The concept of motion in ancient Greek thought: foundations in logic, method, and mathematics
"The main object of this book is to study how the understanding of physical motion in ancient Greek thought developed before and up to Aristotle. It investigates which logical, methodological, and mathematical foundations had to be in place to establish a fullyfledged concept of motion that als...
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| Format: | Buch |
| Sprache: | English |
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Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore
Cambridge University Press
2020
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| Online-Zugang: | Inhaltsverzeichnis Klappentext Inhaltsverzeichnis Klappentext |
| Zusammenfassung: | "The main object of this book is to study how the understanding of physical motion in ancient Greek thought developed before and up to Aristotle. It investigates which logical, methodological, and mathematical foundations had to be in place to establish a fullyfledged concept of motion that also allows for comparing and measuring speed.1 Given that physical motion is the core concept of natural philosophy, this study thereby also seeks to reconstruct in rough outlines how natural philosophy came to be established as a proper scientific endeavour in ancient Greece.2 According to a prevailing picture, scientific investigation of physical motion and change started properly in the West with Aristotle but only achieved its true form in modern times, with the overthrow of central Aristotelian doctrines. In the early modern period, so runs the narrative, Aristotelianism was rejected and the basis laid for what today we consider the science of physics.3 This interpretation is at least doubly misleading." |
| Beschreibung: | x, 427 Seiten Illustrationen |
| ISBN: | 9781108477901 |
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Datensatz im Suchindex
| _version_ | 1804181840896983040 |
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| adam_text | CONTENTS Acknowledgements Introduction page ix 1 Overview of the Project 1 Methodology, Treatment of Sources, and Relationships of Thinkers Investigated 5 Overview of the Chapters 11 1 Conceptual Foundations 17 1.1 The Concepts of Kinesis, Physis, and Natural Philosophy 17 1.1.1 The Concept of Motion (Kinesis) 17 1.1.2 The Ancient Greek Conceptions of Physis and Natural Philosophy 27 1.1.3 The Concept of Being 30 1.2 Criteria of Inquiry 31 1.2.1 The Principle of Non-Contradiction 32 1.2.2 The Principle of Excluded Middle 37 1.2.3 The Principle of Sufficient Reason 39 1.2.4 Rational Admissibility 46 1.2.5 Saving the Phenomena 49 1.3 The Role of Logic 53 1.3.1 Operators and Operands 55 1.3.2 Negation and Identity as Operators 57 1.4 The Role of Mathematics: The Connection between Mathematics and Natural Philosophy 67 1.4.1 The Use of Mathematics for Science in General 67 1.4.2 How to Do Things with Numbers: Measurement and Countability 73 2 Parmenides’ Account of the Object of Philosophy 80 2.1 Introduction 80 2.2 Parmenides’ Criteria for Philosophy and His Logical Apparatus 2.2.1 Criteria for Philosophy 83 2.2.2 Logical Operators 92 2.3 Parmenides’Logical Apparatus as Intimately Tied to His Ontology 2.4 Problems for the Very Possibility of Natural Philosophy 111 v 83 103
vi CONTENTS 2.4.1 The Absence of Adequate Basic Concepts for Natural Philosophy 111 2.4.2 No Distinction between Operators and Operands 114 2.4.3 The Indeterminacy of Background Concepts 116 2.4.4 Problems with Relations 117 2.5 Relation to the Doxa Part: The Role of Cosmology 119 3 Zeno’s Paradoxes of Motion and Plurality 124 3.1 Introduction 124 3.2 The General Aim of Zeno’s Paradoxes 128 3.3 Parmenidean Inheritance 130 3.3.1 Advancing Parmenides’Criteria 130 3.3.2 Deepening of the Challenge Parmenides Poses 134 3.4 The Fragments, Their Sources, and Their Connection 134 3.5 The Paradoxes of Plurality 136 3.6 The Paradoxes of Motion 143 3.6.1 The Dichotomy: Passing Infinitely Many Segments in a Finite Time 144 3.6.2 Achilles: A Variation of the Dichotomy Paradox 155 3.6.3 The Flying Arrow: Motion as a Sequence of Rests 156 3.6.4 The Moving Rows: Double