Quantity and measure in Hegel's 'Science of logic':
Volume II: Quantity and Measure in Hegel's 'Science of Logic' continues the discussion of Hegel's logic of being and considers all aspects of quantity and measure in his logic, including his basic categories of being, writings on calculus, philosophy of mathematics, as well as a...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London ; New York ; Oxford ; New Delhi ; Sydney
Bloomsbury Academic
2022
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| Series: | Hegel on being / Stephen Houlgate
Volume 2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Volume II: Quantity and Measure in Hegel's 'Science of Logic' continues the discussion of Hegel's logic of being and considers all aspects of quantity and measure in his logic, including his basic categories of being, writings on calculus, philosophy of mathematics, as well as a comparative study of Hegel and Frege's approach to logic |
| Physical Description: | xvi, 440 Seiten |
| ISBN: | 9781350189850 |
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| 505 | 8 | |a Preface to Volume II -- Note on References and Abbreviations -- List of Abbreviations -- Part 1 Quantum, Number and the Quantitative Ratio -- Chapter 1. Quantum and Number -- Chapter 2. Excursus: Hegel on the Operations of Arithmetic -- Chapter 3. Excursus: Hegel and Frege -- Similarities and Differences -- Chapter 4. Excursus: Frege's Assumptions -- Chapter 5. Excursus: Hegel and Frege on Number -- Chapter 6. Extensive and Intensive Magnitude -- Chapter 7. Quantitative Infinity -- Chapter 8. Excursus: Hegel and Kant's First Antinomy -- Chapter 9. The Quantitative Relation or Ratio (Verhältnis) -- Chapter 10. Hegel on Differential Calculus -- Part 2 Measure -- Chapter 11. Specific Quantity -- Chapter 12. Real Measure -- Chapter 13. The Nodal Line and the Measureless -- Chapter 14. Indifference -- Chapter 15. From Measure to Essence -- Chapter 16. Conclusion -- Notes -- Bibliography -- Index | |
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| adam_text | CONTENTS Preface to Volume 2 ix Note on References and Abbreviations xi List of Abbreviations xiii Part One: Quantum, Number and the Quantitative Ratio 1 Quantum and Number Continuous and discrete magnitude The limiting of quantity: the quantum Number Amount and unity in number The indifference of numbers Hegel and the Greeks on number 3 3 5 10 14 17 20 2 Excursus: Hegel on the Operations of Arithmetic Numbering and addition Kant and Hegel on “7 + 5 = 12” Multiplication and “raising to a power” 25 25 27 30 3 33 36 42 42 43 Excursus: Hegel and Frege - Similarities and Differences Frege’s project Similarities and differences between Frege and Hegel Logicism The objectivity of logic
vi CONTENTS Logic and psychology Proof Logic and truth Logic as “analytic” 45 49 53 54 4 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 5 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 definition of number Frege’s definitions of 0 and 1 91 91 97 102 112 112 120 132 6 Extensive and Intensive Magnitude Extensive magnitude From extensive to intensive magnitude Intensive magnitude The identity of extensive and intensive magnitude The changing quantum Conclusion 139 139 140 145 148 152 157 7 Quantitative Infinity The quantitative infinite progress The true infinity of the quantum The truly infinite quantum and the direct ratio 8 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 59 59 63 68 72 74 80 84 87 159 160 163 166 171 171 175 176
CONTENTS 9 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 IBI 181 184 187 190 197 202 206 10 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 ax 209 209 211 214 219 — 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” 222 225 228 231 234 236 Part Two: Measure 11 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 245 246 250 257 263 267 272 12 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: Flegel and Berth ollet 277 278 283 287 297 300 302 307 310
