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The Concept of Motion in Ancient Greek Thought : Foundations in Logic, Method, and Mathematics
Cover -- Half-title page -- Title page -- Copyright page -- Contents -- Acknowledgements -- Introduction -- Overview of the Project -- Methodology, Treatment of Sources, and Relationships of Thinkers Investigated -- Overview of the Chapters -- 1 Conceptual Foundations -- 1.1 The Concepts of Kinêsis...
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| Main Author: | |
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| Document Type: | Online Resource Book |
| Language: | English |
| Published: |
Cambridge
: University of Cambridge ESOL Examinations
, 2020
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| Online Access: | http://proxy.fid-lizenzen.de/han/proquest-ebook-central-altertum/ebookcentral.proquest.com/lib/bsbfidaltertumswissenschaften/detail.action?docID=6360473 |
| E-Book Packages: | ProQuest Ebook Central : Classical Studies Collection |
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| 245 | 1 | 4 | |a The Concept of Motion in Ancient Greek Thought |b Foundations in Logic, Method, and Mathematics |
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| 520 | |a Cover -- Half-title page -- Title page -- Copyright page -- Contents -- Acknowledgements -- Introduction -- Overview of the Project -- Methodology, Treatment of Sources, and Relationships of Thinkers Investigated -- Overview of the Chapters -- 1 Conceptual Foundations -- 1.1 The Concepts of Kinêsis, Physis, and Natural Philosophy -- 1.1.1 The Concept of Motion (Kinêsis) -- 1.1.2 The Ancient Greek Conceptions of Physis and Natural Philosophy -- 1.1.3 The Concept of Being -- 1.2 Criteria of Inquiry -- 1.2.1 The Principle of Non-Contradiction -- 1.2.2 The Principle of Excluded Middle -- 1.2.3 The Principle of Sufficient Reason -- 1.2.4 Rational Admissibility -- 1.2.5 Saving the Phenomena -- 1.3 The Role of Logic -- 1.3.1 Operators and Operands -- 1.3.2 Negation and Identity as Operators -- 1.4 The Role of Mathematics: The Connection between Mathematics and Natural Philosophy -- 1.4.1 The Use of Mathematics for Science in General -- 1.4.2 How to Do Things with Numbers: Measurement and Countability -- 2 Parmenides' Account of the Object of Philosophy -- 2.1 Introduction -- 2.2 Parmenides' Criteria for Philosophy and His Logical Apparatus -- 2.2.1 Criteria for Philosophy -- 2.2.2 Logical Operators -- 2.3 Parmenides' Logical Apparatus as Intimately Tied to His Ontology -- 2.4 Problems for the Very Possibility of Natural Philosophy -- 2.4.1 The Absence of Adequate Basic Concepts for Natural Philosophy -- 2.4.2 No Distinction between Operators and Operands -- 2.4.3 The Indeterminacy of Background Concepts -- 2.4.4 Problems with Relations -- 2.5 Relation to the Doxa Part: The Role of Cosmology -- 3 Zeno's Paradoxes of Motion and Plurality -- 3.1 Introduction -- 3.2 The General Aim of Zeno's Paradoxes -- 3.3 Parmenidean Inheritance -- 3.3.1 Advancing Parmenides' Criteria -- 3.3.2 Deepening of the Challenge Parmenides Poses. | ||
