The Deep Metaphysics of Space: An Alternative History and Ontology Beyond Substantivalism and Relationism (European Studies in Philosophy of Science Book 3)

This volume explores the inadequacies of the two standard conceptions of space or spacetime, substantivalism and relationism, and in the process, proposes a new historical interpretation of these physical theories. This book also examines and develops alternative ontological conceptions of space, and explores additional historical elements of seventeenth century theories and other metaphysical themes. The author first discusses the two main opposing theories of the ontology of space. One, known as substantivalism, proposes space to be an entity that can exist independently of material things. The other, relationism, contends that space is a relation among material things. Readers will learn about specific problems with this dichotomy. First, Newton and Leibniz are often upheld as the retrospective forerunners of substantivalism and relationism. But, their work often contradicts the central tenets of these views. Second, these theories have proven problematic when transferred to a modern setting, especially with regards to general relativity and the recent quantum gravity hypotheses. The author details an alternative set of concepts that address these problems. The author also develops a new classificational system that provides a more accurate taxonomy for the elements of all spatial ontologies. This classification obtains successful analogies between Newton, Leibniz, and other natural philosophers with contemporary physical theories. Preface 6 Contents 9 Abbreviations and Other Conventions 14 Introduction 18 Part I: Substantivalism and Relationism Versus Newton and Leibniz 24 Chapter 1: A (Contrarian’s) Reappraisal of the History and Current State of the Ontology Debate in the Philosophy of Space 25 1.1 The Standard Dichotomy: Substantivalism and Relationism 25 1.1.1 Substantivalism, Theoretical Entities, and the Spacetime Approach 26 1.1.2 Relationism 29 1.2 The Third-Way in Spatial Ontology 31 1.2.1 Space as Property 32 1.2.2 Spacetime Structuralism and the Definitional Approach 35 1.3 The Complex Geneses of the Standard Dichotomy 36 1.3.1 The Relativity of Perceived Motion 36 1.3.2 Cartesian Spacetime Revisited 39 1.3.3 Huygens’ Crucial Role in the Evolution of the Standard Dichotomy 45 Chapter 2: Newton’s Neoplatonic Ontology of Space: Substantivalism or Third-Way? 50 2.1 Two Third-Way Conceptions of Newton’s Absolute Space 51 2.2 The Case for a Strong Third-Way Interpretation 54 2.2.1 Space as a Necessary Consequence or Result 55 2.2.2 Efficient Causation and Cambridge Neoplatonism 58 2.3 Neoplatonism and the Determined Quantities of Extension Hypothesis 62 2.3.1 Newton Against Ontological Dualisms 62 2.3.2 The Ontological Foundation of Newton’s Spatial Ontology 65 2.4 Space as an Affection of Being 68 2.4.1 Extension and Accidents 69 2.4.2 Nullibism and Holenmerism 71 2.4.3 Ens Quatenus Ens 73 2.5 Newton’s Spatial Theory and Substance/Property Ontologies 75 2.6 Conclusion 79 Chapter 3: Leibniz’ Ontology of Space: Whither Relationism? 82 3.1 Relationism and Leibnizian Space 83 3.1.1 Relationism Versus Universal Place 83 3.1.2 Universal Place and the Property Theory 86 3.2 The Ontological Foundations of Leibnizian Space 89 3.2.1 The Immensum and Its Immense Importance 89 3.2.2 Substance, Accident, and Relations in Leibniz’ Metaphysics 93 3.2.3 Leibniz’ Physical-Geometric Holism 98 3.3 Final Assessment 100 3.3.1 Space, Property and Nominalism 100 3.3.2 Reconsidering the Leibniz Shift Scenarios 103 3.3.3 A Monadic Conclusion 104 Chapter 4: Motion, Matter, Monads, and Their “Forced” Relationship 107 4.1 The Interpretive Challenge of Leibnizian Motion 108 4.1.1 Overview of Leibnizian Motion and the Equivalence of Hypotheses 109 4.1.2 Leibnizian Motion: An Alternative Account Contra Absolute Speed 112 4.1.3 Realism, Invariantism, and Leibnizian Motion 116 4.1.4 An Outline of a Leibnizian Invariantist Ontology 120 