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[[File:Wissenshaft der logik.jpg|thumb|Title page of original 1816 publication]]
{{Hegelianism}}

[[Hegel]]'s work '''''The Science of Logic''''' ({{lang-de|Wissenschaft der Logik}}) outlined his vision of [[logic]], which is an ontology that incorporates the traditional Aristotelian [[syllogism]] as a sub-component rather than a basis. For Hegel, the most important achievement of [[German Idealism]], starting with [[Immanuel Kant|Kant]] and culminating in his own philosophy, was the demonstration that reality is shaped through and through by mind and, when properly understood, '''is''' mind. Thus ultimately the structures of thought and reality, subject and object, are identical. And 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. '''''The Science of Logic''''' is sometimes referred to as the ''Greater Logic'' to distinguish it from the condensed version of it he presented in what is called the ''Lesser Logic'', namely the Logic section of his ''Encyclopedia of the Philosophical Sciences''.

==Brief history of the book==
Hegel wrote 'The 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 a number of 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]]. ''The 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.” 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, ''un''philosophical consciousness.<ref>{{cite web|last=Hegel|first=G.W.F.|title=§ 35 - § 41|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_43|work=Hegel's Science of Logic|publisher=Allen & Unwin, 1969|accessdate=2 January 2012}}</ref>

The task of extinguishing this opposition within consciousness Hegel believed he had already accomplished in his book '''''[[Phenomenology of Spirit|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.”<ref>{{cite web|last=ibid|title=§ 51|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_43|accessdate=2 January 2012}}</ref>   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.”<ref>{{cite web|last=ibid|title=§ 50 - § 53|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_43|accessdate=2 January 2012}}</ref>  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, [[dialectic]]al 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.<ref>{{cite web|last=ibid|title=§ 78 - § 80|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlintro.htm#HL1_59|accessdate=2 January 2012}}</ref>  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.”<ref>{{cite web|last=ibid|title=§ 1814|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlabsolu.htm#HL3_824|accessdate=2 January 2012}}</ref>

==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 '''''[[Phenomenology of Spirit|Phänomenologie des Geistes]]''''' (1807).<ref>{{cite web|last=ibid|title=§ 93|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbegin.htm#HL1_79|accessdate=26 December 2011}}</ref> 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."<ref name="Science of Logic&nbsp;— web">{{cite web|last=ibid|title=§ 132|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbegin.htm#HL1_79|accessdate=26 December 2011}}</ref>

: EXAMPLE: Hegel claims that the [[Eleatics|Eleatic philosopher]] [[Parmenides]] was the person who "first enunciated the simple thought of pure being as the absolute and sole truth."<ref name="science of logic web">{{cite web|last=ibid|title=§ 136|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl083.htm#HL1_83|accessdate=26 December 2011}}</ref>

'''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.<ref>{{cite web|last=ibid|title=§ 133|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_82|accessdate=26 December 2011}}</ref>

: EXAMPLE: in Hegel's estimation, Pure Nothing is the absolute principle "in the oriental systems, principally in Buddhism."<ref name="science of logic web"/>

'''C. Becoming'''

Pure Being and Pure Nothing are the same, and yet absolutely distinct from each other. This contradiction is resolved by their immediate vanishing, one into the other. The resultant movement, called ''Becoming'', takes the form of reciprocal ''Coming-to-Be'' and ''Ceasing-to-Be''.<ref>{{cite web|last=ibid|title=§ 179|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl083.htm#HL1_105b|accessdate=26 December 2011}}</ref>

: EXAMPLE: Hegel borrows Kant's example of the "hundred dollars" ['''''[[Critique of Pure Reason]]''''' (1787)] to emphasize that the unity of Being and Nothing in Becoming only applies when they are taken in their absolute purity as abstractions.  It is of course not a matter of indifference to one's fortune if $100 ''is'' or ''is not'', but this is only meaningful if it is presupposed that the one whose fortune it might or might not be, already ''is'', i.e., the $100's being or not must be referenced to an other's. This, then, cannot be Pure Being which by definition has no reference outwards.<ref>{{cite web|last=ibid|title=§ 140-§ 146|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl083.htm#HL1_83|accessdate=26 December 2011}}</ref>  [[Heraclitus]] is cited as the first philosopher to think in terms of Becoming.<ref name="science of logic web"/>

====Determinate Being====

=====A. Determinate Being as Such=====

The transition between Becoming and '''(a) ''Determinate Being as Such''''' is accomplished by means of ''[[Aufheben|sublation]]''. This term, the traditional English translation of the German word ''aufheben'', means  to preserve, to maintain, but also to cease, to put an end to. Hegel claims that it is “one of the most important notions in philosophy.” Being and Nothing were complete opposites whose inner unity needed to be expressed, or ''mediated'', by a third term: Becoming. Once having been accomplished through mediation, their unity then becomes ''immediate''. Their opposition, still extant in Becoming, has been “put an end to.” From the newly acquired standpoint of immediacy, Becoming becomes Determinate Being as Such, within which Being and Nothing are no longer discrete terms, but necessarily linked ''moments'' that it has “preserved” within itself. Sublation, then, is the ending of a logical process, yet at the same time it is its beginning again from a new point of view.<ref>{{cite web|last=ibid|title=§ 184 - § 187|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>

