A Commentary to Hegel's Science of Logic

Also by David Gray Carlson

HEGEL'S THEORY OF THE SUBJECT

A Commentary to Hegel'sScience of LogicDavid Gray Carlson

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* © David Gray Carlson 2007 Softcover reprint of the hardcover 1st edition 2007978-1-4039-8628-3

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ISBN 978-1-349-54073-0 DOll 0.1 057/9780230598904

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Library of Congress Cataloging-in-Publication Data Carlson, David (David Gray)

A commentary to Hegel's Science of logic I David Gray Carlson. p.cm.

Includes bibliographical references and index. ISBN 978-1-349-54073-0

1. Hegel. Georg Wilhelm Friedrich, 1770-1831. Wissenschaft der Logik. 2. Logic. I. Title.

B2942.Z7C372006 160-dc22

10 9 8 7 6 5 16 15 14 13 12 11

2006046893

4 3 10 09 08

For Jeanne, my inspiration.

Contents

Acknowledgements xiiiIntroduction 1

Part I Quality 7

Chapter 1. Being-Nothing-Becoming 9A. Pure Being 9B. Pure Nothing 14C. Becoming 15

(a) The Unity of Being and Nothing 15With What Must Science Begin? 26The Opposition of Being and Nothing in Ordinary Thinking 39Defectiveness of the Expression: Unity, Identity of Being and Nothing 42Incomprehensibility of the Beginning 44

(b) Moments of Becoming: Coming-to-Be and Ceasing-to-Be 46(c) Sublation of Becoming 47

The Nature of HegeVs Logic 48

Chapter 2. Determinate Being 54A. Determinate Being as Such 55

(a) Determinate Being in General 55(b) Quality 57(c) Something 63

B. Finitude 69(a) Something and an Other 70(b) Determination, Constitution and Limit 77(c) Finitude 85

(a) The Immediacy of Finitude 86(fi) Limitation and the Ought 86The Ought 89(y) Transition of the Finite into the Infinite 91

C. Infinity 93(a) The Infinite in General 94(b) Alternating Determination of the Finite and the Infinite 94(c) Affirmative Infinity 97

Idealism 101

Chapter 3. Being-For-Self 103A. Being-For-Self as Such 104

(a) Determinate Being and Being-For-Self 104

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(b) Being-For-One 106Was fur ein Ding? 108

(c) The One 109B. The One and the Many 111

(a) The One in Its Own Self 112(b) The One and the Void 115

Atomism 115(c) Many Ones: Repulsion 117

C. Repulsion and Attraction 120(a) Exclusion of the One 120

The Unity of the One and the Many 125(b) The One One of Attraction 127(c) The Relation of Repulsion and Attraction 129

Conclusion 134

Part II Quantity 137

Chapter 4. Pure Quantity 139A. Pure Quantity 142

Quantitative Limit 145Kanfs Second Antinomy 149

B. Continuous and Discrete Magnitude 153C. Limitation of Quantity 155

Chapter 5. Quantum 157A. Number 157

Geometry and Arithmetic 160B. Extensive and Intensive Quantum 166

(a) Their Difference 166(b) Identity of Extensive and Intensive Magnitude 169(c) Alteration of Quantum 171

C. Quantitative Infinity 172(a) Its Notion 172(b) The Quantitative Infinite Progress 174

The High Repute of the Progress to Infinity 175Kant's Antinomy of the Limitation of Time and Space 111

(c) The Infinity of Quantum 179Calculus 181

Chapter 6. Quantitative Relation 183A. The Direct Ratio 185B. Inverse Ratio 186C. The Ratio of Powers 189

Conclusion 192

Part III Measure 195

Chapter 7. Measure and Specific Quantity 197A. The Specific Quantum 204

Contents ix

B. Specifying Measure 208(a) Rule 208(b) Specifying Measure 210(c) Relation of the two Sides as Qualities 212

C. Being-For-Self in Measure 215

Chapter 8. Real Measure 218A. The Relation of Self-Subsistent Measures 220

(a) Combination of Two Measures 220(b) Measure as a Series of Measure Relations 225(c) Elective Affinity 228

B. Nodal Line of Measure-Relations 230C. The Measureless 234

Chapter 9. The Becoming of Essence 239A. Absolute Indifference 239B. Indifference as Inverse Ratio of Its Factors 240C. Transition into Essence 246

Conclusion 248

Part IV Reflection 249

Chapter 10. Illusory Being 251A. The Essential and the Unessential 258B. Illusory Being 261C. Reflection 266

(a) Positing Reflection 268(b) External Reflection 273(c) Determining Reflection 274

Chapter 11. Determinations of Reflection 278A. Identity 279

The First Original Law of Thought 281B. Difference 284

(a) Absolute Difference 284(b) Diversity 285

The Law of Diversity 289(c) Opposition 290

Opposite Magnitudes in Arithmetic and Ethics 294C. Contradiction 297

The Law of the Excluded Middle 302The Law of Contradiction 303

Chapter 12 Ground 306A. Absolute Ground 309

(a) Form and Essence 309(b) Form and Matter 314(c) Form and Content 317

B. Determinate Ground 318

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(a) Formal Ground 318(b) Real Ground 322(c) The Complete Ground 325

