Representation and Spacetime: The Hole Argument Revisited

References

• Arledge C., and R. Rynasiewicz. 2019. “On Some Recent Attempted Non-Metaphysical Dissolutions of the Hole Dilemma.”
   Google Scholar
• Awodey S. 2010. Category Theory. New York: Oxford University Press.
   Google Scholar
• Awodey S. 2014. “Structuralism, Invariance, and Univalence.” Philosophia Mathematica 22 (1): 1–11.
   Web of Science ®Google Scholar
• Bain J. 2003. “Einstein Algebras and the Hole Argument.” Philosophy of Science 70 (5): 1073–1085.
   Web of Science ®Google Scholar
• Bentzen B. 2019. “What Types Should Not Be.” Philosophia Mathematica 28 (1): 60–76.
   Web of Science ®Google Scholar
• Bradley C., and J. O. Weatherall. 2021. “Mathematical Responses to the Hole Argument: Then and Now.” arXiv preprint arXiv:2110.08404.
   Google Scholar
• Brezis H. 2010. Functional Analysis, Sobolev Spaces and Partial Differential Equations. New York: Springer Science & Business Media.
   Google Scholar
• Butterfield J. 1989. “The Hole Truth.” The British Journal for The Philosophy of Science 40 (1): 1–28.
   Web of Science ®Google Scholar
• Clarke C. J. 1970. “On the Global Isometric Embedding of Pseudo-Riemannian Manifolds.” Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 314 (1518): 417–428.
   Web of Science ®Google Scholar
• Dougherty J. 2020. “The Hole Argument, Take N.” Foundations of Physics 50 (4): 330–347.
   Web of Science ®Google Scholar
• Earman J. 1989. World Enough and Space-time: Absolute Versus Relational Theories of Space and Time. Cambridge, Massachusetts: A Bradford Book: MIT Press.
   Google Scholar
• Earman J., and J. Norton. 1987. “What Price Spacetime Substantivalism? The Hole Story.” British Journal for the Philosophy of Science 38: 515–525.
   Web of Science ®Google Scholar
• Fletcher S. C. 2020. “On Representational Capacities, with An Application to General Relativity.” Foundations of Physics 50 (4): 228–249.
   Web of Science ®Google Scholar
• French S. 1998. “On The Withering Away of Physical Objects.” In Interpreting Bodies: Classical and Quantum Objects in Modern Physics, edited E. Castellani, 93–113. Princeton: Princeton University Press.
   Google Scholar
• French S. 2012. “The Presentation of Objects and The Representation of Structure.” In Structural Realism, edited by E. M. Landry and D. Rickles, 3–28. Dordrecht: Springer.
   Google Scholar
• Frigg R., and J. Nguyen. 2020. Modelling Nature: An Opinionated Introduction to Scientific Representation. Cham: Springer.
   Google Scholar
• Halvorson H., and J. B. Manchak. 2022. “Closing the Hole Argument.” British Journal for the Philosophy of Science: 1–29.
   Google Scholar
• Hawking S. W., and G. F. R. Ellis. 1973. The Large Scale Structure of Space-time. Cambridge: Cambridge University Press.
   Google Scholar
• Hawley K. 2006. “Science As a Guide to Metaphysics?” Synthese 149 (3): 451–470.
   Web of Science ®Google Scholar
• Hoefer C. 1996. “The Metaphysics of Space-time Substantivalism.” The Journal of Philosophy 93 (1): 5–27.
   Web of Science ®Google Scholar
• Holmes M. R. 2017. “Alternative Axiomatic Set Theories.” In The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta, (Winter 2017 ed.). Metaphysics Research Lab, Stanford: Stanford University.
   Google Scholar
• Iftime M., and J. Stachel. 2006. “The Hole Argument for Covariant Theories.” General Relativity and Gravitation 38 (8): 1241–1252.