So, ''as'' moments of Determinate Being, Being and Nothing take on new characteristics as aspects of '''(b) ''Quality'''''. Being becomes emphasized, and, as Quality, is ''Reality''; Nothing, or ''Non-Being'', is concealed in Being’s background serving only delimit it as a specific Quality distinct from others, and, in so doing, is ''Negation in General'', i.e., Quality in the form of a deficiency. Quality, then, comprises both what a Determinate Being ''is'' and ''is not'', viz., that which makes it determinate in the first place.<ref>{{cite web|last=ibid|title=§ 195 - § 198|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref> Within Quality, however, Reality and Negation are still distinct from one another, are still ''mediated'', just like Being and Nothing were in Becoming. Taken in their ''unity'', that is, in their immediacy as, again, sublated, they are now only moments of '''(c) ''Something'''''.<ref>{{cite web|last=ibid|title=§ 208 - § 209|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>

: EXAMPLE: Hegel contrasts his logically derived notion of Reality from the earlier metaphysical one present in the [[ontological argument|ontological “proof” of God’s existence]], specifically [[Leibniz]]’s formulation of it. In this theory, God was held to be the sum-total of all realities. These realities are taken to be “perfections,” their totality therefore comprising the most perfect being imaginable: God. Speculative logic, however, shows that Reality is inextricably bound up with its own negation, and so any grand total of these realities would not result in something strictly positive, e.g., God, but would inevitably retain, to an equal degree, the negation of all these realities. The mere addition of realities to each other, then, would not in any way alter their principle, and so the sum of all realities would be no more or less than what each of them already was: a Reality and its Negation.<ref>{{cite web|last=ibid|title=§ 201 - § 202|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>

Something is the first instance in '''''The Science of Logic''''' of the “negation of the negation”. The first negation, Negation in General, is simply what a Determinate Being is ''not''. Hegel calls this “abstract negation”. When this negation itself is negated, which is called “absolute negation,” what a Determinate Being ''is'', is no longer dependent on what it is ''not'' for its own determination, but becomes an actual particular Something in its own right: a ''Being-Within-Self''. Its negation, what it is not, is now “cut off” from it and becomes another Something, which, from the first Something’s point of view, is an ''Other'' in general. Finally, just as Becoming mediated between Being and Nothing, ''Alteration'' is now the mediator between Something and Other.<ref>{{cite web|last=ibid|title=§ 210 - § 212|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_106b|accessdate=12 January 2012}}</ref>

=====B. Finitude=====

'''(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.<ref>{{cite web|last=ibid|title=§ 219 - § 224|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> (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.)<ref>{{cite web|last=ibid|title=§ 227|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

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''''';<ref>{{cite web|last=ibid|title=§ 231|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> what it is in ''relation'' to an Other is its '''''Constitution'''''.<ref>{{cite web|last=ibid|title=§ 233 - § 235|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

: EXAMPLE: A human being’s Determination is thinking reason, since that is what she unalterably is in ''opposition'' to her Other: nature. However, humans are entangled in nature in myriad other ways than just thinking rationally about it, and ''how'' humans react to this external influence ''also'' tells us about what they are. This is their Constitution, the part of their being that undergoes alteration in ''relation'' to its Others.<ref>{{cite web|last=ibid|title=§ 232|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

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.<ref>{{cite web|last=ibid|title=§ 239|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

: 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.<ref>{{cite web|last=ibid|title=§ 246|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

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 is only relative and entirely dependent on what it isn’t to be what it is. It 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.”<ref>{{cite web|last=ibid|title=§ 247 - § 249|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> 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.<ref>{{cite web|last=ibid|title=§ 254|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref> The flip side of this, though, is that the Limit also takes its negative along with it back into the Something, this 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 becomes the Other to its own self, 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.<ref>{{cite web|last=ibid|title=§ 255 - § 261|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

: 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 it Ought not to feel pain]. If it were not above and beyond the determinateness, it would not feel it as its negation and would feel no pain."<ref>{{cite web|last=ibid|title=§ 266|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

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''.<ref>{{cite web|last=ibid|title=§ 269|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl109.htm#HL1_117|accessdate=23 January 2012}}</ref>

=====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, 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.”<ref>{{cite web|last=ibid|title=§ 273 - § 274|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>

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'''''.<ref>{{cite web|last=ibid|title=§ 275 - § 286|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>

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.<ref>{{cite web|last=ibid|title=§ 300 - § 304|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>

: EXAMPLE: Hegel gives as a symbol of the Infinite Progress the straight line which stretches out to infinity in both directions. This Infinity is, at all times, the ''beyond'' of the Determinate Being of the line itself. True Infinity is properly represented by the “''circle'', the line which has reached itself, which is closed and wholly present, without ''beginning'' and ''end''.”<ref>{{cite web|last=ibid|title=§ 302|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>

