Geometric Possibility

Relationalism about space is a venerable doctrine that is enjoying renewed attention among philosophers and physicists. Relationalists deny that space is ontologically prior to matter and seek to ground all claims about the structure of space in facts about actual and possible configurations of matter. Thus, many relationalists maintain that to say that space is infinite is to say that certain sorts of infinite arrays of material points are possible (even if, in fact, the world contains only a finite amount of matter). Gordon Belot investigates the distinctive notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility. This contribution to the debate concerning the nature of space will be of interest not only to philosophers and metaphysicians concerned with space and time, but also to those interested in laws of nature, modal notions, or more general issues in ontology. Cover......Page 1 Contents......Page 10 Introduction......Page 12 1. Introduction......Page 19 2. Distance......Page 21 3. Candidates for Spatial Structure......Page 25 4. Plenitude of Possibilities......Page 41 5. Distance Relations?......Page 42 1. Substantivalism and the Structure of Space......Page 46 2. Conservative Relationalism......Page 48 3. Modal Relationalism......Page 60 1. Introduction......Page 65 2. Lewis on Physical Possibility......Page 66 3. Huggett on Geometric Possibility......Page 68 4. Worries About Best-System Approaches......Page 71 5. Summation......Page 87 1. Introduction......Page 89 2. A First Primitivist Approach......Page 94 3. Geometric Facts for Substantivalists......Page 97 4. Another Primitivist Strategy......Page 101 5. Beyond Metricity......Page 106 6. Summation......Page 111 1. Introduction......Page 113 2. Necessitarianism about Laws......Page 114 3. Compatibility Properties......Page 125 4. Necessitarianism about Geometry......Page 128 5. Super-Grounding and Necessitarianism......Page 132 6. Summation......Page 143 Conclusion......Page 145 Appendix A. Simplicity and Ontology......Page 150 Appendix B. Limits of Sequences of Metric Spaces......Page 161 Appendix C. Some Background to the Absolute-Relational Debate......Page 168 Appendix D. Leibniz and Modal Relationalism......Page 184 Appendix E. More on Congruence and Superposability......Page 197 References......Page 210 C......Page 224 E......Page 225 J......Page 226 N......Page 227 R......Page 228 V......Page 229 Y......Page 230 Relationalists deny that space is ontologically prior to matter and seek to ground all claims about the structure of space in facts about actual and possible configurations of matter. Thus, many relationalists maintain that to say that space is infinite is to say that certain sorts of infinite arrays of material points are possible (even if, in fact, the world contains only a finite amount of matter). The author investigates the notion of geometric possibility that relationalists rely upon. He examines the prospects for adapting to the geometric case the standard philosophical accounts of the related notion of physical possibility, with particular emphasis on Humean, primitivist, and necessitarian accounts of physical and geometric possibility Relationalism seeks to ground all claims about the structure of space in facts about actual and possible configurations of matter. Gordon Belot elucidates the prospects for this view of the nature of space by investigating the kew notion of geometric possibility in relation to philosophical notions of physical possibility