Science of Logic

Contents

1. Preface to the First Edition 13 min 10

   Written at Nuremberg in March 1812. Hegel observes that the old metaphysics has vanished from German intellectual life, undermined by Kant’s critique and by a practical age that prizes useful training, while logic survives only as an empty school subject. He announces a new philosophical method: Understanding fixes distinctions, Reason dissolves them dialectically and grasps the unity that results, and this self-movement of the content is “the Absolute Method”. He explains how the Logic relates to the Phenomenology of Spirit, which leads consciousness up to pure knowing, and sets out the plan of the three Books: Being, Essence and the Notion.

2. Preface to the Second Edition 35 min 7

   Dated 7 November 1831, a week before Hegel’s death. He notes that the forms of thought are deposited first in language, and praises German for words with opposed meanings. Following Aristotle, he says pure thought arises only once life’s necessities are met. Categories are not tools we use; they pervade everything we think and will, and Logic’s task is to make them conscious and free. He rejects Kant’s thing-in-itself as an empty abstraction, complains of critics who attack the beginning with unexamined categories, and regrets lacking the leisure to revise the work, like Plato’s Republic, “seventy times and seven”.

3. Introduction 1 h 1 min 14

   Logic cannot begin with definitions or a borrowed method, since these belong to its own subject. Hegel attacks the view of logic as an empty form waiting for content from experience, and Kant’s critical philosophy, which left the categories subjective and the thing-in-itself unknown. The Phenomenology has deduced the standpoint of pure science, where thought and object are one; the Logic’s content is thus “God as he is in his eternal essence”. Its method is determinate negation: self-contradiction yields a richer concept, not nothing. Kant’s antinomies showed contradiction to be necessary. Logic divides into Objective Logic (Being, Essence) and Subjective Logic (the Notion).

4. I With What Must the Science Begin? 32 min 5

   Where should philosophy start? A mediated beginning depends on something prior; an immediate one seems arbitrary. Hegel answers that pure knowing, the result of the Phenomenology, collapses into simple immediacy, which is pure being: the beginning presupposes nothing within the Logic. The system is a circle in which the end proves to be the ground of the beginning, a point Reinhold half grasped. The bare idea of a beginning already contains being and nothing, so it leads to the same place. Starting from the Ego, as Fichte did, is rejected: the pure I is not the familiar self, and keeps the opposition of consciousness alive.

5. I General Classification of Being 4 min 2

   A provisional outline of Book One. Being is first opposed to Essence; within itself it unfolds as Quality, Quantity and Measure; and as immediate it is the beginning. Hegel defends putting quality before quantity, against the usual order, since quantity is quality that has become indifferent to the thing. He notes how his scheme departs from Kant’s table of categories: Kant’s relational categories belong to Essence, and modality concerns only the relation of content to thought.

6. I.1 Determinateness (Quality) 1 min

   A short preview of Section One. Indeterminate being has, in its very indeterminacy, a quality; it therefore passes into determinate being, which as finite transcends itself into being-for-self, the infinite relation of being to itself.

7. I.1.1 Being 1 h 16 min 13

   Pure being, without any determination, is empty, and so is nothing; pure nothing is the same emptiness, and so is being. Their truth is Becoming, each vanishing into the other. Four Observations defend this against common sense: on Parmenides and Heraclitus, “nothing comes from nothing”, and Kant’s hundred thalers; on why a single proposition cannot state a speculative truth; on Jacobi’s, Fichte’s and Plato’s ways of handling abstraction; and on arguments against the world’s beginning and against infinitesimals. Becoming’s moments, arising and passing away, collapse into a stable result, determinate being. A closing note explains aufheben, to cancel and preserve.

8. I.1.2 Determinate Being 2 h 19 min 19

   Determinate Being (Dasein) is being with a quality, at once reality and negation. Quality makes a “something” set against an “other”, defined by its limit. A thing that has its limit within it is finite and bound to perish. The finite strains against its limit as barrier and ought, which produces the infinite. Hegel separates the “bad” infinite, an endless beyond, from the true infinite, which contains the finite as a moment. Remarks attack the ontological proof, Kant's thing-in-itself and Kant and Fichte's ethics of endless ought, and argue that every philosophy is idealism.