This move is highly significative of Hegels’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.”<ref>{{cite web|last=ibid|title=§ 316|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>

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''.<ref>{{cite web|last=ibid|title=§ 318|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl136.htm#HL1_137a|accessdate=1 February 2012}}</ref>

====Being-For-Self====

=====A. Being-for-Self as Such=====

At this point we have arrived back at simple Being from which all the previous developments had initially proceeded. This Being, though, is now in the standpoint of Infinity from which these developments can be seen as moments of itself and so it is '''(a) ''Being-for-Self as Such'''''. Until this point Determinate Being was burdened with Finitude, depended on the Other for its own determination, and so was only ''relatively'' determined Being. From the Ideal standpoint of Infinity, Being-for-Self has become free from this burden and so is ''absolutely'' determined Being.<ref>{{cite web|last=ibid|title=§ 320 - § 321|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>

As a consequence of having overcome this relativity, however, both sides of the relationship between Something and Other are now also in equal relation to the Infinite Being that they have become Ideal moments of. So, although through their relationship Something and Other mutually determine ''each other’s'' inner Qualities, they do not have the same effect on the Infinite Being―be it God, spirit or ego (in the [[Fichte]]an sense)―to which they are now objects. This Being is not just another Finite Other, but is the One for which they are and of which they are a part. The Being-for-Other of Finitude has become the '''(b) ''Being-for-One''''' of Infinity.<ref>{{cite web|last=ibid|title=§ 322|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>

: EXAMPLE: This Being-for-One recalls [[Leibniz]]’s [[monadology|monad]] because it involves a simple oneness that maintains itself throughout the various determinations that might take place within it. Hegel, however, is critical of Leibniz’s construction because, since these monads are indifferent to each other and, strictly speaking, are not Others to one another, they cannot determine each other and so no origin can be found for the harmony that is claimed to exist between them. Being-for-One, containing as it does the moments of determination within it, avoids this contradiction.<ref>{{cite web|last=ibid|title=§ 326|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>

If we now take in isolation that to which all the preceding moments refer, i.e., that which we now have immediately before us, we end up with '''(c) the ''One'''''.<ref>{{cite web|last=ibid|title=§ 328|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl157.htm#HL1_158|accessdate=13 February 2012}}</ref>

=====B. The One and the Many=====

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.<ref>{{cite web|last=ibid|title=§ 332 - § 334|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref> 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.<ref>{{cite web|last=ibid|title=§ 335 - § 336|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref>

: 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 [[atomic theory|scientific one]] of modern physics because the former understood the void not just as the empty space between atoms, but as the atom’s own inherent principle of unrest and self-movement. “Physics with its molecules and particles suffers from the atom ... just as much as does that theory of the State which starts from the particular will of individuals.”<ref>{{cite web|last=ibid|title=§ 338 - § 339|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref>

The original transition of Being and Nothing to Determinate Being is again echoed here in the sphere of Being-for-Self. The One, though, as negatively related to all aspects of Quality excepting its own Quality of being the Void, cannot take on a Qualitative determinateness like Determinate Being did. In its own self-differentiation, it can only relate to itself as another self identical to it, that is, as another One. Since no new Quality has been taken on, we cannot call this transition a Becoming, but rather a ''Repulsion'', i.e., the positing of '''(c) ''Many''''' Ones.<ref>{{cite web|last=ibid|title=§ 340 - § 342|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl164.htm#HL1_164|accessdate=13 February 2012}}</ref>

=====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 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.<ref>{{cite web|last=ibid|title=§ 349 - § 352|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>

: 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.”<ref>{{cite web|last=ibid|title=§ 356|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>

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.<ref>{{cite web|last=ibid|title=§ 358|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>

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''.<ref>{{cite web|last=ibid|title=§ 361 - § 365|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>

: EXAMPLE: Although in Hegel’s estimation a triumph of the explanatory power of metaphysics over the physics based on sense perception as it was then practised, he believed that [[Immanuel Kant|Kant]]’s '''''Metaphysische Anfangsgründe der Naturwissenschaft''''' ['''''[[Metaphysical Foundations of Natural Science]]'''''] (1786) retained many of the errors committed by the latter, foremost among these being that, since matter is given to the senses as already formed and constituted, it is taken to be such by the mind as well. The forces of Attraction and Repulsion that are supposed to act ''upon'' matter to set it in motion, then, are not seen also to be the very forces though which matter itself comes into being in the first place.<ref>{{cite web|last=ibid|title=§ 374, § 385|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_178|accessdate=13 February 2012}}</ref>

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''.<ref>{{cite web|last=ibid|title=§ 370|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl170.htm#HL1_170|accessdate=13 February 2012}}</ref>

===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 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.<ref>{{cite web|last=ibid|title=§ 395 - § 398|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_187|accessdate=21 February 2012}}</ref>