4.2 The Mystery of Monadic Situation 124 4.2.1 Monads and Spatiality 125 4.2.2 Monads and the Extension of Power 128 4.2.3 Monadic Activity and Derivative Force 135 4.3 Final Synthesis 137 Part II: Third-Way Spatial Ontologies: Past and Present 139 Chapter 5: From Property to Structure: Exploring Contemporary Third-Way Conceptions of the Ontology of Space 140 5.1 The Property Theory of Space 140 5.1.1 An Historical Precedent: Philoponus 141 5.1.2 Contemporary Versions of the Property Theory 144 5.1.3 Critiquing the Property Theory 149 5.1.4 Concluding Assessment 154 5.2 The Structuralist Aftermath of the Ontology Debate in General Relativity 155 5.2.1 The Hole Argument and Recent Substantivalist and Relationist Ontologies 156 5.2.2 The Structural Realist Alternative 161 5.3 Conclusion 166 Chapter 6: Newton’s Immobility Arguments and the Holism of Spatial Ontology 168 6.1 Newton’s Immobility Arguments 169 6.2 The Historical Background to Newton’s Immobility Arguments 170 6.2.1 Oneness, Indiscerpibility and Simplicity 171 6.2.2 Simplicity and Spatial Holism 174 6.2.3 The Order of Position of Spatial Parts 177 6.2.4 The Least Distance Hypothesis 181 6.3 Contemporary Spacetime Ontology and the Immobility Arguments 183 6.3.1 Spatial Transformations and Leibniz Shifts 183 6.3.2 Conclusion: Modern Spacetime Ontologies and Newton’s Immobility Arguments 188 Chapter 7: The ‘Space’ at the Intersection of Physics, Metaphysics, and Mathematics 193 7.1 Platonism, Nominalism, and Structuralism in Spacetime Theories and Mathematics 194 7.1.1 The Spatial Context of Platonism and Nominalism 195 7.1.2 Fictionalist Nominalism Versus Truth-Based Nominalism 199 7.2 Causation, Explanation, and Instrumentalist Rip-Offs 202 7.2.1 Spacetime Structure and Non-inertial Forces 202 7.2.2 Instrumentalism and Mathematical Structure 206 7.3 Platonism/Nominalism in Newton and Leibniz’ Spatial Ontologies 210 7.3.1 Newton 210 7.3.2 Leibniz 212 7.4 Platonism/Nominalism and Contemporary Spacetime Philosophies 216 7.4.1 Nominalist Substantivalism 216 7.4.2 Nominalist Counter-Arguments 219 7.4.3 Scientific Realism and Platonism/Nominalism 223 7.5 Conclusion 224 Chapter 8: The Multiple Paths Towards an Epistemic Structural Realist Spatial Ontology 226 8.1 Structural Realism, Underdetermination, and Spacetime Theories 228 8.1.1 OSR and ESR-L 228 8.1.2 Entity Underdetermination 230 8.1.3 Formalism Underdetermination 234 8.2 ESR, OSR, and Platonism/Nominalism 237 8.3 First Reflections on Non-spacetime Hypotheses 240 8.3.1 Quantum Mechanics, Quantum Gravity, and Spacetime 241 8.3.2 Non-spacetime Theories and Inference to the Best Explanation 243 8.3.3 Structural Realism and Beables 245 8.4 Non-realist Structuralisms and ESR-L 246 8.4.1 Early Structuralism and ESR/OSR 246 8.4.2 Freidman’s Relativized a Priori Structuralism 248 8.4.3 Convergence, the Relativized a Priori, and Realism 249 8.5 Multiple Routes and ESR-L 251 8.5.1 Convergence and the Multiple Routes Hypothesis 251 8.5.2 Constraints, Compensatory Adjustments, and the Two Requirements of Multiple Routes ESR-L 253 8.5.3 OSR and Multiple Routes 256 8.6 Conclusion: OSR, ESR, and Historical Analogies 258 Part III: The Deep Metaphysics of Space from the Seventeenth Century to Quantum Gravity 259 Chapter 9: A New Taxonomy Beyond Substantivalism and Relationism I: Early Modern Spatial Ontologies 260 9.1 Introduction: Quantum Gravity and The Substantivalist/Relationist Dichotomy 260 9.2 A New Taxonomy for Spatial Ontologies 262 9.2.1 Equivalent Geometric Structure and Ontological Levels 262 9.2.2 Platonism/Nominalism and Ontological Levels 266 9.3 Applying the New Taxonomy: The Early Modern Period 267 9.3.1 Newton and the (Later) More on Spatial Ontology 268 9.3.2 Gassendi and (Early) More on Spatial Ontology 269 9.3.3 Patrizi and the Origins of Seventeenth Century Virtual-Platonism 271 9.3.4 Leibniz on Spatial Ontology 273 9.3.5 The Pre-critical Kant on Spatial Ontology 275 9.3.6 Barrow and Descartes on Spatial Ontology 279 9.4 Reflections on Seventeenth Century