9. I.1.3 Being for Self 1 h 19 min 9

   The true infinite, taken as a simple self-relation, is Being-for-Self. Its first form is the One, which excludes all else and so has the Void beside it, the logic of ancient atomism. The One repels itself into many Ones; because each is just like the others, repulsion passes into attraction, and their balance makes difference indifferent: quality has become quantity. Remarks discuss Malebranche's and Leibniz's idealism, the atomism of social-contract theory, abstract freedom as evil, and Kant's construction of matter from attractive and repulsive forces, which Hegel finds confused, along with the centripetal and centrifugal forces of planetary mechanics.

10. I.2 Magnitude (Quantity) 6 min 1

    A short introduction to the second section of the Doctrine of Being. Quantity is a determinateness indifferent to being: a field enlarged is still a field, a red darkened still red. Hegel outlines the section's course from pure quantity through quantum and the quantitative infinite to ratio, which leads to measure, and criticises the textbook definition of magnitude as what can be increased or diminished.

11. I.2.1 Quantity 42 min 7

    Pure quantity unites continuity (from attraction) and discreteness (from repulsion); space, time, matter and the ego are examples. Hegel quotes Spinoza on quantity as imagined and as understood, then dissects Kant's second antinomy on simple parts and infinite divisibility, arguing that each proof assumes its conclusion and that the antinomy only separates the two moments of quantity. He praises Zeno's paradoxes and Aristotle's solution against Bayle, and then distinguishes continuous from discrete magnitude. Limited, each becomes a quantum.

12. I.2.2 Quantum 1 h 50 min 19

    Hegel develops quantum, or determinate quantity, whose complete form is Number (Unit and Amount). Two Observations criticise Kant’s claim that 7 + 5 = 12 is synthetic and attack the use of numbers to express thought, including Pythagorean and contemporary number-symbolism and arithmetic as the basis of education. Extensive magnitude (a sum) and intensive magnitude (a degree) prove to be one determination. Because a quantum’s limit is indifferent, it keeps passing beyond itself: the bad quantitative infinite. Hegel criticises it in Kant’s sublime, in Kant’s and Fichte’s moral infinite progress, and in Kant’s first antinomy. Grasped truly, quantum is related to itself through another quantum, and so becomes Ratio.

13. I.2.2 Quantum: The Mathematical Infinite 1 h 33 min 23

    The first Observation on the mathematical infinite. Hegel argues that the calculus works but cannot explain why. In his account its true infinite is qualitative: ratios whose sides are nothing apart from the relation, as in dy/dx. He distinguishes the bad infinity of series from the true infinity of their finite sums, citing Spinoza. He then reviews attempted foundations: Newton’s ultimate ratios (praised), Leibniz’s and Wolff’s neglect of the small, Euler’s zeros, Newton’s flawed product rule and Principia error, Carnot’s compensation of errors, and Lagrange’s series and limits. He ends by denouncing mathematical “proofs” of physical laws, Newton’s included.

14. I.2.2 Quantum: The Differential Calculus 1 h 52 min 14

    Observations 2 and 3 of Hegel’s long Remark on the mathematical infinite. He argues that the calculus’s rules are easy and arose as empirical tricks (Barrow, Fermat), with principles invented afterwards. Its true object is the relation between a function involving powers and its derivative function, which acquires meaning when matched to lines and areas of a figure. He praises Descartes’s double-root method and Lagrange’s series approach over infinitesimals, treats integration as the inverse problem, and then examines Kepler, Cavalieri and Barrow on the dissolution of the continuous into indivisibles. The infinitesimal, he concludes, is a negative notion that obscures an affirmative qualitative relation.