: EXAMPLE: “[S]pecific examples of pure quantity, if they are wanted, are space and time, also matter as such, light, and so forth, and the ego itself.”<ref>{{cite web|last=ibid|title=§ 402|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl186.htm#HL1_188|accessdate=21 February 2012}}</ref>  Hegel here sharply criticizes Kant’s antinomy, put forth in his '''''[[Critique of Pure Reason]]''''', between indivisibility and infinite divisibility in time, space and matter. By taking continuity and discreteness to be entirely antithetical to one another, instead of in their truth which is their dialectical unity, Kant becomes embroiled in self-contradiction.<ref>{{cite web|last=ibid|title=§ 404 - § 406, § 425|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl186.htm#HL1_188|accessdate=21 February 2012}}</ref>

'''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''.<ref>{{cite web|last=ibid|title=§ 429 - § 431|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl186.htm#HL1_188|accessdate=21 February 2012}}</ref>

'''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''.<ref>{{cite web|last=ibid|title=§ 434 - § 436|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_200|accessdate=21 February 2012}}</ref>

====Quantum====

=====A. [[Number]]=====
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.<ref>{{cite web|last=ibid|title=§ 438 - § 444|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_202a|accessdate=30 March 2012}}</ref>

: EXAMPLE: The species of [[calculation]]—[[counting]], [[addition]]/[[subtraction]], [[multiplication]]/[[Division (mathematics)|division]], [[Exponentiation|powers]]/[[nth root|roots]]—are the different modes of bringing Numbers into relation with each other. Although the progress through these modes displays the same sort of dialectical evolution as does the Logic proper, they are nonetheless entirely external to it because there is no inner necessity in the various arrangements imposed on them by [[arithmetic]]al procedure. With the expression 7 + 5 = 12, although 5 added to 7 necessarily equals 12, there is nothing internal to the 7 or the 5 themselves that indicates that they should be brought in any sort of relation with one another in the first place.<ref>{{cite web|last=ibid|title=§ 445 - § 451|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl205.htm#HL1_205|accessdate=30 March 2012}}</ref> For this reason, number cannot be relied upon to shed any light on strictly philosophical notions, despite the ancient attempt by [[Pythagoras]] to do so. It can however be used to ''symbolize'' certain philosophical ideas. As for [[math]] as a pedagogical tool, Hegel presciently had this to say: “Calculation being so much an external and therefore mechanical process, it has been possible to construct [[Mechanical calculator|machines]] which perform arithmetical operations with complete accuracy. A knowledge of just this one fact about the nature of calculation is sufficient for an appraisal of the idea of making calculation the principal means for educating the mind and stretching it on the rack in order to perfect it as a machine.”<ref>{{cite web|last=ibid|title=§ 462 - § 471|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl205.htm#HL1_205|accessdate=30 March 2012}}</ref>

=====B. Extensive and Intensive Quantum=====
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.<ref>{{cite web|last=ibid|title=§ 472 - § 478|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>

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.<ref>{{cite web|last=ibid|title=§ 479 - § 482|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>

: EXAMPLE: [[Weight]] exerts a certain [[pressure]] which is its Intensive Magnitude. This pressure, however, can be measured Extensively, in [[Pound (mass)|pounds]], [[kilogram]]s, etc. [[Heat]] or [[cold]] can be Qualitatively experienced as different [[Degree (temperature)|Degrees of temperature]], but can also be Extensively measured in a [[thermometer]]. High and low Intensities of [[note]]s 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.”<ref>{{cite web|last=ibid|title=§ 488 - § 491|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>

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'''.<ref>{{cite web|last=ibid|title=§ 493 - § 496|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl217.htm#HL1_217|accessdate=30 March 2012}}</ref>

=====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.<ref>{{cite web|last=ibid|title=§ 497 - § 499|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref> 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 “[[Infinitesimal|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.<ref>{{cite web|last=ibid|title=§ 500 - § 503|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref>

: EXAMPLE: Hegel here gives several examples of the appearance of the Spurious Quantitative Infinite in philosophy, namely in Kant’s notion of the [[Critique of Judgment|sublime]] and his [[categorical imperative]], as well as Fichte’s infinite ego as outlined in his '''''[http://www.marxists.org/reference/subject/philosophy/works/ge/fichte.htm Theory of Science]''''' (1810). At bottom of all these ideas, says Hegel, is an absolute opposition that is held to exist between the ego and its other, this latter taking the form, respectively, of art, nature and the non-ego in general. The opposition is supposed to be overcome by the positing of an infinite relation between the two sides, the ego’s level of morality, for example, ever increasing in proportion to a decrease in the power of the senses over it. According with the nature of the Spurious Quantitative Infinite, however, it does not matter how great a level the ego raises itself to, the absolute opposition between it and its other is there and everywhere reasserted and the whole process can have no other outcome than a desperate and futile longing.<ref>{{cite web|last=ibid|title=§ 504 - § 517|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref>