viii CONTENTS 13 The Nodal Line and the Measureless The nodal line of measure-relations Jumps in nature (and examples) The measureless 315 317 323 328 14 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 337 337 340 346 349 353 356 15 From Measure to Essence Indifference and essence Essence as “non-immediacy” Essence and being 359 359 362 364 16 Conclusion 369 Notes 373 Bibliography 415 Index 421
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| adam_txt |
CONTENTS Preface to Volume 2 ix Note on References and Abbreviations xi List of Abbreviations xiii Part One: Quantum, Number and the Quantitative Ratio 1 Quantum and Number Continuous and discrete magnitude The limiting of quantity: the quantum Number Amount and unity in number The indifference of numbers Hegel and the Greeks on number 3 3 5 10 14 17 20 2 Excursus: Hegel on the Operations of Arithmetic Numbering and addition Kant and Hegel on “7 + 5 = 12” Multiplication and “raising to a power” 25 25 27 30 3 33 36 42 42 43 Excursus: Hegel and Frege - Similarities and Differences Frege’s project Similarities and differences between Frege and Hegel Logicism The objectivity of logic
vi CONTENTS Logic and psychology Proof Logic and truth Logic as “analytic” 45 49 53 54 4 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 5 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 definition of number Frege’s definitions of 0 and 1 91 91 97 102 112 112 120 132 6 Extensive and Intensive Magnitude Extensive magnitude From extensive to intensive magnitude Intensive magnitude The identity of extensive and intensive magnitude The changing quantum Conclusion 139 139 140 145 148 152 157 7 Quantitative Infinity The quantitative infinite progress The true infinity of the quantum The truly infinite quantum and the direct ratio 8 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 59 59 63 68 72 74 80 84 87 159 160 163 166 171 171 175 176
CONTENTS 9 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 IBI 181 184 187 190 197 202 206 10 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 ax 209 209 211 214 219 — 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” 222 225 228 231 234 236 Part Two: Measure 11 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 245 246 250 257 263 267 272 12 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: Flegel and Berth ollet 277 278 283 287 297 300 302 307 310
viii CONTENTS 13 The Nodal Line and the Measureless The nodal line of measure-relations Jumps in nature (and examples) The measureless 315 317 323 328 14 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 337 337 340 346 349 353 356 15 From Measure to Essence Indifference and essence Essence as “non-immediacy” Essence and being 359 359 362 364 16 Conclusion 369 Notes 373 Bibliography 415 Index 421 |
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| contents | Preface to Volume II -- Note on References and Abbreviations -- List of Abbreviations -- Part 1 Quantum, Number and the Quantitative Ratio -- Chapter 1. Quantum and Number -- Chapter 2. Excursus: Hegel on the Operations of Arithmetic -- Chapter 3. Excursus: Hegel and Frege -- Similarities and Differences -- Chapter 4. Excursus: Frege's Assumptions -- Chapter 5. Excursus: Hegel and Frege on Number -- Chapter 6. Extensive and Intensive Magnitude -- Chapter 7. Quantitative Infinity -- Chapter 8. Excursus: Hegel and Kant's First Antinomy -- Chapter 9. The Quantitative Relation or Ratio (Verhältnis) -- Chapter 10. Hegel on Differential Calculus -- Part 2 Measure -- Chapter 11. Specific Quantity -- Chapter 12. Real Measure -- Chapter 13. The Nodal Line and the Measureless -- Chapter 14. Indifference -- Chapter 15. From Measure to Essence -- Chapter 16. Conclusion -- Notes -- Bibliography -- Index |