15. I.2.3 The Quantitative Ratio 34 min 3

    The last chapter of the Doctrine of Quantity. A quantum gets its determinateness in another quantum, and ratio results. In direct ratio a fixed exponent links two sides; in inverse ratio the sides limit each other, approaching their product as a bad-infinite beyond that is in fact present as the exponent; in the ratio of powers a number relates only to itself. Quantity thereby proves to be qualitative, and Hegel stresses that both transitions, quality into quantity and back, are needed. The result is Measure. An Observation rejects Schelling’s use of “powers” for philosophical concepts.

16. I.3 Measure 16 min 3

    The introduction to Measure, the third section of the Doctrine of Being, in which quality and quantity are united. Hegel explains why Kant failed to find this third term, compares Spinoza’s mode and the Indian trimurti, and praises the Greek sense that everything has a measure, a step towards necessity and essence. He outlines the section’s course: specific quantity, real measure and the measureless, leading into Essence. He warns that measure is clearest in mechanics and blurred in organic and spiritual life, where the size of states shows proportions but no laws.

17. I.3.1 The Specific Quantity 41 min 6

    Measure first appears as a specific quantum: everything that exists has a magnitude whose change can destroy it. Hegel discusses conventional standards, the ancient paradoxes of the Bald Man and the Heap, and the “cunning of the Notion”, by which things perish through quantity. Measure then becomes a rule and a specifying measure, which reshapes an external quantity, as bodies absorb heat unevenly. Finally it becomes a relation of two qualities, such as space and time in falling and orbital motion. Hegel criticises Newton for merely reformulating Kepler, and ends with measure as a self-standing “something”.

18. I.3.2 Real Measure 1 h 12 min 13

    Measures now belong to material things. Hegel treats specific gravity and mixture, then chemical neutralisation, where a substance’s character is a series of ratios to others (Richter’s equivalents) and elective affinity marks exclusive bonds. Long Observations criticise Berthollet’s and especially Berzelius’s atomism and electrochemistry. The “nodal line” follows: quantitative change proceeds gradually until it leaps into a new quality, as in numbers, music, chemical compounds, freezing water, birth and death, crime and the size of states. In the measureless, the alternating qualities become states of one persisting substratum.

19. I.3.3 The Becoming of Essence 28 min 4

    Book I closes. The substratum of all measures is “absolute indifference”, whose differences are only quantitative: two factors in inverse relation, each the whole in itself. Hegel shows this structure is contradictory, since neither factor can preponderate without the other vanishing, and illustrates the point with critiques of centripetal and centrifugal force, of sensibility and irritability, and of Spinoza’s substance. Resolving the contradiction means that differences are posited by the unity itself through self-repulsion, so Being becomes Essence.

20. II The Doctrine of Essence 9 min 4

    The introduction to Book II. Being has proved to be essence: what remains when immediacy has been seen through, or being that has “passed away” non-temporally (the Wesen/gewesen pun). Hegel insists that this movement belongs to being itself, not merely to our knowing. An essence reached by external abstraction would be empty. Essence proper is self-relating negativity, or Reflection, whose determinations are posited by it and stay within it. Midway between Being and Notion, essence first shows into itself, then appears, then manifests itself as actuality, which gives the three sections of the book.

21. II.1 Essence as Reflection into Self 1 min 1

    The short heading of Section One. Essence comes out of being, and what stands opposed to it is only Show, essence’s own self-positing. The section will treat reflection, then the determinations of reflection (the essentialities), and then ground, through which essence passes into existence and appearance.

22. II.1.1 Show 42 min 6

    Being reappears inside essence first as the unessential and then as Show (Schein), an immediacy whose whole being is to be null. Hegel argues that the show of the sceptics and the appearance of the idealists (Leibniz, Kant, Fichte) both take their content as given, whereas Show is essence’s own showing of itself. That self-movement is Reflection: positing reflection, external reflection (with a remark on Kant’s reflecting judgment) and determining reflection. Determining reflection yields posited determinations that are reflected into themselves, the essentialities, which look like fixed, free-floating categories.