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 ''[[Ratio|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 (geometry)|line]] or a [[curve]].<ref>{{cite web|last=ibid|title=§ 530 - § 537|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl225.htm#HL1_225|accessdate=30 March 2012}}</ref>

: EXAMPLE: Hegel here engages in a lengthy survey of the history and development of the [[Differential calculus|Differential]] and [[Integral Calculus]], citing the works of [[Cavalieri]], [[Descartes]], [[Fermat]], [[Isaac Barrow|Barrow]], [[Isaac Newton|Newton]], [[Gottfried Wilhelm Leibniz|Leibniz]], [[Euler]], [[Lagrange]], [[John Landen|Landen]], and [[Lazare Carnot|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, primarily from their failure to distinguish between Quantum as the ''Quantity'' that each individual term of a [[Differential of a function|differential co-efficient]] represents, and the ''Qualitative'' nature of their relationship when in the form of a ratio. “''Dx'', ''dy'', are no longer quanta, nor are they supposed to signify quanta; it is solely in their relation to each other that they have any meaning, ''a meaning merely as moments''.”<ref>{{cite web|last=ibid|title=§ 538 - § 570|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl240.htm#HL1_240|accessdate=30 March 2012}}</ref>

====The Quantitative Relation====

'''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),
:<math> k =  {y \over x}.</math>
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,
:<math> y = kx ;\,</math>
if ''x'' is Amount, then ''k'' is the Unit, the amount of which, ''y'', determines it,
:<math> x = y/k .\,</math>
As in themselves ''incomplete'' in this way, these Quanta serve only as the Qualitative moments of one another.<ref>{{cite web|last=ibid.|title=§ 674 - § 678|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl314.htm|accessdate=18 May 2012}}</ref>

'''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.,
:<math> k = xy\,</math>
or
:<math>y = {k \over x}.</math>
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.<ref>{{cite web|last=ibid.|title=§ 679 - § 687|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl314.htm|accessdate=18 May 2012}}</ref>

'''C. The Ratio of Powers'''

The ''Ratio of Powers'' takes the following form:
:<math>y = k^x.\,</math>
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''.<ref>{{cite web|last=ibid.|title=§ 688 - § 694|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl314.htm|accessdate=18 May 2012}}</ref>

===Measure===

====Specific Quantity====

=====A. The Specific Quantum=====

“Measure is the simple relation of the quantum to itself ... ; the quantum is thus qualitative.” Previously, Quantum was held to be indifferent to the Quality of that which it quantified. Now, as Measure, Quality and Quantity though still distinct from one another are inseparable and in their unity comprise a specific Determinate Being: “Everything that exists has a magnitude and this magnitude belongs to the nature of the something itself.” The indifference of Quantum is retained in Measure insofar as the magnitude of things can increase or decrease without fundamentally altering their Quality, and yet their essential unity nevertheless manifests at the Limit where an alteration in Quantity ''will'' bring about a change in Quality.<ref>{{cite web|last=ibid|title=§§712-717|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>

: EXAMPLE: [[Aristotle]] gives the example of a head from which hairs are plucked one by one. It’s Quality of being a head of hair remains if only a few hairs are gone, but at a certain point, it undergoes Qualitative Alteration and become a bald head. Although the Quantitative change is gradual, the Qualitative one, oftentimes, is “unexpected”. “It is the cunning of the Notion to seize on this aspect of a reality where its quality does not seem to come into play; and such is its cunning that the aggrandizement of a State or of a fortune, etc., which leads finally to disaster for the state or for the owner, even appears at first to be their good fortune.”<ref>{{cite web|last=ibid|title=§§718-722|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>

=====B. Specifying Measure=====

Insofar as Quantity describes the upper and lower Limits between which a specific Quality can maintain itself, it serves as a '''(a) ''Rule'''''. The Rule is an arbitrary external standard or Amount that measures something other than itself. Although it is often tempting to assume so, there is in actuality no object that can serve as a completely universal standard of measurement, i.e., be pure Quantity. Rather, what is involved in measurement is a ratio between two Qualities and their inherent Quantities, the one made to act as the '''(b) ''Specifying Measure''''' of the other, this other, however, being itself just as capable of measuring that which it is being measured by.<ref>{{cite web|last=ibid|title=§§725-729|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>

: EXAMPLE: In the measure of [[temperature]], we take the expansion and contraction of [[Mercury (element)|mercury]] relative to the [[heat]] it contains as a Quantitative Rule for the increase or decrease of temperature in general by dividing the range of its change in magnitude into a scale of [[arithmetical progression]]. Tempting though it is to believe, this is not the measure of temperature ''as such'', but only the measure of how Quantitative change specifically affects the Quality of mercury. The water or air the mercury [[thermometer]] measures has a very different Qualitative relationship to changes in the Quantity of heat which do not necessarily bear any direct relation to mercury’s. Thus, what is actually going on when we take a temperature is a relationship of comparison between two Qualities and their respective natures when exposed to a Quantitative increase or decrease in heat, and ''not'' a universal determination by some disembodied, abstract “thing” that is temperature ''itself''.<ref>{{cite web|last=ibid|title=§730|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=26 August 2012}}</ref>