the Time Is Half the Time 164 3.6.5 The Basic Problems of All Paradoxes of Motion 174 4 The Atomistic Foundation for an Account of Motion 176 4.1 Introduction 176 4.2 Eleatic Inheritance in the Atomists 178 4.2.1 Rational Admissibility 179 4.2.2 Consistency 182 4.2.3 The Principle of Sufficient Reason 183 4.3 Atomistic Changes 184 4.3.1 What Truly Is Must Explain the Phenomena 184 4.3.2 A Physical Theory 185 4.3.3 Change of Logical Operators 187 4.3.4 The Atomistic Account of What Is 190 4.3.5 New Physical Features and Their Functions 191 4.4 Consequences of the Atomistic Changes for Natural Philosophy 4.4.1 Reply to Eleatic Problems 194 4.4.2 Motion and Changes in the Atomistic Framework 198 4.4.3 Problems that Remain 200 5
The Possibility of Natural Philosophy According to Plato I: The Logical Basis 202 5.1 Introduction: The Investigation of the Natural World as an Eikös Mythos 202 5.2 The Sophist 210 5.2.1 The Reinterpretation of Negation and the Connection Operator 211 194
vii CONTENTS 5.2.2 The Reinterpretation of the Criteria for Philosophy 1: The Principle of Non-Contradiction and the Principle of Excluded Middle 225 5.2.3 Widening the Conceptual Possibilities 230 5.2.4 Possible Answers to Parmenides’ Problems 232 5.3 The Timaeus: Logical Advances 235 5.3.1 The Reinterpretation of the Criteria for Philosophy 2: The Principle of Sufficiënt Reason and Rational Admissibility 236 5.3.2 An Eikös Mythos 240 6 The Possibility of Natural Philosophy According to Plato II: Mathematical Advances and Ultimate Problems 245 6.1 Introduction 245 6.2 Introducing Mathematical Structures 246 6.3 Locomotion and Mathematical Structures 253 6.3.1 Time and Eternity 253 6.3.2 Time as the Measure of Motion 256 6.3.3 Space as Excluded from the Measurement Process 6.4 Problems with a Simple Measure 269 6.4.1 Restricted Comparability 274 6.4.2 Lacking Consistency: The Tortoise Wins the Race 7 266 274 Aristotle’s Notion of Continuity: The Structure Underlying Motion 277 7.1 Introduction 277 7.2 Notions of Magnitude Influencing Aristotle’s Concept of a Continuum 284 7.2.1 Parmenides’ Suneches 285 7.2.2 Atomistic Notions of Magnitude 289 7.2.3 A Mathematical Notion of Suneches 291 7.3 Aristotle’s Two Accounts of the Continuum 295 7.3.1 Things Whose Limits Touch and Are One 296 7.3.2 Things Being Divisible without Limits 299 7.4 Implications of Aristotle’s Concept of a Continuum 303 7.4.1 A New Understanding of the Part-Whole Relation 305 7.4.2 A New Twofold Concept of a Limit 311 7.4.3 A New Conception of Infinity 328 8 Time and Space: The Implicit Measure of Motion in
Aristotle’s Physics 335 8.1 The General Concept of Measure in Aristotle’s Metaphysics 337 8.1.1 A Simple Measure: Being One-Dimensional and of the Same Kind as What Is Measured 338 8.1.2 Comparison with a Modern Conception and the Relation between Counting and Measuring 344
CONTENTS 8.2 The Measure of Movement in Aristotle’s Physics 350 8.2.1 Time as a One-Dimensional Measure and Number of Motion 351 8.2.2 The Search for a Measure of the Same Kind as Motion 8.2.3 The Relation of Time and Space 374 9 Time as the Simple Measure of Motion 385 9.1 Other Accounts of Speed 385 9.2 Reasons Why Aristotle did not Explicitly Use a Complex Measure 9.3 Constructive Developments: A Résumé 403 Bibliography Index Locorum General Index 404 423 426 356 393
This book examines the birth of the scientific understanding ot motion. It investigates which logical tools and methodological principles had to be in place to gi e a consistent account ot motion, and which mathematical notions were introduced to gain control over conceptual problems of motiem. It shows how the idea ot motion raised two fundamental problems in the fifth and fourth centu։՜}՜ ВСЕ: bringing together Being and nonBeing, and bringing together time and space. The first problem leads to the exclusion of motion trom the realm ot rational investigation in Parmenides, the second to Zeno s paradoxes ot motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitlv in the atomists, and explicitly in Plato, who also emplovs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline ot the fundamental framework with which we conceptualise motion todav.