| 520 | |a 3.4 The Fragments, Their Sources, and Their Connection -- 3.5 The Paradoxes of Plurality -- 3.6 The Paradoxes of Motion -- 3.6.1 The Dichotomy: Passing Infinitely Many Segments in a Finite Time -- 3.6.2 Achilles: A Variation of the Dichotomy Paradox -- 3.6.3 The Flying Arrow: Motion as a Sequence of Rests -- 3.6.4 The Moving Rows: Double the Time Is Half the Time -- 3.6.5 The Basic Problems of All Paradoxes of Motion -- 4 The Atomistic Foundation for an Account of Motion -- 4.1 Introduction -- 4.2 Eleatic Inheritance in the Atomists -- 4.2.1 Rational Admissibility -- 4.2.2 Consistency -- 4.2.3 The Principle of Sufficient Reason -- 4.3 Atomistic Changes -- 4.3.1 What Truly Is Must Explain the Phenomena -- 4.3.2 A Physical Theory -- 4.3.3 Change of Logical Operators38 -- 4.3.4 The Atomistic Account of What Is -- 4.3.5 New Physical Features and Their Functions -- 4.4 Consequences of the Atomistic Changes for Natural Philosophy -- 4.4.1 Reply to Eleatic Problems -- 4.4.2 Motion and Changes in the Atomistic Framework -- 4.4.3 Problems that Remain -- 5 The Possibility of Natural Philosophy According to Plato I: The Logical Basis -- 5.1 Introduction: The Investigation of the Natural World as an Eikôs Mythos -- 5.2 The Sophist -- 5.2.1 The Reinterpretation of Negation and the Connection Operator -- 5.2.2 The Reinterpretation of the Criteria for Philosophy 1: The Principle of Non-Contradiction and the Principle of Excluded Middle -- 5.2.3 Widening the Conceptual Possibilities -- 5.2.4 Possible Answers to Parmenides' Problems -- 5.3 The Timaeus: Logical Advances -- 5.3.1 The Reinterpretation of the Criteria for Philosophy 2: The Principle of Sufficient Reason and Rational Admissibility -- 5.3.2 An Eikôs Mythos -- 6 The Possibility of Natural Philosophy According to Plato II: Mathematical Advances and Ultimate Problems -- 6.1 Introduction. | ||
| 520 | |a 6.2 Introducing Mathematical Structures -- 6.3 Locomotion and Mathematical Structures -- 6.3.1 Time and Eternity -- 6.3.2 Time as the Measure of Motion -- 6.3.3 Space as Excluded from the Measurement Process -- 6.4 Problems with a Simple Measure -- 6.4.1 Restricted Comparability -- 6.4.2 Lacking Consistency: The Tortoise Wins the Race -- 7 Aristotle's Notion of Continuity: The Structure Underlying Motion -- 7.1 Introduction -- 7.2 Notions of Magnitude Influencing Aristotle's Concept of a Continuum -- 7.2.1 Parmenides' Suneches -- 7.2.2 Atomistic Notions of Magnitude -- 7.2.3 A Mathematical Notion of Suneches -- 7.3 Aristotle's Two Accounts of the Continuum -- 7.3.1 Things Whose Limits Touch and Are One -- 7.3.2 Things Being Divisible without Limits -- 7.4 Implications of Aristotle's Concept of a Continuum -- 7.4.1 A New Understanding of the Part-Whole Relation -- 7.4.2 A New Twofold Concept of a Limit -- 7.4.3 A New Conception of Infinity -- 8 Time and Space: The Implicit Measure of Motion in Aristotle's Physics -- 8.1 The General Concept of Measure in Aristotle's Metaphysics -- 8.1.1 A Simple Measure: Being One-Dimensional and of the Same Kind as What Is Measured -- 8.1.2 Comparison with a Modern Conception and the Relation between Counting and Measuring -- 8.2 The Measure of Movement in Aristotle's Physics -- 8.2.1 Time as a One-Dimensional Measure and Number of Motion -- 8.2.2 The Search for a Measure of the Same Kind as Motion -- 8.2.3 The Relation of Time and Space -- 9 Time as the Simple Measure of Motion -- 9.1 Other Accounts of Speed -- 9.2 Reasons Why Aristotle did not Explicitly Use a Complex Measure -- 9.3 Constructive Developments: A Résumé -- Bibliography -- Index Locorum -- General Index. | ||
| 520 | |a This book explores the birth of the scientific understanding of motion in early Greek thought up to Aristotle | ||
| 650 | 0 | |a Philosophy, Ancient | |
| 650 | 0 | |a Motion | |
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