So long as we arbitrarily use the Quantitative properties of some Quality or other as a Rule to Measure the magnitude of other Qualities, we abstract from it its Qualitative nature. However, once we have established a Quantitative ratio between two or more Qualities, we can give this ratio an independent existence that Quantitatively unites things that are Qualitatively distinct. We can thus take the Qualities of both sides into account, the independent, or ''Realized'', Measure serving as their '''(c) ''Relation'''''. This Measure necessarily involves variable magnitudes since the Qualitatively distinct ways in which different things relate to Quantity can only be registered in their respective rates of increase or decrease relative to each other. Further, in order for each side of the ratio to fully reflect the distinctiveness of the Quality it represents, both sides must be Quantitatively self-related, i.e., take the form of powers as in the case of the Ratio of Powers explicated above.<ref>{{cite web|last=ibid|title=§§731-734|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=27 August 2012}}</ref>

: EXAMPLE: [[Velocity]] is the ratio of [[space]]’s relation to [[time]]:
:: <math>v = {d \over t}.</math>
: It is only an intellectual abstraction, though, since it merely serves to measure space by the Rule of time or time by the Rule of space. It supplies no objective standard for the inherent Quantitative relation to each other that pertains to their specific Qualities. The [[Equations for a falling body|formula for a falling body]] comes closer,
:: <math> d = at^2\,</math>
: but here time is still serving as an arbitrary Rule, that is, it is assumed to vary in a simple arithmetical progression. It is the form of motion described by [[Kepler's laws of planetary motion|Kepler’s third law of planetary motion]] that comes closest for Hegel to being a Realized Measure of the relation between the inherent Qualities of space and time:
:: <math> d^3 = at^2\,.</math><ref>{{cite web|last=ibid|title=§735|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=27 August 2012}}</ref>

=====C. Being-For-Self in Measure=====

Although now united by the Quantitative Ratio, the two or more Qualities thus brought into relation retain their mutual separation as distinct Qualities. For example, even though we can determine the Quantitative relationship between space and time in the example of a falling body, each of them can still be considered on its own, independent of the other. However, if we then take the constant produced by the ratio of the two sides as a self-subsistent Something in its own right, that is, a ''Being-For-Self'', then the two formerly entirely distinct Qualities become its own sublated moments, their very natures now seen to have been in fact derived from this relation of Measure in the first place.<ref>{{cite web|last=ibid|title=§§738-741|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl333.htm#HL1_333a|accessdate=27 August 2012}}</ref>

====Real Measure====

=====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.<ref>{{cite web|last=ibid|title=§§745-748|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>

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 Affinities|Elective Affinity]]''''' between their different Qualities, but not these Qualities themselves.<ref>{{cite web|last=ibid|title=§§749-753|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>

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.<ref>{{cite web|last=ibid|title=§§755-756|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>

: EXAMPLE: Hegel makes it clear that the above analysis applies to the system of chemical affinities and that of [[Harmony|musical harmony]]. In the case of the latter, for example, each individual [[Musical note|note]] is a Real, self-subsistent Measure, consisting as it does of a specific internal ratio between, say, the length and thickness of a guitar string. An individual note, however, only achieves meaning in its relation to a system of other notes that are brought into Quantitative relation to each other through a specific note that serves as the Unit, or [[Key (music)|key]]. A note serving as the key in one system, is equally an individual member in other systems in which other notes play this role. Notes that harmonize when played together are demonstrating their Elective Affinity for one another, that is, the higher Qualitative unity that results from a combination in which each individual note nevertheless retains its self-subsistence.<ref>{{cite web|last=ibid|title=§754|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>

=====B. Nodal Line of Measure-Relations=====

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.<ref>{{cite web|last=ibid|title=§§769-773|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_348|accessdate=27 November 2012}}</ref>

: 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]], [[Exponentiation|power]] or [[Root (mathematics)|root]], etc., and thus constitute “Nodes.” Transition from the liquid to the [[Freezing point|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.<ref>{{cite web|last=ibid|title=§§774-778|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_368|accessdate=27 November 2012}}</ref>

=====C. The Measureless=====
Measure, being the unity of Quality and Quantity, now transitions into its version of the Infinite, the ''Measureless'', which accordingly is the unity of the Qualitative and Quantitative Infinites. In the Measureless, the Quantitative Infinite is manifested in the potential of the Nodal line to increase endlessly; the Qualitative Infinite is manifested as the eternal beyond of any particular Qualitative determination. Seeing as the successive determinations are self-generated by an internal Quantitative Alteration of Measure, they can now be seen, from the standpoint of the Measureless, to be different ''States'' of one and the same ''Substrate''. The nature of the Substrate is not tied, like the Something was, to a merely external Qualitative appearance, but represents the underlying unity of a variety of internally determined appearances, which are its States.<ref>{{cite web|last=ibid|title=§§779-84|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl348.htm#HL1_371|accessdate=27 November 2012}}</ref>