and Contemporary Spatial Ontologies 281 9.5 Platonism/Nominalism, Geometric Background, and Leibniz Shifts 283 9.5.1 Background Dependence/Independence 283 9.5.2 The Shift Scenarios and Platonism/Nominalism 284 9.5.3 Maudlin’s Ontological Classification 287 Chapter 10: A New Taxonomy Beyond Substantivalism and Relationism II: Some Philosophical Prehistory of Quantum Gravity 289 10.1 Introduction: Geometric Levels and Quantum Gravity 289 10.2 Applying The New Taxonomy: Quantum Gravity Hypotheses and Their Seventeenth Century Analogues 291 10.2.1 QG Metric Structure and Newton 291 10.2.2 QG Topological Structure and Gassendi 293 10.2.3 QG Pregeometric Structure and Leibniz 294 10.3 Quantum Gravity and Nominalism 299 10.3.1 Background Independence, Nominalism, and the Void 299 10.3.2 Pre-established Harmony and QG 304 10.4 Alternative Interpretations: Ubeity and Local Beables 305 10.5 Overview and Conclusion 308 10.5.1 Assessing the New Taxonomy 308 10.5.2 The Sophisticated Relationist Counter-Offensive 312 10.5.3 Synopsis of General Themes 315 Chapter 11: Epilogue: The Post-Seventeenth Century Evolution of the Standard Dichotomy 317 11.1 Spatial Ontology in the Eighteenth Century 317 11.1.1 Who Banished God from Space? 318 11.1.2 The Rise of the Empiricist Approach to Space: Berkeley as Exemplar 320 11.1.3 The Fate of Third-Way Spatial Ontologies After Newton and Leibniz 324 11.2 The Kantian Synthesis of Relationism and Newtonian Physics 326 11.2.1 The Center-of-Mass Frame as Absolute Space 327 11.2.2 Kant’s Relationist “Applied Metaphysics” of Motion and Its Aftermath 331 11.2.3 Conclusion: A Note on Kant as Precursor of Mach 337 References 339 Index 353 Front Matter....Pages i-xxiv Front Matter....Pages 1-1 A (Contrarian’s) Reappraisal of the History and Current State of the Ontology Debate in the Philosophy of Space....Pages 3-27 Newton’s Neoplatonic Ontology of Space: Substantivalism or Third-Way?....Pages 29-60 Leibniz’ Ontology of Space: Whither Relationism?....Pages 61-85 Motion, Matter, Monads, and Their “Forced” Relationship....Pages 87-118 Front Matter....Pages 119-119 From Property to Structure: Exploring Contemporary Third-Way Conceptions of the Ontology of Space....Pages 121-148 Newton’s Immobility Arguments and the Holism of Spatial Ontology....Pages 149-173 The ‘Space’ at the Intersection of Physics, Metaphysics, and Mathematics....Pages 175-207 The Multiple Paths Towards an Epistemic Structural Realist Spatial Ontology....Pages 209-241 Front Matter....Pages 243-243 A New Taxonomy Beyond Substantivalism and Relationism I: Early Modern Spatial Ontologies....Pages 245-273 A New Taxonomy Beyond Substantivalism and Relationism II: Some Philosophical Prehistory of Quantum Gravity....Pages 275-302 Epilogue: The Post-Seventeenth Century Evolution of the Standard Dichotomy....Pages 303-324 Back Matter....Pages 325-342 This volume explores the inadequacies of the two standard conceptions of space and time, and in the process, proposes a new historical interpretation of these physical theories. This book also examines and develops alternative ontological conceptions of space, and explores additional historical elements of seventeenth century theories and other metaphysical themes. Readers will learn about specific problems with the dichotomy of substantivalism and relationism. First, Newton and Leibniz are often upheld as the retrospective forerunners of substantivalism and relationism. But, their work often contradicts the central tenets of these views. Second, these theories have proven problematic when transferred to a modern setting, especially with regards to general relativity and the recent quantum gravity hypotheses. The authors detail an alternative set of concepts that address these problems. They also develop a new classificational system that provides a more accurate taxonomy for the elements of all spatial ontologies. This classification obtains successful analogies between Newton, Leibniz, and other natural philosophers with contemporary physical theories