CONTENTS Acknowledgements Introduction page ix 1 Overview of the Project 1 Methodology, Treatment of Sources, and Relationships of Thinkers Investigated 5 Overview of the Chapters 11 1 Conceptual Foundations 17 1.1 The Concepts of Kinesis, Physis, and Natural Philosophy 17 1.1.1 The Concept of Motion (Kinesis) 17 1.1.2 The Ancient Greek Conceptions of Physis and Natural Philosophy 27 1.1.3 The Concept of Being 30 1.2 Criteria of Inquiry 31 1.2.1 The Principle of Non-Contradiction 32 1.2.2 The Principle of Excluded Middle 37 1.2.3 The Principle of Sufficient Reason 39 1.2.4 Rational Admissibility 46 1.2.5 Saving the Phenomena 49 1.3 The Role of Logic 53 1.3.1 Operators and Operands 55 1.3.2 Negation and Identity as Operators 57 1.4 The Role of Mathematics: The Connection between Mathematics and Natural Philosophy 67 1.4.1 The Use of Mathematics for Science in General 67 1.4.2 How to Do Things with Numbers: Measurement and Countability 73 2 Parmenides’ Account of the Object of Philosophy 80 2.1 Introduction 80 2.2 Parmenides’ Criteria for Philosophy and His Logical Apparatus 2.2.1 Criteria for Philosophy 83 2.2.2 Logical Operators 92 2.3 Parmenides’Logical Apparatus as Intimately Tied to His Ontology 2.4 Problems for the Very Possibility of Natural Philosophy 111 v 83 103
vi CONTENTS 2.4.1 The Absence of Adequate Basic Concepts for Natural Philosophy 111 2.4.2 No Distinction between Operators and Operands 114 2.4.3 The Indeterminacy of Background Concepts 116 2.4.4 Problems with Relations 117 2.5 Relation to the Doxa Part: The Role of Cosmology 119 3 Zeno’s Paradoxes of Motion and Plurality 124 3.1 Introduction 124 3.2 The General Aim of Zeno’s Paradoxes 128 3.3 Parmenidean Inheritance 130 3.3.1 Advancing Parmenides’Criteria 130 3.3.2 Deepening of the Challenge Parmenides Poses 134 3.4 The Fragments, Their Sources, and Their Connection 134 3.5 The Paradoxes of Plurality 136 3.6 The Paradoxes of Motion 143 3.6.1 The Dichotomy: Passing Infinitely Many Segments in a Finite Time 144 3.6.2 Achilles: A Variation of the Dichotomy Paradox 155 3.6.3 The Flying Arrow: Motion as a Sequence of Rests 156 3.6.4 The Moving Rows: Double the Time Is Half the Time 164 3.6.5 The Basic Problems of All Paradoxes of Motion 174 4 The Atomistic Foundation for an Account of Motion 176 4.1 Introduction 176 4.2 Eleatic Inheritance in the Atomists 178 4.2.1 Rational Admissibility 179 4.2.2 Consistency 182 4.2.3 The Principle of Sufficient Reason 183 4.3 Atomistic Changes 184 4.3.1 What Truly Is Must Explain the Phenomena 184 4.3.2 A Physical Theory 185 4.3.3 Change of Logical Operators 187 4.3.4 The Atomistic Account of What Is 190 4.3.5 New Physical Features and Their Functions 191 4.4 Consequences of the Atomistic Changes for Natural Philosophy 4.4.1 Reply to Eleatic Problems 194 4.4.2 Motion and Changes in the Atomistic Framework 198 4.4.3 Problems that Remain 200 5
The Possibility of Natural Philosophy According to Plato I: The Logical Basis 202 5.1 Introduction: The Investigation of the Natural World as an Eikös Mythos 202 5.2 The Sophist 210 5.2.1 The Reinterpretation of Negation and the Connection Operator 211 194
