Skip to main content Accessibility help
×
Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T01:45:10.829Z Has data issue: false hasContentIssue false

Structure and Equivalence

Published online by Cambridge University Press:  16 February 2022

Neil Dewar
Affiliation:
Ludwig-Maximilians-Universität Munchen

Summary

This Element explores what it means for two theories in physics to be equivalent (or inequivalent), and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics.
Get access
Type
Element
Information
Online ISBN: 9781108914581
Publisher: Cambridge University Press
Print publication: 17 March 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alexander, H. G., editor (1956). The Leibniz-Clarke Correspondence. Manchester University Press, Manchester.Google Scholar
Andreas, H. (2017). Theoretical Terms in Science. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, fall 2017 edition. https://plato.stanford.edu/archives/fall2017/entriesheoretical-terms-science/.Google Scholar
Andréka, H., Madarász, J. X., and Németi, I. (2007). Logic of Space-Time and Relativity Theory. In Aiello, M., Pratt-Hartmann, I., and van Benthem, J., editors, Handbook of Spatial Logics, 607711. Springer Netherlands, Dordrecht.CrossRefGoogle Scholar
Andréka, H., Madarász, J. X., and Németi, I. (n.d.). Defining New Universes in Many-Sorted Logic. https://old.renyi.hu/pub/algebraic-logic/kurzus10/amn-defi.pdf.Google Scholar
Awodey, S. (2010). Category Theory. Oxford University Press, Oxford.Google Scholar
Barbour, J. B. (1989). Absolute or Relative Motion: A Study from a Machian Point of View of the Discovery and the Structure of Dynamical Theories. Cambridge University Press, Cambridge.Google Scholar
Barrett, T. W. (2015a). On the Structure of Classical Mechanics. British Journal for the Philosophy of Science, 66(4):801828.Google Scholar
Barrett, T. W. (2015b). Spacetime Structure. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 51:3743.Google Scholar
Barrett, T. W. (2020). Structure and Equivalence. Philosophy of Science, 87(5):11841196.Google Scholar
Barrett, T. W., and Halvorson, H. (2016a). Glymour and Quine on Theoretical Equivalence. Journal of Philosophical Logic, 45(5):467483.CrossRefGoogle Scholar
Barrett, T. W., and Halvorson, H. (2016b). Morita Equivalence. Review of Symbolic Logic, 9(3):556582.Google Scholar
Barrett, T. W., and Halvorson, H. (n.d.). Mutual Translatability, Equivalence, and the Structure of Theories.Google Scholar
Brading, K., and Brown, H. R. (2004). Are Gauge Symmetry Transformations Observable? British Journal for the Philosophy of Science, 55(4):645665.Google Scholar
Brading, K., and Castellani, E., editors (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press, Cambridge.Google Scholar
Brown, H. R. (2005). Physical Relativity: Space-Time Structure from a Dynamical Perspective. Oxford University Press, Oxford.Google Scholar
Butterfield, J. (2006). Against Pointillisme about Mechanics. British Journal for the Philosophy of Science, 57(4):709753.Google Scholar
Butterfield, J. (2011a). Emergence, Reduction and Supervenience: A Varied Landscape. Foundations of Physics, 41(6):920959.CrossRefGoogle Scholar
Butterfield, J. (2011b). Less Is Different: Emergence and Reduction Reconciled. Foundations of Physics, 41(6):10651135.Google Scholar
Button, T., and Walsh, S. (2018). Philosophy and Model Theory. Oxford University Press, Oxford.CrossRefGoogle Scholar
Carnap, R. (1958). Beobachtungssprache und Theoretische Sprache. Dialectica, 12(3–4):236248.CrossRefGoogle Scholar
Caulton, A., and Butterfield, J. (2012). On Kinds of Indiscernibility in Logic and Metaphysics. British Journal for the Philosophy of Science, 63(1):2784.Google Scholar
Coffey, K. (2014). Theoretical Equivalence as Interpretative Equivalence. British Journal for the Philosophy of Science, 65(4):821844.Google Scholar
Curiel, E. (2014). Classical Mechanics Is Lagrangian; It Is Not Hamiltonian. British Journal for the Philosophy of Science, 65(2):269321.Google Scholar
Curiel, E. (2019). On Geometric Objects, the Non-existence of a Gravitational Stress-Energy Tensor, and the Uniqueness of the Einstein Field Equation. Studies in History and Philosophy of Science, Part B: Studies in History and Philosophy of Modern Physics, 66:90102.Google Scholar