====The Becoming of Essence====

'''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.<ref>{{cite web|last=ibid|title=§§785-786|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl375.htm#HL1_375|accessdate=29 April 2013}}</ref>

'''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.<ref>{{cite web|last=ibid|title=§§787-796|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl375.htm#HL1_375|accessdate=29 April 2013}}</ref>

: EXAMPLE: Here, Hegel makes a powerful argument in favour of the explanatory powers of his speculative philosophy over those of empirical science, specifically with regards to the concepts of [[centripetal]] and [[centrifugal]] forces as they are supposed to relate the [[elliptical motion]] of celestial bodies. If, as is supposed by science, such an orbit is made up of an inverse relation of centripetal and centrifugal forces—the former predominating over the other as the body approaches [[perihelion]], the reverse if approaching [[aphelion]]—then the sudden overtaking of the stronger force by the weaker that takes place on either end of the orbit can only be explained by some mysterious ''third'' force. Indeed, what is to stop the dominant force from completely overtaking the weaker, causing the body either to crash into whatever it is orbiting or to fly off at ever accelerating speeds into space? Only the inherent unity of the two Qualities, centripetal and centrifugal, arrived at by the ascension of thought to Absolute Indifference, can adequately explain the Notion of the elliptical orbit, says Hegel.<ref>{{cite web|last=ibid|title=§§797-802|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl375.htm#HL1_375|accessdate=29 April 2013}}</ref>

'''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''.<ref>{{cite web|last=ibid|title=§§803-806|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlbeing.htm#HL1_383|accessdate=29 April 2013}}</ref>

==Objective Logic: Doctrine of Essence==

===Reflection-Within-Self===

====Illusory Being====

=====A. The Essential and the Unessential=====

The immediate characteristic displayed by Essence, once it finally emerges from Being, is simply that it is ''not'' Being.  This apparently puts us back into the sphere of Determinate Being (see above), where each side of a relation mutually determined the Other side as being ''not'' what ''it'' is. In this immediate, merely relative relation, Essence and Being thus become the ''Essential'' and the ''Unessential'', respectively. There is nothing arising within this relation, however, to tell us ''what'' it is about something that is Essential and what Unessential. Those that apply this mode of thinking to something are making an arbitrary distinction, the opposite of which could always be claimed with equal justification. What saves Essence from falling back in to the relativism of Determinate Being is the very radical and absolute distinction from Being that defines it as Essence in the first place. Being cannot therefore simply preserve itself as an Other relative to Essence, but, having been sublated by Essence, it has for that very reason itself become ''nothingness'', a ''non-essence'', ''Illusory Being''.<ref>{{cite web|last=ibid|title=§§819-822|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlessenc.htm#HL2_394a|accessdate=5 August 2013}}</ref>

=====B. Illusory Being=====

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 [[Philosophical skepticism|ancient skepticism]] as well as the “modern” [[German idealism|idealism]] of [[Leibniz]], [[Immanuel Kant|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''.<ref>{{cite web|last=ibid|title=§§823-832|url=http://www.marxists.org/reference/archive/hegel/works/hl/hlessenc.htm#HL2_394a|accessdate=5 August 2013}}</ref>

=====C. Reflection=====

Refection 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'''''.<ref>{{cite web|last=ibid|title=§§833-845|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>

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 Refection 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.<ref>{{cite web|last=ibid|title=§§846-849|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>

: EXAMPLE: Hegel offers for comparison with his notion of External Reflection the “reflective judgement” of Kant, which, in the '''''[[Critique of Judgement]]''''', is described as the faculty of the mind that determines the ''universals'' that lie behind immediately given ''particulars''. This action is similar to that of External Reflection with the crucial difference that, for Hegel, the universal does not simply lie “behind” the particular, but ''generates'' the particular from itself and so is the particular's own true ''Essence''. The immediate particular upon which Kant's judgement works is, in actuality, simply a ''nothingness'' posited by Reflection itself solely in order to generate its equally null universal, Essence.<ref>{{cite web|last=ibid|title=§§850-852|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>

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.”<ref>{{cite web|last=ibid|title=§§853-859|url=http://www.marxists.org/reference/archive/hegel/works/hl/hl399.htm#HL2_399|accessdate=5 August 2013}}</ref>

===Identity, Difference, Contradiction===

Identity holds high importance for Hegel, writing that "all thinking involves identity and difference." Indeed it is hard to imagine any sort of life at all if we could not make use of identity, difference, and related concepts such as likeness; these principles constitute the backbone of Hegel's view of essence. Initially he claims that "so far, then, identity is still in general the same as essence" and reminds us that identity is usually held to be the "First Original Law of Thought." The problem with identity, however, is that a statement such as [[A=A]] is a limited, one-sided statement of identity, a mere "empty [[tautology (logic)|tautology]]" that has "no content." If someone declares that the book in front of him is the book in front of him it leads nowhere, in the same way that a person claiming that "God is--God" is wasting our time. These are "boring and tedious" statements utilizing the "pure law of identity" which merely "reiterate the same thing" in Hegel's view.