23. II.1.2 The Essentialities or Determinations of Reflection 1 h 44 min 14

    Hegel examines identity, difference and contradiction, together with the “laws of thought” that school logic built on them. Abstract identity (A = A) is an empty tautology. Identity contains difference, which unfolds as variety (likeness and unlikeness, with Leibniz’s leaves) and then as opposition of positive and negative, illustrated by arithmetic, debts and journeys. Each opposite includes and excludes the other: this is contradiction, which Hegel calls the root of all movement and life, illustrated by Zeno’s paradoxes of motion. Contradiction resolves itself by “going to the ground”, and so passes into Ground.

24. II.1.3 Ground 1 h 43 min 11

    Ground is essence as the unity in which contradiction is resolved. Absolute ground unfolds as form and essence, form and matter, and form and content. Determined ground is first formal ground, empty tautologies such as Newtonian “attractive force”; then real ground, whose contents differ but are linked arbitrarily, as in the competing grounds of punishment or of an official’s appointment; then complete ground. Ground requires conditions, and conditions require a ground. Their unity is the unconditioned fact (Sache), which enters existence when all its conditions are present.

25. II.2 Appearance 3 min 1

    Introduction to the second section of the Doctrine of Essence. “Essence must appear”: Hegel now follows essence out into immediate existence. The section has three stages: Existence, the Thing with its properties; Appearance, whose stable side is law; and Essential Relation, in which the apparent and the essential are bound together. Their complete interpenetration will be Actuality.

26. II.2.1 Existence 54 min 6

    Whatever is, exists: existence is being that has come out of ground. After a digression on the proofs of God and faith in the “abyss” of the divine, Hegel analyses the Thing. The Kantian thing-in-itself, stripped of all determination, proves empty; a thing has its determinations in itself as properties, which hold only in relation to other things. Properties then harden into independent “matters” (heat, colour, smell), and the thing becomes a mere collection of them, porous and self-contradictory. A thing that rests on what it is not is Appearance.

27. II.2.2 Appearance 38 min 6

    Appearance is not opposed to essence but is essence existing, a higher truth than bare existence. Its stable side is law, the “quiescent image” of the changing world; but an empirical law, such as Galileo’s law of fall, only joins two contents without showing why they belong together. Developed into a totality, the realm of laws becomes a world in itself set against the world of appearance, its inversion, where north is south and evil good. The two worlds collapse into each other, and law becomes Essential Relation.

28. II.2.3 Essential Relation 50 min 4

    Three relations of increasing unity. Whole and parts depend on each other but each claims independence; the saying that the whole equals its parts turns out to be a tautology, and Kant’s antinomy of divisibility is traced to it. Force and its manifestation follow: a force must be solicited by another, yet each solicits only because it is solicited, so its outward relation is self-relation. Finally inner and outer prove to have one content: what is only inner is only outer. The closing Observation breaks off in this text.

29. II.3 Actuality 2 min 1

    The short introduction to Section Three. Actuality (Wirklichkeit, from wirken, to act) is the unity of essence and existence prepared by the relation of inner and outer. The Section treats it three ways: as the Absolute; as Actuality proper, with the formal moments of possibility and necessity; and as the Absolute Relation, or Substance.

30. II.3.1 The Absolute 32 min 4

    Hegel asks how the Absolute can be stated. Denying it every predicate, or granting it all, are external procedures; the Absolute must expound itself. Following Spinoza’s order of substance, attribute and mode, he argues that the mode, the Absolute’s outward form, is where it shows itself as showing, so the Absolute becomes self-manifestation, or Actuality. A long Observation praises Spinoza’s principle “determination is negation” but faults his merely defined substance, his externally added attributes and lack of personality, then treats the theory of emanation and Leibniz’s monads.