Curiel, E. (n.d.). On the Propriety of Physical Theories as a Basis for Their Semantics. http://philsci-archive.pitt.edu/8702/.Google Scholar
Dasgupta, S. (2016). Symmetry as an Epistemic Notion (Twice Over). British Journal for the Philosophy of Science, 67(3):837878.CrossRefGoogle Scholar
de Bouvère, K. (1965). Synonymous Theories. In Addison, J. W., Henkin, L., and Tarski, A., editors, The Theory of Models: Proceedings of the 1963 International Symposium at Berkeley, Studies in Logic and the Foundations of Mathematics, 402406. North-Holland, Amsterdam.Google Scholar
Demopoulos, W., and Friedman, M. (1985). Bertrand Russell’s the Analysis of Matter: Its Historical Context and Contemporary Interest. Philosophy of Science, 52(4):621639.Google Scholar
Dewar, N. (2019a). Ramsey Equivalence. Erkenntnis, 84(1):7799.CrossRefGoogle Scholar
Dewar, N. (2019b). Supervenience, Reduction, and Translation. Philosophy of Science, 86(5):942954.CrossRefGoogle Scholar
Dewar, N., Fletcher, S. C., and Hudetz, L. (2019). Extending List’s Levels. In Kuś, M., and Skowron, B., editors, Category Theory in Physics, Mathematics, and Philosophy, Springer Proceedings in Physics, 6381. Springer Nature, Cham.CrossRefGoogle Scholar
Earman, J. (1989). World Enough and Space-Time: Absolute versus Relational Theories of Space and Time. MIT Press, Cambridge, MA.Google Scholar
French, S. and Ladyman, J. (2010). In Defence of Ontic Structural Realism. In Bokulich, A., and Bokulich, P., editors, Scientific Structuralism, 2542. Springer Netherlands, Dordrecht.CrossRefGoogle Scholar
Friedman, M. (1983). Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science. Princeton University Press, Princeton, NJ.Google Scholar
Frigg, R., and Votsis, I. (2011). Everything You Always Wanted to Know about Structural Realism but Were Afraid to Ask. European Journal for Philosophy of Science, 1(2):227276.Google Scholar
Glymour, C. (1977). The Epistemology of Geometry. Noûs, 11(3):227251.CrossRefGoogle Scholar
Greaves, H., and Wallace, D. (2014). Empirical Consequences of Symmetries. British Journal for the Philosophy of Science, 65(1):5989.CrossRefGoogle Scholar
Halvorson, H. (2019). The Logic in Philosophy of Science. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Healey, R. (2009). Perfect Symmetries. British Journal for the Philosophy of Science, 60(4):697720.Google Scholar
Hellman, G. P., and Thompson, F. W. (1975). Physicalism: Ontology, Determination, and Reduction. Journal of Philosophy, 72(17):551564.Google Scholar
Hodges, W. (1993). Model Theory. Number 42 in Encyclopedia of Mathematics and Its Applications. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Hudetz, L. (2019). Definable Categorical Equivalence. Philosophy of Science, 86(1):4775.Google Scholar
Ismael, J., and van Fraassen, B. C. (2003). Symmetry as a Guide to Superfluous Theoretical Structure. In Brading, K., and Castellani, E., editors, Symmetries in Physics: Philosophical Reflections, 371392. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Jacobs, C. (forthcoming). Absolute Velocities Are Unmeasurable: Response to Middleton and Murgueitio Ramírez. Australasian Journal of Philosophy.Google Scholar
Ketland, J. (2004). Empirical Adequacy and Ramsification. British Journal for the Philosophy of Science, 55(2):287300.Google Scholar
Knox, E. (2014). Newtonian Spacetime Structure in Light of the Equivalence Principle. British Journal for the Philosophy of Science, 65(4):863880.Google Scholar
Kosso, P. (2000). The Empirical Status of Symmetries in Physics. British Journal for the Philosophy of Science, 51(1):8198.Google Scholar
Lévy-Leblond, J.-M. (1971). Galilei Group and Galilean Invariance. In Loebl, E. M., editor, Group Theory and Its Applications, 221299. Academic Press, New York and London.Google Scholar
Lewis, D. (1994). Humean Supervenience Debugged. Mind, 103(412): 473490.Google Scholar
List, C. (2019). Levels: Descriptive, Explanatory, and Ontological. Noûs, 53(4):852883.Google Scholar
Lutz, S. (2012). Criteria of Empirical Significance: Foundations, Relations, Applications. PhD thesis, University of Utrecht. http://dspace.library.uu.nl/handle/1874/241030.Google Scholar