vii CONTENTS 5.2.2 The Reinterpretation of the Criteria for Philosophy 1: The Principle of Non-Contradiction and the Principle of Excluded Middle 225 5.2.3 Widening the Conceptual Possibilities 230 5.2.4 Possible Answers to Parmenides’ Problems 232 5.3 The Timaeus: Logical Advances 235 5.3.1 The Reinterpretation of the Criteria for Philosophy 2: The Principle of Sufficiënt Reason and Rational Admissibility 236 5.3.2 An Eikös Mythos 240 6 The Possibility of Natural Philosophy According to Plato II: Mathematical Advances and Ultimate Problems 245 6.1 Introduction 245 6.2 Introducing Mathematical Structures 246 6.3 Locomotion and Mathematical Structures 253 6.3.1 Time and Eternity 253 6.3.2 Time as the Measure of Motion 256 6.3.3 Space as Excluded from the Measurement Process 6.4 Problems with a Simple Measure 269 6.4.1 Restricted Comparability 274 6.4.2 Lacking Consistency: The Tortoise Wins the Race 7 266 274 Aristotle’s Notion of Continuity: The Structure Underlying Motion 277 7.1 Introduction 277 7.2 Notions of Magnitude Influencing Aristotle’s Concept of a Continuum 284 7.2.1 Parmenides’ Suneches 285 7.2.2 Atomistic Notions of Magnitude 289 7.2.3 A Mathematical Notion of Suneches 291 7.3 Aristotle’s Two Accounts of the Continuum 295 7.3.1 Things Whose Limits Touch and Are One 296 7.3.2 Things Being Divisible without Limits 299 7.4 Implications of Aristotle’s Concept of a Continuum 303 7.4.1 A New Understanding of the Part-Whole Relation 305 7.4.2 A New Twofold Concept of a Limit 311 7.4.3 A New Conception of Infinity 328 8 Time and Space: The Implicit Measure of Motion in
Aristotle’s Physics 335 8.1 The General Concept of Measure in Aristotle’s Metaphysics 337 8.1.1 A Simple Measure: Being One-Dimensional and of the Same Kind as What Is Measured 338 8.1.2 Comparison with a Modern Conception and the Relation between Counting and Measuring 344
CONTENTS 8.2 The Measure of Movement in Aristotle’s Physics 350 8.2.1 Time as a One-Dimensional Measure and Number of Motion 351 8.2.2 The Search for a Measure of the Same Kind as Motion 8.2.3 The Relation of Time and Space 374 9 Time as the Simple Measure of Motion 385 9.1 Other Accounts of Speed 385 9.2 Reasons Why Aristotle did not Explicitly Use a Complex Measure 9.3 Constructive Developments: A Résumé 403 Bibliography Index Locorum General Index 404 423 426 356 393
This book examines the birth of the scientific understanding ot motion. It investigates which logical tools and methodological principles had to be in place to gi e a consistent account ot motion, and which mathematical notions were introduced to gain control over conceptual problems of motiem. It shows how the idea ot motion raised two fundamental problems in the fifth and fourth centu։՜}՜ ВСЕ: bringing together Being and nonBeing, and bringing together time and space. The first problem leads to the exclusion of motion trom the realm ot rational investigation in Parmenides, the second to Zeno s paradoxes ot motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitlv in the atomists, and explicitly in Plato, who also emplovs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline ot the fundamental framework with which we conceptualise motion todav.