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| spelling | Houlgate, Stephen 1954- Verfasser (DE-588)132366746 aut Quantity and measure in Hegel's 'Science of logic' Stephen Houlgate Hegel on being: euantity and measure in Hegel's 'Science of logic' London ; New York ; Oxford ; New Delhi ; Sydney Bloomsbury Academic 2022 xvi, 440 Seiten txt rdacontent n rdamedia nc rdacarrier Hegel on being / Stephen Houlgate Volume 2 Preface to Volume II -- Note on References and Abbreviations -- List of Abbreviations -- Part 1 Quantum, Number and the Quantitative Ratio -- Chapter 1. Quantum and Number -- Chapter 2. Excursus: Hegel on the Operations of Arithmetic -- Chapter 3. Excursus: Hegel and Frege -- Similarities and Differences -- Chapter 4. Excursus: Frege's Assumptions -- Chapter 5. Excursus: Hegel and Frege on Number -- Chapter 6. Extensive and Intensive Magnitude -- Chapter 7. Quantitative Infinity -- Chapter 8. Excursus: Hegel and Kant's First Antinomy -- Chapter 9. The Quantitative Relation or Ratio (Verhältnis) -- Chapter 10. Hegel on Differential Calculus -- Part 2 Measure -- Chapter 11. Specific Quantity -- Chapter 12. Real Measure -- Chapter 13. The Nodal Line and the Measureless -- Chapter 14. Indifference -- Chapter 15. From Measure to Essence -- Chapter 16. Conclusion -- Notes -- Bibliography -- Index Volume II: Quantity and Measure in Hegel's 'Science of Logic' continues the discussion of Hegel's logic of being and considers all aspects of quantity and measure in his logic, including his basic categories of being, writings on calculus, philosophy of mathematics, as well as a comparative study of Hegel and Frege's approach to logic Hegel, Georg Wilhelm Friedrich 1770-1831 Wissenschaft der Logik (DE-588)4113863-6 gnd rswk-swf Metrologie (DE-588)4169749-2 gnd rswk-swf Quantität (DE-588)4245395-1 gnd rswk-swf Hegel, Georg Wilhelm Friedrich / 1770-1831 / Wissenschaft der Logik / English Logic Wissenschaft der Logik (Hegel, Georg Wilhelm Friedrich) Hegel, Georg Wilhelm Friedrich 1770-1831 Wissenschaft der Logik (DE-588)4113863-6 u Quantität (DE-588)4245395-1 s Metrologie (DE-588)4169749-2 s DE-604 Print version Erscheint auch als Online-Ausgabe 978-1-350-18988-1 Erscheint auch als Online-Ausgabe 9781-350-18986-7 Stephen Houlgate Hegel on being Volume 2 (DE-604)BV047883999 2 Digitalisierung BSB München - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033243659&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Houlgate, Stephen 1954- Quantity and measure in Hegel's 'Science of logic' Preface to Volume II -- Note on References and Abbreviations -- List of Abbreviations -- Part 1 Quantum, Number and the Quantitative Ratio -- Chapter 1. Quantum and Number -- Chapter 2. Excursus: Hegel on the Operations of Arithmetic -- Chapter 3. Excursus: Hegel and Frege -- Similarities and Differences -- Chapter 4. Excursus: Frege's Assumptions -- Chapter 5. Excursus: Hegel and Frege on Number -- Chapter 6. Extensive and Intensive Magnitude -- Chapter 7. Quantitative Infinity -- Chapter 8. Excursus: Hegel and Kant's First Antinomy -- Chapter 9. The Quantitative Relation or Ratio (Verhältnis) -- Chapter 10. Hegel on Differential Calculus -- Part 2 Measure -- Chapter 11. Specific Quantity -- Chapter 12. Real Measure -- Chapter 13. The Nodal Line and the Measureless -- Chapter 14. Indifference -- Chapter 15. From Measure to Essence -- Chapter 16. Conclusion -- Notes -- Bibliography -- Index Hegel, Georg Wilhelm Friedrich 1770-1831 Wissenschaft der Logik (DE-588)4113863-6 gnd Metrologie (DE-588)4169749-2 gnd Quantität (DE-588)4245395-1 gnd |
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| title | Quantity and measure in Hegel's 'Science of logic' |
| title_alt | Hegel on being: euantity and measure in Hegel's 'Science of logic' |
| title_auth | Quantity and measure in Hegel's 'Science of logic' |
| title_exact_search | Quantity and measure in Hegel's 'Science of logic' |
| title_exact_search_txtP | Quantity and measure in Hegel's 'Science of logic' |
| title_full | Quantity and measure in Hegel's 'Science of logic' Stephen Houlgate |
| title_fullStr | Quantity and measure in Hegel's 'Science of logic' Stephen Houlgate |
| title_full_unstemmed | Quantity and measure in Hegel's 'Science of logic' Stephen Houlgate |
| title_short | Quantity and measure in Hegel's 'Science of logic' |
| title_sort | quantity and measure in hegel s science of logic |
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| topic_facet | Hegel, Georg Wilhelm Friedrich 1770-1831 Wissenschaft der Logik Metrologie Quantität |
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