Lutz, S. (2015). What Was the Syntax-Semantics Debate in the Philosophy of Science About? Philosophy and Phenomenological Research, 95(2), 319352.CrossRefGoogle Scholar
Malament, D. (1977). Causal Theories of Time and the Conventionality of Simultaneity. Noûs, 11(3):293300.Google Scholar
Malament, D. B. (2012). Topics in the Foundations of General Relativity and Newtonian Gravitation Theory. University of Chicago Press, Chicago.CrossRefGoogle Scholar
Manzano, M. (1996). Extensions of First Order Logic. Cambridge University Press, Cambridge.Google Scholar
Maudlin, T. (2018). Ontological Clarity via Canonical Presentation: Electromagnetism and the Aharonov–Bohm Effect. Entropy, 20(6):465.Google Scholar
Maxwell, G. (1968). Scientific Methodology and the Causal Theory of Perception. In Studies in Logic and the Foundations of Mathematics, vol. 49, pp. 148177. North-Holland Publishing Co., Amsterdam.Google Scholar
Maxwell, G. (1970). Structural Realism and the Meaning of Theoretical Terms. Minnesota Studies in the Philosophy of Science, 4:181192.Google Scholar
Maxwell, G. (1971). Theories, Perception, and Structural Realism. In Colodny, R. G., editor, The Nature and Function of Scientific Theories: Essays in Contemporary Science and Philosophy, 334. University of Pittsburgh Press, Pittsburgh.Google Scholar
McLaughlin, B., and Bennett, K. (2018). Supervenience. In Zalta, E. N., editor, The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, spring 2018 edition. https://plato.stanford.edu/archives/spr2018/entries/supervenience/.Google Scholar
Middleton, B., and Ramírez, S. M. (2021). Measuring Absolute Velocity. Australasian Journal of Philosophy 99(4), 806816.Google Scholar
Møller-Nielsen, T. (2017). Invariance, Interpretation, and Motivation. Philosophy of Science, 84(5):12531264.Google Scholar
Nagel, E. (1979). The Structure of Science: Problems in the Logic of Scientific Explanation. Hackett, Indianapolis.Google Scholar
Newman, M. H. A. (1928). Mr. Russell’s “Causal Theory of Perception.Mind, 37(146):137148.Google Scholar
Ney, A., and Albert, D. Z., editors (2013). The Wave Function: Essays on the Metaphysics of Quantum Mechanics. Oxford University Press, Oxford.Google Scholar
Nguyen, J., Teh, N. J., and Wells, L. (2020). Why Surplus Structure Is Not Superfluous. The British Journal for the Philosophy of Science, 71(2):665695.Google Scholar
North, J. (2009). The “Structure” of Physics: A Case Study. Journal of Philosophy, 106(2):5788.CrossRefGoogle Scholar
Pitts, J. B. (2010). Gauge-Invariant Localization of Infinitely Many Gravitational Energies from All Possible Auxiliary Structures. General Relativity and Gravitation, 42(3):601622.CrossRefGoogle Scholar
Pooley, O. (2006). Points, Particles, and Structural Realism. In Rickles, D., French, S., and Saatsi, J., editors, The Structural Foundations of Quantum Gravity, 83120. Oxford University Press, Oxford.Google Scholar
Przełecki, M. (1969). The Logic of Empirical Theories. Routledge and Kegan Paul, London.Google Scholar
Psillos, S. (2000). Carnap, the Ramsey-Sentence and Realistic Empiricism. Erkenntnis, 52(2):253279.Google Scholar
Quine, W. V. (1951). Ontology and Ideology. Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition, 2(1):1115.Google Scholar
Ramsey, F. P. (1931). Theories (1929). In Braithwaite, R. B., editor, The Foundations of Mathematics and Other Logical Essays. Routledge and Kegan Paul, London.Google Scholar
Read, J. (forthcoming). Geometric Objects and Perspectivalism. In Read, J., and Teh, N., editors, The Philosophy and Physics of Noether’s Theorems. Cambridge University Press, Cambridge. http://philsci-archive.pitt.edu/18911/.Google Scholar
Read, J., and Møller-Nielsen, T. (2020). Motivating Dualities. Synthese, 197(1):263291.Google Scholar
Read, J., and Teh, N. J. (2018). The Teleparallel Equivalent of Newton–Cartan Gravity. Classical and Quantum Gravity, 35(18):18LT01.CrossRefGoogle Scholar
Redhead, M. L. G. (1975). Symmetry in Intertheory Relations. Synthese, 32(1-2):77112.Google Scholar
Roberts, J. T. (2008). A Puzzle about Laws, Symmetries and Measurability. British Journal for the Philosophy of Science, 59(2):143168.Google Scholar
Rosenstock, S., and Weatherall, J. O. (2016). A Categorical Equivalence between Generalized Holonomy Maps on a Connected Manifold and Principal Connections on Bundles over That Manifold. Journal of Mathematical Physics, 57(10):102902.Google Scholar