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| adam_txt |
CONTENTS Acknowledgements Introduction page ix 1 Overview of the Project 1 Methodology, Treatment of Sources, and Relationships of Thinkers Investigated 5 Overview of the Chapters 11 1 Conceptual Foundations 17 1.1 The Concepts of Kinesis, Physis, and Natural Philosophy 17 1.1.1 The Concept of Motion (Kinesis) 17 1.1.2 The Ancient Greek Conceptions of Physis and Natural Philosophy 27 1.1.3 The Concept of Being 30 1.2 Criteria of Inquiry 31 1.2.1 The Principle of Non-Contradiction 32 1.2.2 The Principle of Excluded Middle 37 1.2.3 The Principle of Sufficient Reason 39 1.2.4 Rational Admissibility 46 1.2.5 Saving the Phenomena 49 1.3 The Role of Logic 53 1.3.1 Operators and Operands 55 1.3.2 Negation and Identity as Operators 57 1.4 The Role of Mathematics: The Connection between Mathematics and Natural Philosophy 67 1.4.1 The Use of Mathematics for Science in General 67 1.4.2 How to Do Things with Numbers: Measurement and Countability 73 2 Parmenides’ Account of the Object of Philosophy 80 2.1 Introduction 80 2.2 Parmenides’ Criteria for Philosophy and His Logical Apparatus 2.2.1 Criteria for Philosophy 83 2.2.2 Logical Operators 92 2.3 Parmenides’Logical Apparatus as Intimately Tied to His Ontology 2.4 Problems for the Very Possibility of Natural Philosophy 111 v 83 103
vi CONTENTS 2.4.1 The Absence of Adequate Basic Concepts for Natural Philosophy 111 2.4.2 No Distinction between Operators and Operands 114 2.4.3 The Indeterminacy of Background Concepts 116 2.4.4 Problems with Relations 117 2.5 Relation to the Doxa Part: The Role of Cosmology 119 3 Zeno’s Paradoxes of Motion and Plurality 124 3.1 Introduction 124 3.2 The General Aim of Zeno’s Paradoxes 128 3.3 Parmenidean Inheritance 130 3.3.1 Advancing Parmenides’Criteria 130 3.3.2 Deepening of the Challenge Parmenides Poses 134 3.4 The Fragments, Their Sources, and Their Connection 134 3.5 The Paradoxes of Plurality 136 3.6 The Paradoxes of Motion 143 3.6.1 The Dichotomy: Passing Infinitely Many Segments in a Finite Time 144 3.6.2 Achilles: A Variation of the Dichotomy Paradox 155 3.6.3 The Flying Arrow: Motion as a Sequence of Rests 156 3.6.4 The Moving Rows: Double the Time Is Half the Time 164 3.6.5 The Basic Problems of All Paradoxes of Motion 174 4 The Atomistic Foundation for an Account of Motion 176 4.1 Introduction 176 4.2 Eleatic Inheritance in the Atomists 178 4.2.1 Rational Admissibility 179 4.2.2 Consistency 182 4.2.3 The Principle of Sufficient Reason 183 4.3 Atomistic Changes 184 4.3.1 What Truly Is Must Explain the Phenomena 184 4.3.2 A Physical Theory 185 4.3.3 Change of Logical Operators 187 4.3.4 The Atomistic Account of What Is 190 4.3.5 New Physical Features and Their Functions 191 4.4 Consequences of the Atomistic Changes for Natural Philosophy 4.4.1 Reply to Eleatic Problems 194 4.4.2 Motion and Changes in the Atomistic Framework 198 4.4.3 Problems that Remain 200 5
The Possibility of Natural Philosophy According to Plato I: The Logical Basis 202 5.1 Introduction: The Investigation of the Natural World as an Eikös Mythos 202 5.2 The Sophist 210 5.2.1 The Reinterpretation of Negation and the Connection Operator 211 194
vii CONTENTS 5.2.2 The Reinterpretation of the Criteria for Philosophy 1: The Principle of Non-Contradiction and the Principle of Excluded Middle 225 5.2.3 Widening the Conceptual Possibilities 230 5.2.4 Possible Answers to Parmenides’ Problems 232 5.3 The Timaeus: Logical Advances 235 5.3.1 The Reinterpretation of the Criteria for Philosophy 2: The Principle of Sufficiënt Reason and Rational Admissibility 236 5.3.2 An Eikös Mythos 240 6 The Possibility of Natural Philosophy According to Plato II: Mathematical Advances and Ultimate Problems 245 6.1 Introduction 245 6.2 Introducing Mathematical Structures 246 6.3 Locomotion and Mathematical Structures 253 6.3.1 Time and Eternity 253 6.3.2 Time as the Measure of Motion 256 6.3.3 Space as Excluded from the Measurement Process 6.4 Problems with a Simple Measure 269 6.4.1 Restricted Comparability 274 6.4.2 Lacking Consistency: The Tortoise Wins