Quantity and Measure in Hegel’s Science of Logic (Hegel on Being, Volume 2)

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