence, content, relation, and condition. The chapter on ground concludes by describing how these elements, properly conditioned, ultimately will bring a fact into existence (a segue to the subsequent chapter on existence).

Hegel considers form to be the focal point of "absolute ground," saying that form is the "completed whole of reflection." Broken into components, form taken together with essence gives us "a substrate for the ground relation" (Hegel seems to mean relation in a quasi-universal sense). When we combine form with matter the result is "determinate matter." Hegel thinks that matter itself "cannot be seen": only a determination of matter resulting from a specific form can be seen. Thus the only way to see matter is by combining matter with form (given a literal reading of his text). Finally, content is the unity of form and determinate matter. Content is what we perceive.

"Determinate ground" consists of "formal ground," "real ground," and "complete ground." Remember with Hegel that when we classify something as determinate we are not referring to absolute abstractions (as in absolute ground, above) but now (with determinate ground) have some values attached to some variables—or to put it in Hegel's terminology, ground is now "posited and derived" with "determinate content."

In formal ground, Hegel seems to be referring to those causal explanations of some phenomena that make it what it is.

Hegel considers form to be the focal point of "absolute ground," saying that form is the "completed whole of reflection." Broken into components, form taken together with essence gives us "a substrate for the ground relation" (Hegel seems to mean relation in a quasi-universal sense). When we combine form with matter the result is "determinate matter." Hegel thinks that matter itself "cannot be seen": only a determination of matter resulting from a specific form can be seen. Thus the only way to see matter is by combining matter with form (given a literal reading of his text). Finally, content is the unity of form and determinate matter. Content is what we perceive.

"Determinate ground" consists of "formal ground," "real ground," and "complete ground." Remember with Hegel that when we classify something as determinate we are not referring to absolute abstractions (as in absolute ground, above) but now (with determinate ground) have some values attached to some variables—or to put it in Hegel's terminology, ground is now "posited and derived" with "determinate content."

In formal ground, Hegel seems to be referring to those causal explanations of some phenomena that make it what it is. In a (uncharacteristically) readable three paragraph remark, Hegel criticizes the misuse of formal grounds, claiming that the sciences are basically built upon empty tautologies. Centrifugal force, Hegel states as one of several examples drawn from the physical sciences, may be given as prime grounds (i.e. "explanation of") some phenomena, but we may later find upon critical examination that this phenomenon supposedly explained by centrifugal force is actually used to infer centrifugal force in the first place. Hegel characterizes this sort of reasoning as a "witch's circle" in which "phenomena and phantoms run riot."

Real ground is external and made up of two substrates, both directly applicable to content (which evidently is what we seem to perceive). The first is the relation between the ground and the grounded and the second substrate handles the diversity of content. As an example Hegel says that an official may hold an office for a variety of reasons—suitable connections, made an appearance on such and such occasion, and so forth. These various factors are the grounds for his holding office. It is real ground that serves to firstly make the connection between holding office and these reasons, and secondly to bind the various reasons, i.e. diverse content, together. Hegel points out that "the door is wide open" to infinite determinations that are external to the thing itself (recall that real ground is external). Potentially any set of reasons could be given for an official to be holding office.

In complete ground, Hegel brings together formal and real ground, now saying that formal ground presupposes real ground and vice versa. Complete ground Hegel says is the "total ground-relation."

This "volume" is the third major piece within the Science of Logic. Here Hegel introduces his Notion within which he extends Kant's basic schemes of judgement and syllogism classification. Hegel shows that the true idea can only be based upon valid reasoning and objectivity.

Editions of Science of Logic