the Race 7 266 274 Aristotle’s Notion of Continuity: The Structure Underlying Motion 277 7.1 Introduction 277 7.2 Notions of Magnitude Influencing Aristotle’s Concept of a Continuum 284 7.2.1 Parmenides’ Suneches 285 7.2.2 Atomistic Notions of Magnitude 289 7.2.3 A Mathematical Notion of Suneches 291 7.3 Aristotle’s Two Accounts of the Continuum 295 7.3.1 Things Whose Limits Touch and Are One 296 7.3.2 Things Being Divisible without Limits 299 7.4 Implications of Aristotle’s Concept of a Continuum 303 7.4.1 A New Understanding of the Part-Whole Relation 305 7.4.2 A New Twofold Concept of a Limit 311 7.4.3 A New Conception of Infinity 328 8 Time and Space: The Implicit Measure of Motion in
Aristotle’s Physics 335 8.1 The General Concept of Measure in Aristotle’s Metaphysics 337 8.1.1 A Simple Measure: Being One-Dimensional and of the Same Kind as What Is Measured 338 8.1.2 Comparison with a Modern Conception and the Relation between Counting and Measuring 344
CONTENTS 8.2 The Measure of Movement in Aristotle’s Physics 350 8.2.1 Time as a One-Dimensional Measure and Number of Motion 351 8.2.2 The Search for a Measure of the Same Kind as Motion 8.2.3 The Relation of Time and Space 374 9 Time as the Simple Measure of Motion 385 9.1 Other Accounts of Speed 385 9.2 Reasons Why Aristotle did not Explicitly Use a Complex Measure 9.3 Constructive Developments: A Résumé 403 Bibliography Index Locorum General Index 404 423 426 356 393
This book examines the birth of the scientific understanding ot motion. It investigates which logical tools and methodological principles had to be in place to gi\e a consistent account ot motion, and which mathematical notions were introduced to gain control over conceptual problems of motiem. It shows how the idea ot motion raised two fundamental problems in the fifth and fourth centu։՜}՜ ВСЕ: bringing together Being and nonBeing, and bringing together time and space. The first problem leads to the exclusion of motion trom the realm ot rational investigation in Parmenides, the second to Zeno's paradoxes ot motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitlv in the atomists, and explicitly in Plato, who also emplovs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline ot the fundamental framework with which we conceptualise motion todav.
CONTENTS Acknowledgements Introduction page ix 1 Overview of the Project 1 Methodology, Treatment of Sources, and Relationships of Thinkers Investigated 5 Overview of the Chapters 11 1 Conceptual Foundations 17 1.1 The Concepts of Kinesis, Physis, and Natural Philosophy 17 1.1.1 The Concept of Motion (Kinesis) 17 1.1.2 The Ancient Greek Conceptions of Physis and Natural Philosophy 27 1.1.3 The Concept of Being 30 1.2 Criteria of Inquiry 31 1.2.1 The Principle of Non-Contradiction 32 1.2.2 The Principle of Excluded Middle 37 1.2.3 The Principle of Sufficient Reason 39 1.2.4 Rational Admissibility 46 1.2.5 Saving the Phenomena 49 1.3 The Role of Logic 53 1.3.1 Operators and Operands 55 1.3.2 Negation and Identity as Operators 57 1.4 The Role of Mathematics: The Connection between Mathematics and Natural Philosophy 67 1.4.1 The Use of Mathematics for Science in General 67 1.4.2 How to Do Things with Numbers: Measurement and Countability 73 2 Parmenides’ Account of the Object of Philosophy 80 2.1 Introduction 80 2.2 Parmenides’ Criteria for Philosophy and His Logical Apparatus 2.2.1 Criteria for Philosophy 83 2.2.2 Logical Operators 92 2.3 Parmenides’Logical Apparatus as Intimately Tied to His Ontology 2.4 Problems for the Very Possibility of Natural Philosophy 111 v 83 103