As soon as "A is..." completes (is predicated by something), says Hegel, difference emerges. Thus he claims broadly that "everything is inherently contradictory." Taking "the camera is black" as our example, a camera is not the same thing as the color black, yet it is what it is (a black camera) through this resolved contradiction.

Hegel identifies three types of difference. "Absolute difference" is the most general and abstract (mental reflection) sense. "Diversity" includes the "otherness of reflection" meaning that we essentially think of how "A" is different from all other possible cases. Finally, "Opposition" is the "completion of determinate difference" with "moments that are different in one identity."

Regarding diversity, let's assume there is some person "A" who is overweight. In considering the obesity of "A" in our mental reflection we at the same time consider all the potential and possible weights that "A" is not along some continuum. "A" is not thin nor of normal weight either and this needs to be taken into consideration. Hegel says that things are different through unlikeness: this is the so-called "Law of Diversity."

===Ground===

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. 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."

==Subjective Logic or the Doctrine of the Notion==
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.

==References==
{{Reflist}}

==Editions of ''Science of Logic''==
* translated by [[W. H. Johnston]] and [[L. G. Struthers]]. London: George Allen & Unwin, 1929
* translated by [[Henry S. Macran]] (''Hegel's Logic of World and Idea'') (Bk III Pts II, III only). Oxford, Clarendon Press, 1929
* translated by [[Arnold V. Miller|A. V. Miller]]; Foreword by [[John Niemeyer Findlay|J. N. Findlay]]. London: G. Allen & Unwin, 1969
* translated by George di Giovanni, Cambridge: Cambridge University Press, 2010

==Secondary literature==
* Bencivenga, Ermanno 2000. '' Hegel's Dialectical Logic'' Oxford.
* Burbidge, John W., 1995. ''On Hegel's Logic. Fragments of a Commentary Atlantic Highlands, N.J.
* Burbidge, John W. 2006. ''The Logic of Hegel's Logic. An Introduction''Peterborough, ON.
* Butler, Clark. 1996. ''Hegel's Logic. Between Dialectic and History'' Evanston.
* Carlson, David 2007. ''A Commentary on Hegel's Science of Logic'' New York: Palgrave MacMillan. 978-1403986283
* Di Giovanni, George (ed) 1990. ''Essays on Hegel's Logic'' Albany: New York State University Press.
* Harris, Errol E. 1983. ''An Interpretation of the Logic of Hegel'' Lanham.
* Harris, William T. 1985. ''Hegel's Logic: A Book on the Genesis of the Categories of the Mind. A Critical Exposition'' Chicago.
* Hartnack, Justus, 1998. ''An Introduction to Hegel's Logic''. Indianapolis: Hackett. ISBN 0-87220-424-3
* Houlgate, Stephen, 2006. ''The Opening of Hegel's Logic: From Being to Infinity'' Purdue: University Press.
* Rinaldi, Giacomo, 1992. ''A History and Interpretation of the Logic of Hegel'' Lewiston: Edwin Mellen Press.
* Roser, Andreas, 2009. ''Ordnung und Chaos in Hegels Logik''. 2 Volumes, New York, Frankfurt, Wien. ISBN 978-3-631-58109-4
* Trisokkas, Ioannis, 2012. ''Pyrrhonian Scepticism and Hegel's Theory of Judgement. A Treatise on the Possibility of Scientific Inquiry'' Boston: Brill. 
* Winfield, Richard Dien, 2006. ''From Concept to Objectivity. Thinking Through Hegel's Subjective Logic'' Aldershot: Ashgate. ISBN 0-7546-5536-9.

==External links==
* Source text (German) ''Wissenschaft der Logik'' [http://www.gutenberg.org/etext/6729 Vol. 1] [http://www.gutenberg.org/etext/6834 Vol. 2]
* [http://www.marxists.org/reference/archive/hegel/ollindex.htm Outline of Hegel's Logic at marxists.org]
* [[s:The Meaning of Hegel's Logic/Introduction|The Meaning of Hegel's Logic]] (commentary at Wikisource)
* [http://www.marxists.org/archive/dunayevskaya/works/1961/01/26.htm Dunayevskaya : Rough Notes on Hegel's SCIENCE OF LOGIC]
* [http://www.marxistoutlook.com/article7.htm Terry Button : Hegel’s Logic&nbsp;– A Brief Synopsis]
* [http://www.marxists.org/archive/lenin/works/1914/cons-logic/ch01.htm Lenin : Consepectus of Hegel’s Science of Logic]
* [http://archive.org/details/LectureCourseInHegelsScienceOfLogic-RichardDienWinfield Lecture Course in Hegel's Science of Logic - Richard Dien Winfield (Audio)]

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