Russell, B. (1927). The Analysis of Matter. Kegan Paul, London.Google Scholar
Saunders, S. (2003). Physics and Leibniz’s principles. In Brading, K. and Castellani, E., editors, Symmetries in Physics: Philosophical Reflections, 289308. Cambridge University Press, Cambridge.Google Scholar
Saunders, S. (2013). Rethinking Newton’s Principia. Philosophy of Science, 80(1):2248.Google Scholar
Shapiro, S. (1991). Foundations without Foundationalism: A Case for Second-Order Logic. Oxford University Press, Oxford.Google Scholar
Sider, T. (2010). Logic for Philosophy. Oxford University Press, Oxford.Google Scholar
Sklar, L. (1982). Saving the Noumena. Philosophical Topics, 13(1):89110.Google Scholar
Stein, H. (1967). Newtonian Space-Time. Texas Quarterly, 10:174200.Google Scholar
Swanson, N., and Halvorson, H. (n.d.). On North’s “The Structure of Physics”. http://philsci-archive.pitt.edu/9314/.Google Scholar
Teitel, T. (2021). What theoretical equivalence could not be. Philosophical Studies, 178(12), 41194149.Google Scholar
van Benthem, J., and Pearce, D. (1984). A Mathematical Characterization of Interpretation between Theories. Studia Logica, 43(3):295303.Google Scholar
Wallace, D. (2019). Who’s Afraid of Coordinate Systems? An Essay on Representation of Spacetime Structure. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 67:125136.Google Scholar
Wallace, D. (n.d.-a). Isolated Systems and Their Symmetries, Part I: General Framework and Particle-Mechanics Examples. http://philsci-archive.pitt.edu/16623/.Google Scholar
Wallace, D. (n.d.-b). Observability, Redundancy and Modality for Dynamical Symmetry Transformations. http://philsci-archive.pitt.edu/16622/.Google Scholar
Washington, E. E. (2018). On the Equivalence of Logical Theories. Senior thesis, Princeton University, Princeton, NJ.Google Scholar
Weatherall, J. O. (2016). Are Newtonian Gravitation and Geometrized Newtonian Gravitation Theoretically Equivalent? Erkenntnis, 81(5):10731091.Google Scholar
Weatherall, J. O. (2017). Inertial Motion, Explanation, and the Foundations of Classical Spacetime Theories. In Lehmkuhl, D., Schiemann, G., and Scholz, E., editors, Towards a Theory of Spaceme Theories, number 13 in Einstein Studies. Birkhäuser, Basel.Google Scholar
Weatherall, J. O. (2021). Why Not Categorical Equivalence? In Madarász, J. X., and Szekely, G., editors, Hajnal Andréka and István Németi on Unity of Science, number 19 in Outstanding Contributions to Logic, 427451. Springer, Cham.Google Scholar
Weatherall, J. O. (2020). Equivalence and Duality in Electromagnetism. Philosophy of Science, 87(5), 11721183.Google Scholar
Wheeler, J. T. (2007). Gauging Newton’s Law. Canadian Journal of Physics, 85(4):307344.Google Scholar
Wilhelm, I. (2021). Comparing the structures of mathematical objects. Synthese, 199(3), 63576369.Google Scholar
Winnie, J. A. (1986). Invariants and Objectivity: A Theory with Applications to Relativity and Geometry. In Colodny, R. G., editor, From Quarks to Quasars, University of Pittsburgh Press, Pittsburgh, 71180. University of Pittsburgh Press, Pittsburgh.Google Scholar
Worrall, J. (1989). Structural Realism: The Best of Both Worlds? Dialectica, 43(1-2):99124.Google Scholar
Worrall, J. (2007). Miracles and Models: Why Reports of the Death of Structural Realism May Be Exaggerated. Royal Institute of Philosophy Supplements, 61:125154.Google Scholar
Zahar, E. (2001). Poincaré’s Philosophy: From Conventionalism to Phenomenology. Open Court, Chicago.Google Scholar
Zahar, E. G. (2004). Ramseyfication and Structural Realism. Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia, 19(1):530.Google Scholar

Save element to Kindle

To save this element to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Structure and Equivalence
  • Neil Dewar, Ludwig-Maximilians-Universität Munchen
  • Online ISBN: 9781108914581
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Structure and Equivalence
  • Neil Dewar, Ludwig-Maximilians-Universität Munchen
  • Online ISBN: 9781108914581
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Structure and Equivalence
  • Neil Dewar, Ludwig-Maximilians-Universität Munchen
  • Online ISBN: 9781108914581
Available formats
×