C. Condition 328(a) The Relatively Unconditioned 328(b) The Absolutely Unconditioned 331(c) Emergence of the Fact [Sache] into Existence 334Conclusion 337

Part V Appearance 339

Chapter 13. Existence 341A. The Thing and Its Properties 346

(a) The Thing-in-Itself and Existence 346(b) Property 349(c) The Reciprocal Action of Things 351

B. The Constitution of the Thing Out of Matters 354C. Dissolution of the Thing 357

Chapter 14. Appearance 360A. The Law of Appearance 361B. The World of Appearance and the World-in-Itself 368C. Dissolution of Appearance 372

Chapter 15. Essential Relation 375A. Relation of Whole and Parts 376B. Relation of Force and Its Expression 381

(a) The Conditionedness of Force 383(b) The Solicitation of Force 384(c) The Infinity of Force 386

C. The Relation of Outer and Inner 387

Part VI Actuality 391

Chapter 16. The Absolute 393A. The Exposition of the Absolute 394B. The Absolute Attribute 397C. The Mode of the Absolute 398

Chapter 17. Actuality 402A. Contingency 403B. Real Actuality, Possibility, and Necessity 407C. Absolute Necessity 410

Chapter 18. The Absolute Relation 414A. The Relation of Substantiality 415B. The Relation of Causality 418

(a) Formal Causality 419(b) The Determinate Relation of Causality 420

Contents xi

(c) Action and Reaction 424C. Reciprocity 426

Conclusion 431

Part VII Subjectivity 433

Chapter 19. The Notion 435A. The Universal Notion 445B. The Particular Notion 449C. The Individual 454

Chapter 20. Judgment 459A. The Judgment of Existence (Inherence) 464

(a) The Positive Judgment 466(b) The Negative Judgment 469(c) The Infinite Judgment 473

B. The Judgment of Reflection 477(a) The Singular Judgment 478(b) The Particular Judgment 479(c) The Universal Judgment 480

C. The Judgment of Necessity 482(a) The Categorical Judgment 483(b) The Hypothetical Judgment 484(c) The Disjunctive Judgment 486

D. The Judgment of the Notion 488(a) The Assertoric Judgment 488(b) The Problematic Judgment 490(c) The Apodeictic Judgment 491

Chapter 21. Syllogism 495A. The Syllogism of Existence 497

(a) IPU 498(b) PIU 500(c) IUP 502(d) Mathematical Syllogism 503

B. The Syllogism of Reflection 505(a) The Syllogism of Allness 505(b) The Syllogism of Induction 507(c) The Syllogism of Analogy 508

C. The Syllogism of Necessity 512(a) The Categorical Syllogism 512(b) The Hypothetical Syllogism 514(c) The Disjunctive Syllogism 517

Part VIII Objectivity 521

Chapter 22. Mechanism 523A. The Mechanical Object 526B. The Mechanical Process 529

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(a) The Formal Mechanical Process 530(b) The Real Mechanical Process 532(c) The Product of the Mechanical Process 535

C. Absolute Mechanism 536(a) The Center 536(b) Law 538(c) Transition of Mechanism 539

Chapter 23. Chemism 541A. The Chemical Object 542B. The Chemical Process 543C. Transition of Chemism 546

Chapter 24. Teleology 547A. Subjective End 550B. Means 552C. The Realized End 553

Part IX Idea 561

Chapter 25. Life 563A. The Living Individual 564B. The Life-Process 567C. Genus 569

Chapter 26. Cognition 572A. The Idea of the True 576

(a) Analytic Cognition 579(b) Synthetic Cognition 582

1. Definition 5832. Division 5873. Theorem 587

B. The Idea of the Good 588

Chapter 27. Absolute Idea 593

Chapter 28. Conclusion 604

Bibliography 608

Index 617Appendix: The Steps of the Logic 629

Acknowledgements

I have incurred countless debts in producing this work. I owe much toeight years worth of students at the Benjamin N. Cardozo School ofLaw in New York who have suffered through a seminar on the Scienceof Logic and who never failed to teach me something about the subject.I also owe a debt of gratitude to the Cardozo Law School itself forallowing the course to be taught in the first place and for a researchprofessorship that helped me finish this work in 2005. Thanks go to theeditors of the Cardozo Law Review, who worked diligently to improvethe preliminary versions of first nine chapters of this book, to mybeloved partner Jeanne Schroeder, whose expertise in Hegel andJacques Lacan (Hegel's modern disciple) have been a sine qua non ofthis project, to Arthur Jacobson, without whose patience andprodigious knowledge of Hegel and mathematics I could never havefathomed Hegel's seemingly endless commentary on the calculus, toJon Heiner, who skeptically read this manuscript from an empiricistperspective, to Drucilla Cornell, who first convinced me that Hegel wasworth the considerable investment in learning his vocabulary, to CynGabriel, who worked diligently and faithfully for years on the artworkfor this project, to John Burbidge, Stephen Houlgate, Jean Hyppolyte,Herbert Marcuse, Robert Pippen, Stanley Rosen, Richard DienWinfield, and Slavoj £i2ek (to mention just a few), whose works havebeen essential in expanding my understanding of the Science of Logic.

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