   Web of Science ®Google Scholar
• Jech T. 2003. Set Theory. Berlin: Springer.
   Google Scholar
• Kunen K. 2011. Set Theory. London: College Publications Studies in logic.
   Google Scholar
• Ladyman J., and S. Presnell. 2015. “Identity in Homotopy Type Theory, Part I: The Justification of Path Induction.” Philosophia Mathematica 23 (3): 386–406.
   Web of Science ®Google Scholar
• Ladyman J., and S. Presnell. 2016. “Does Homotopy Type Theory Provide a Foundation for Mathematics?” British Journal for the Philosophy of Science 69: axw006.
   Web of Science ®Google Scholar
• Ladyman J., and S. Presnell. 2017. “Identity in Homotopy Type Theory: Part II, the Conceptual and Philosophical Status of Identity in HoTT.” Philosophia Mathematica 25 (2): 210–245.
   Web of Science ®Google Scholar
• Ladyman J., and S. Presnell. 2019a. “The Hole Argument in Homotopy Type Theory.” Foundations of Physics 50: 319–329.
   Web of Science ®Google Scholar
• Ladyman J., and S. Presnell. 2019b. “Universes and Univalence in Homotopy Type Theory.” The Review of Symbolic Logic 12 (3): 426–455.
   Web of Science ®Google Scholar
• Landry E. M. 2012. “Methodological Structural Realism.” In Structural Realism: Structure, Object, and Causality, edited by E. M. Landry and D. Rickles, 29–57. Dordrecht: Springer Netherlands.
   Google Scholar
• Norton J. D. 2019. “The Hole Argument.” In The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta, (Summer 2019 ed.). Metaphysics Research Lab, Stanford: Stanford University.
   Google Scholar
• O'Neill B. 1983. Semi-Riemannian Geometry with Applications to Relativity. New York: Academic Press.
   Google Scholar
• Pooley O. 2013. “Substantivalist and Relationalist Approaches to Spacetime.” In The Oxford Handbook of Philosophy of Physics, edited by R. Batterman, 522–586. New York: Oxford University Press.
   Google Scholar
• Pooley O. 2017. “Background Independence, Diffeomorphism Invariance and The Meaning of Coordinates.” In Towards a Theory of Spacetime Theories, edited by D. Lehmkuhl, G. Schiemann, and E. Scholz, 105–143. New York, NY: Springer New York.
   Google Scholar
• Pooley O., and J. A. M. Read. 2021. “On the Mathematics and Metaphysics of the Hole Argument.” The British Journal for the Philosophy of Science.
   Google Scholar
• Program T. U. F. 2013. Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton: Univalent Foundations Program.
   Google Scholar
• Roberts B. W. 2020. “Regarding Leibniz Equivalence.” Foundations of Physics 50: 250–269.
   Web of Science ®Google Scholar
• Sachs R. K., and H.-H. Wu. 2012. General Relativity for Mathematicians. New York: Springer Science & Business Media.
   Google Scholar
• Shulman M. 2017. “Homotopy Type Theory: A Synthetic Approach to Higher Equalities.” In Categories for the Working Philosopher, edited by E. Landry, 36–57. Oxford: Oxford University Press.
   Google Scholar
• Sklar L. 1981. “Time, Reality and Relativity.” In Reduction, Time and Reality, edited by R. Healey, 129–142. Cambridge: Cambridge University Press.
   Google Scholar
• Stachel J. 2014. “The Hole Argument and Some Physical and Philosophical Implications.” Living Reviews in Relativity 17 (1): 1.
   PubMed Web of Science ®Google Scholar
• Suárez M., and F. Pero. 2019. “The Representational Semantic Conception.” Philosophy of Science86 (2): 344–365.
   Web of Science ®Google Scholar
• Weatherall J. O. 2018. “Regarding the Hole Argument.” The British Journal for the Philosophy of Science 69 (2): 329–350.
   Web of Science ®Google Scholar