vi CONTENTS 2.4.1 The Absence of Adequate Basic Concepts for Natural Philosophy 111 2.4.2 No Distinction between Operators and Operands 114 2.4.3 The Indeterminacy of Background Concepts 116 2.4.4 Problems with Relations 117 2.5 Relation to the Doxa Part: The Role of Cosmology 119 3 Zeno’s Paradoxes of Motion and Plurality 124 3.1 Introduction 124 3.2 The General Aim of Zeno’s Paradoxes 128 3.3 Parmenidean Inheritance 130 3.3.1 Advancing Parmenides’Criteria 130 3.3.2 Deepening of the Challenge Parmenides Poses 134 3.4 The Fragments, Their Sources, and Their Connection 134 3.5 The Paradoxes of Plurality 136 3.6 The Paradoxes of Motion 143 3.6.1 The Dichotomy: Passing Infinitely Many Segments in a Finite Time 144 3.6.2 Achilles: A Variation of the Dichotomy Paradox 155 3.6.3 The Flying Arrow: Motion as a Sequence of Rests 156 3.6.4 The Moving Rows: Double the Time Is Half the Time 164 3.6.5 The Basic Problems of All Paradoxes of Motion 174 4 The Atomistic Foundation for an Account of Motion 176 4.1 Introduction 176 4.2 Eleatic Inheritance in the Atomists 178 4.2.1 Rational Admissibility 179 4.2.2 Consistency 182 4.2.3 The Principle of Sufficient Reason 183 4.3 Atomistic Changes 184 4.3.1 What Truly Is Must Explain the Phenomena 184 4.3.2 A Physical Theory 185 4.3.3 Change of Logical Operators 187 4.3.4 The Atomistic Account of What Is 190 4.3.5 New Physical Features and Their Functions 191 4.4 Consequences of the Atomistic Changes for Natural Philosophy 4.4.1 Reply to Eleatic Problems 194 4.4.2 Motion and Changes in the Atomistic Framework 198 4.4.3 Problems that Remain 200 5
The Possibility of Natural Philosophy According to Plato I: The Logical Basis 202 5.1 Introduction: The Investigation of the Natural World as an Eikös Mythos 202 5.2 The Sophist 210 5.2.1 The Reinterpretation of Negation and the Connection Operator 211 194
vii CONTENTS 5.2.2 The Reinterpretation of the Criteria for Philosophy 1: The Principle of Non-Contradiction and the Principle of Excluded Middle 225 5.2.3 Widening the Conceptual Possibilities 230 5.2.4 Possible Answers to Parmenides’ Problems 232 5.3 The Timaeus: Logical Advances 235 5.3.1 The Reinterpretation of the Criteria for Philosophy 2: The Principle of Sufficiënt Reason and Rational Admissibility 236 5.3.2 An Eikös Mythos 240 6 The Possibility of Natural Philosophy According to Plato II: Mathematical Advances and Ultimate Problems 245 6.1 Introduction 245 6.2 Introducing Mathematical Structures 246 6.3 Locomotion and Mathematical Structures 253 6.3.1 Time and Eternity 253 6.3.2 Time as the Measure of Motion 256 6.3.3 Space as Excluded from the Measurement Process 6.4 Problems with a Simple Measure 269 6.4.1 Restricted Comparability 274 6.4.2 Lacking Consistency: The Tortoise Wins the Race 7 266 274 Aristotle’s Notion of Continuity: The Structure Underlying Motion 277 7.1 Introduction 277 7.2 Notions of Magnitude Influencing Aristotle’s Concept of a Continuum 284 7.2.1 Parmenides’ Suneches 285 7.2.2 Atomistic Notions of Magnitude 289 7.2.3 A Mathematical Notion of Suneches 291 7.3 Aristotle’s Two Accounts of the Continuum 295 7.3.1 Things Whose Limits Touch and Are One 296 7.3.2 Things Being Divisible without Limits 299 7.4 Implications of Aristotle’s Concept of a Continuum 303 7.4.1 A New Understanding of the Part-Whole Relation 305 7.4.2 A New Twofold Concept of a Limit 311 7.4.3 A New Conception of Infinity 328 8 Time and Space: The Implicit Measure of Motion in
Aristotle’s Physics 335 8.1 The General Concept of Measure in Aristotle’s Metaphysics 337 8.1.1 A Simple Measure: Being One-Dimensional and of the Same Kind as What Is Measured 338 8.1.2 Comparison with a Modern Conception and the Relation between Counting and Measuring 344
CONTENTS 8.2 The Measure of Movement in Aristotle’s Physics 350 8.2.1 Time as a One-Dimensional Measure and Number of Motion 351 8.2.2 The Search for a Measure of the Same Kind as Motion 8.2.3 The Relation of Time and Space 374 9 Time as the Simple Measure of Motion 385 9.1 Other Accounts of Speed 385 9.2 Reasons Why Aristotle did not Explicitly Use a Complex Measure 9.3 Constructive Developments: A Résumé 403 Bibliography Index Locorum General Index 404 423 426 356 393
