Quantity and Measure in Hegel’s Science of Logic Volume 2: Hegel on Being

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Hegel on Being provides an authoritative treatment of Hegel’s entire logic of being. Stephen Houlgate presents the Science of Logic as an important and neglected text within Hegel’s oeuvre that should occupy a more significant place in the history of philisophy. In the Science of Logic, Hegel set forth a distinctive conception of the most fundamental forms of being through a close study of quality, quantity and measure. Exploring the full trajectory of Hegel's logic of being from quality to measure, this two-volumework by a preeminent Hegel scholar situates Hegel's text in relation to the work of Plato, Aristotle, Descartes, Spinoza, Kant, and Frege. Lucidly written, with characteristic philosophical depth and analysis, Houlgate’s Hegel on Being explicates one of Hegel’s most complex works, providing a vital reference for a generation of Hegel scholars and a major contribution to the literature on 19th-century German philosophy. Cover Halftitle page Title page Copyright page CONTENTS PREFACE TO VOLUME 2 NOTE ON REFERENCES AND ABBREVIATIONS ABBREVIATIONS PART ONE Quantum, Number and the Quantitative Ratio CHAPTER ONE Quantum and Number CONTINUOUS AND DISCRETE MAGNIT THE LIMITING OF QUANTITY: THE QUANTUM NUMBER AMOUNT AND UNITY IN NUMBER THE INDIFFERENCE OF NUMBERS HEGEL AND THE GREEKS ON NUMBER CHAPTER TWO Excursus: Hegel on the Operations of Arithmetic NUMBERING AND ADDITION KANT AND HEGEL ON “7 + 5 = 12” MULTIPLICATION AND “RAISING TO A POWER” CHAPTER THREE Excursus: Hegel and Frege – Similarities and Differences FREGE’S PROJECT SIMILARITIES AND DIFFERENCES BETWEEN FREGE AND HEGEL Logicism The objectivity of logic Logic and psychology Proof Logic and truth Logic as “analytic” CHAPTER FOUR Excursus: Frege’s Assumptions FORMAL AND SPECULATIVE LOGIC LOGIC AND ARITHMETIC “FUNCTION” AND “ARGUMENT” IN FREGE’S THOUGHT CONCEPT AND OBJECT THE UNIVERSAL QUANTIFIER THE CONCEPT . . . THE EXTENSION OF A CONCEPT FREGE’S CONTEXT PRINCIPLE CHAPTER FIVE Excursus: Hegel and Frege on Number FREGE’S CRITIQUE OF THE TRADITIONAL (GREEK) CONCEPTION OF NUMBER HEGEL ON “SOMETHING” AND THE “ONE” FREGE ON NUMBERS, OBJECTS AND CONCEPTS FREGE’S DEFINITION OF NUMBER The criterion of identity for numbers Frege’s direct def nition of number Frege’s definitions of 0 and 1 CHAPTER SIX Extensive and Intensive Magnitude EXTENSIVE MAGNITUDE FROM EXTENSIVE TO INTENSIVE MAGNITUDE INTENSIVE MAGNITUDE THE IDENTITY OF EXTENSIVE AND INTENSIVE MAGNITUDE THE CHANGING QUANTUM CONCLUSION CHAPTER SEVEN Quantitative Infinity THE QUANTITATIVE INFINITE PROGRESS THE TRUE INFINITY OF THE QUANTUM THE TRULY INFINITE QUANTUM AND THE DIRECT RATIO CHAPTER EIGHT Excursus: Hegel and Kant’s First Antinomy KANT’S FIRST ANTINOMY: THE THESIS, ITS PROOF AND HEGEL’S CRITIQUE KANT’S FIRST ANTINOMY: THE ANTITHESIS, ITS PROOF AND HEGEL’S CRITIQUE THE RESOLUTION OF THE FIRST ANTINOMY: QUANTITY, SPACE AND TIME CHAPTER NINE The Quantitative Relation or Ratio (Verhältnis) THE DIRECT RATIO THE TRANSITION TO THE INVERSE RATIO THE INVERSE RATIO FURTHER COMPLEXITY IN THE INVERSE RATIO THE TRANSITION TO THE RATIO OF POWERS THE RATIO OF POWERS THE TRANSITION TO MEASURE CHAPTER TEN Excursus: Hegel on Differential Calculus THE PHILOSOPHICAL JUSTIFICATION OF CALCULUS PROBLEMS WITH THE COMMON CONCEPTION OF CALCULUS THE TRUE QUANTITATIVE INFINITE AND THE MATHEMATICAL INFINITE FRACTIONS AND SERIES AS THE RELATION BETWEEN THE “ELEMENTS” OF QUANTITIES NEWTON AND EULER AS A DERIVED FUNCTION OR “DERIVATIVE” (OF A POWER-FUNCTION) FINDING DERIVATIVES BY EXPANDING (OR “DEVELOPING”) BINOMIALS DERIVED FUNCTIONS AS “COEFFICIENTS” AS A RELATION WITH NO “REAL MEANING” PART TWO Measure CHAPTER ELEVEN1 Specific Quantity MEASURE AS A SPECIFIC QUANTUM THE SPECIFYING MEASURE AND SPECIFIC HEAT THE REALIZED MEASURE: GALILEO AND KEPLER QUALITY AND QUANTITY IN THE REALIZED MEASURE BEING-FOR-SELF IN MEASURE: THE “EMPIRICAL COEFFICIENT” THE TRANSITION TO REAL MEASURE CHAPTER TWELVE Real Measure REAL MEASURE AS THE RELATION BETWEEN TWO RATIOS: SPECIFIC GRAVITY REAL MEASURE AS THE COMBINATION OF TWO MEASURES REAL MEASURE AS A SERIES OF MEASURES MEASURES AS EXCLUSIVE UNITIES ELECTIVE AFFINITIES THE “MORE OR LESS” ELECTIVE AFFINITY AND “INTENSITY” COMPLICATIONS: HEGEL AND BERTHOLLET CHAPTER THIRTEEN The Nodal Line and the Measureless THE NODAL LINE OF MEASURE-RELATIONS JUMPS IN NATURE (AND EXAMPLES) THE MEASURELESS CHAPTER FOURTEEN Indifference ABSOLUTE INDIFFERENCE INDIFFERENCE AS THE INVERSE RATIO OF ITS FACTORS INDIFFERENCE AND ITS DASEIN THE CONTRADICTION IN INDIFFERENCE CENTRIPETAL AND CENTRIFUGAL FORCE HEGEL AND SPINOZA CHAPTER FIFTEEN From Measure to Essence INDIFFERENCE AND ESSENCE ESSENCE AS “NON-IMMEDIACY” ESSENCE AND BEING CHAPTER SIXTEEN Conclusion NOTES BIBLIOGRAPHY INDEX