31. II.3.2 Actuality 41 min 6

    Hegel’s chapter on modality. Formal possibility, mere absence of contradiction, is empty: anything is possible and also impossible. The contingent is what is actual but might not be, and has both no ground and a ground. Real possibility is the presence of existing conditions; when they are complete the result cannot be otherwise, so real possibility is relative necessity. Absolute necessity, groundless and self-grounding, is “blind”: it breaks out on free-standing actualities like fate. Its self-identity in this negation is Substance.

32. II.3.3 The Absolute Relation 56 min 7

    The last chapter of the Doctrine of Essence follows Kant’s categories of relation. Substance is the power that makes accidents arise and perish, creation and destruction in one. As cause it posits effects, but cause and effect have the same content, which makes finite causal explanation tautological and unsuited to life and history. Finite causality runs into an endless regress until action and reaction bend it back into reciprocity, where each substance is cause and effect of the other. Necessity then becomes freedom, and the Notion emerges with its moments universal, particular and individual.

33. III Advertisement 3 min 4

    Hegel’s notice for Book III, dated Nuremberg, 21 July 1816. The Doctrine of the Notion also appears separately as “Subjective Logic”. It inherits a finished but “ossified” school logic that must be made fluid, like replanning an old, inhabited city. The greatness of its subject, truth, and the distractions of his office excuse its imperfections.

34. III On the Notion in General 1 h 1 min 10

    Hegel introduces the Notion as the truth of Being and Essence. It arises from substance through causality and reciprocity, so freedom proves to be the truth of necessity, and this development is the only real refutation of Spinoza. The Notion is illustrated by the self-conscious “I”, at once universal and individual. Hegel praises Kant’s unity of apperception but rejects Kant’s view that concepts are empty without intuition and that things in themselves are unknowable. Logic is the science of absolute form, with its own content. The Book divides into Subjectivity, Objectivity and the Idea.

35. III.1 Subjectivity 2 min 1

    A short outline of the first section. The formal Notion is at first an immediate unity of its moments. It then divides into independent moments related only externally, which is the Judgment. The Syllogism makes their mediating unity explicit, and its contradictions carry the subjective Notion over into objectivity.

36. III.1.1 The Notion 1 h 7 min 7

    Hegel develops the three moments of the Notion: universality, particularity and individuality. The true universal is concrete. It is a self-differentiating principle at home in its determinations, not a common feature left after abstraction. Particularity is the universal’s own difference; nature’s untidy profusion of species shows its “impotence” to hold to the Notion. He defends understanding’s power to fix concepts and attacks textbook classifications of concepts, Kant’s borrowed categories, and Euler’s and Lambert’s diagrams. Individuality, the Notion’s self-relating negativity, both completes it and divides it, and so produces the Judgment.

37. III.1.2 The Judgment 1 h 57 min 13

    Judgment is the Notion’s original self-division (Urteil) into subject and predicate, whose copula asserts that the individual is universal. Hegel reorders Kant’s table into four classes, each passing into the next through its own inadequacy. The judgment of inherence runs from positive through negative to infinite judgments, with crime as the infinite one. The judgment of subsumption runs from singular through particular to universal, ending in the genus. The judgment of necessity is categorical, hypothetical and disjunctive. The judgment of the Notion (assertoric, problematic, apodeictic) measures things against their “ought”. When the apodeictic judgment states its ground, the copula becomes a middle term, and judgment becomes syllogism.

38. III.1.3 The Syllogism 1 h 56 min 17

    Hegel argues that the syllogism reunites the terms the judgment split apart, and that whatever is rational has its form: a universal joined to an individual through a particular. He runs through three families. The Qualitative Syllogism and its four figures show that any single term in the middle gives contingent or empty results. Syllogisms of Reflection (allness, induction, analogy) each presuppose their own conclusions. Syllogisms of Necessity (categorical, hypothetical, disjunctive) make the genus the middle, until mediator and mediated coincide. Along the way he attacks Leibniz’s and Ploucquet’s logical calculi, and he ends with the passage of the Notion into Objectivity.