This book examines the birth of the scientific understanding ot motion. It investigates which logical tools and methodological principles had to be in place to gi\e a consistent account ot motion, and which mathematical notions were introduced to gain control over conceptual problems of motiem. It shows how the idea ot motion raised two fundamental problems in the fifth and fourth centu։՜}՜ ВСЕ: bringing together Being and nonBeing, and bringing together time and space. The first problem leads to the exclusion of motion trom the realm ot rational investigation in Parmenides, the second to Zeno's paradoxes ot motion. Methodological and logical developments reacting to these puzzles are shown to be present implicitlv in the atomists, and explicitly in Plato, who also emplovs mathematical structures to make motion intelligible. With Aristotle we finally see the first outline ot the fundamental framework with which we conceptualise motion todav. |
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| author | Sattler, Barbara 1974- |
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| spelling | Sattler, Barbara 1974- Verfasser (DE-588)13210749X aut The concept of motion in ancient Greek thought foundations in logic, method, and mathematics Barbara M. Sattler Cambridge ; New York ; Port Melbourne ; New Delhi ; Singapore Cambridge University Press 2020 x, 427 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier "The main object of this book is to study how the understanding of physical motion in ancient Greek thought developed before and up to Aristotle. It investigates which logical, methodological, and mathematical foundations had to be in place to establish a fullyfledged concept of motion that also allows for comparing and measuring speed.1 Given that physical motion is the core concept of natural philosophy, this study thereby also seeks to reconstruct in rough outlines how natural philosophy came to be established as a proper scientific endeavour in ancient Greece.2 According to a prevailing picture, scientific investigation of physical motion and change started properly in the West with Aristotle but only achieved its true form in modern times, with the overthrow of central Aristotelian doctrines. In the early modern period, so runs the narrative, Aristotelianism was rejected and the basis laid for what today we consider the science of physics.3 This interpretation is at least doubly misleading." Philosophie (DE-588)4045791-6 gnd rswk-swf Bewegung (DE-588)4006311-2 gnd rswk-swf Griechenland Altertum (DE-588)4093976-5 gnd rswk-swf Motion Philosophy, Ancient Bewegung (DE-2581)TH000005884 gbd Philosophie der Antike (DE-2581)TH000006619 gbd Griechenland Altertum (DE-588)4093976-5 g Philosophie (DE-588)4045791-6 s Bewegung (DE-588)4006311-2 s DE-604 Erscheint auch als Online-Ausgabe 978-1-108-80408-0 (DE-604)BV046965644 Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032348308&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032348308&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032348308&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032348308&sequence=000007&line_number=0004&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Sattler, Barbara 1974- The concept of motion in ancient Greek thought foundations in logic, method, and mathematics Philosophie (DE-588)4045791-6 gnd Bewegung (DE-588)4006311-2 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4006311-2 (DE-588)4093976-5 |
| title | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics |
| title_auth | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics |
| title_exact_search | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics |
| title_exact_search_txtP | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics |
| title_full | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics Barbara M. Sattler |
| title_fullStr | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics Barbara M. Sattler |
| title_full_unstemmed | The concept of motion in ancient Greek thought foundations in logic, method, and mathematics Barbara M. Sattler |
| title_short | The concept of motion in ancient Greek thought |
| title_sort | the concept of motion in ancient greek thought foundations in logic method and mathematics |
| title_sub | foundations in logic, method, and mathematics |
| topic | Philosophie (DE-588)4045791-6 gnd Bewegung (DE-588)4006311-2 gnd |
| topic_facet | Philosophie Bewegung Griechenland Altertum |
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