39. III.2 Objectivity 17 min 3

    Hegel introduces the second section of the Doctrine of the Notion. He claims that the passage from Notion to Objectivity just completed is the logical truth of the ontological proof of God’s existence, and he answers Kant’s hundred thalers. He lists the successive forms of immediacy (Being, Existence, Actuality, Objectivity) and distinguishes two senses of “objective”: what stands over against a subject, and what is valid in and for itself. He then outlines the plan: mechanism, chemism, teleology, leading to the Idea.

40. III.2.1 Mechanism 45 min 6

    Mechanism is objectivity as a set of independent objects whose relations are external to them: aggregates, mixtures, and causal chains that explain nothing, since each object is determined only by another. Hegel compares the object with Leibniz’s monad, analyses communication, resistance and rest, and discusses fate as blind power over those who act. In absolute mechanism a centre gathers the objects into three interlocking syllogisms, as in the solar system or the relation of government, citizens and needs. A rule of collision becomes a law of the system, which passes into chemism.

41. III.2.2 Chemism 18 min 4

    In chemism objects are defined by their tension towards an opposite, as in chemical affinity, the sexes, or love and friendship. Opposed objects combine through a neutral medium such as water, or language in the mind, and yield a neutral product; separation then restores the extremes. The three resulting syllogisms still depend on conditions supplied from outside. When the object produces its own presuppositions, as in a substance that oxidizes part of itself, the Notion is freed from externality and becomes an End.

42. III.2.3 Teleology 1 h 0 min 9

    Hegel takes up the old opposition of mechanism and purpose and argues that purpose is the truth of mechanism. He credits Kant’s idea of internal purposiveness but criticizes the third antinomy and Kant’s treatment of purpose as a mere maxim of judgment. Purpose forms a syllogism: the subjective end works through a means on external objects. By the “cunning of Reason” the end lets its tools bear the wear, and the plough outranks the enjoyments it yields. Since every realized external end proves to be only a means, the concept’s unity with objectivity is the Idea.

43. III.3 The Idea 17 min 6

    Hegel defines the Idea as the adequate Notion: a concept united with a reality that fully corresponds to it, and so truth in the full sense. Against Kant, for whom Ideas of reason are goals no experience can match, Hegel argues that whatever is actual is so only in so far as it expresses the Idea. Things, states and churches fall apart when concept and reality separate, though even the worst state still embodies its Idea. The Idea is a process, not a resting state. It unfolds as Life, then as Cognition (the True and the Good), and finally as the Absolute Idea.

44. III.3.1 Life 42 min 8

    Life is the Idea in immediate form: a concept present everywhere in an organised body. Hegel distinguishes this logical life from biology and spirit. He then treats the living individual, whose organism consists of members, not parts, and whose functions are sensibility, irritability and reproduction. Next comes the life-process, in which need and pain, contradiction actually existing, drive the organism to assimilate its environment. Last comes the kind, in which individuals find themselves in each other, reproduce and die. That death of immediate life turns into the emergence of spirit and the transition to cognition.

45. III.3.2 The Idea of Cognition 2 h 18 min 14

    Cognition is the Idea that has itself for object but still faces a given world. Hegel first criticises Kant’s treatment of the soul and of the thing-in-itself. He then follows the Idea of the True. Analytic cognition finds determinations in its object. Synthetic cognition proceeds by definition, classification and theorem, with examples from arithmetic, Euclid, natural history and physics, and shows the limits of the geometrical method in philosophy. The Idea of the Good, or will, is higher because it aims at actuality, but against an alien world it stays an endless “ought”. Its reunion with cognition yields the Absolute Idea.

46. III.3.3 The Absolute Idea 59 min 11

    The Absolute Idea unites theoretical and practical Ideas, and it is the only object of philosophy. It has no new content, so the chapter sets out the method of the whole Logic. The method begins with an abstract universal. That universal shows itself to be its own other (the dialectical moment), and the negation of the negation restores a richer unity, which becomes a new beginning. The science is therefore a circle of circles. The Logic ends with the Idea freely releasing itself as nature, the transition to the philosophy of nature and spirit.