In this essay, I examine the curved spacetime formulation of Newtonian gravity known as Newton–Cartan gravity and compare it with flat spacetime formulations. Two versions of Newton–Cartan gravity can be identified in the physics literature—a ‘‘weak’’ version and a ‘‘strong’’ version. The strong version has a constrained Hamiltonian formulation and consequently a well-defined gauge structure, whereas the weak version does not (with some qualifications). Moreover, the strong version is best compared with the structure of what Earman (World enough and spacetime. Cambridge: MIT Press) has dubbed Maxwellian spacetime. This suggests that there are also two versions of Newtonian gravity in flat spacetime—a ‘‘weak’’ version in Maxwellian spacetime, and a ‘‘strong’’ version in Neo-Newtonian spacetime. I conclude by indicating how these alternative formulations of Newtonian gravity impact the notion of empirical indistinguishability and the debate over scientific realism. r 2004 Elsevier Ltd. All rights reserved.
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DOI 10.1016/j.shpsb.2003.10.004
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References found in this work BETA

What is Structural Realism?James Ladyman - 1998 - Studies in History and Philosophy of Science Part A 29 (3):409-424.
Underdetermination, Realism, and Reason.John Earman - 1993 - Midwest Studies in Philosophy 18 (1):19-38.

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Structural Realism.James Ladyman - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
Fundamental and Emergent Geometry in Newtonian Physics.David Wallace - 2020 - British Journal for the Philosophy of Science 71 (1):1-32.
Theoretical Equivalence as Interpretative Equivalence.Kevin Coffey - 2014 - British Journal for the Philosophy of Science 65 (4):821-844.
I—James Ladyman: On the Identity and Diversity of Objects in a Structure.James Ladyman - 2007 - Aristotelian Society Supplementary Volume 81 (1):23-43.
What is Ontic Structural Realism?Peter Mark Ainsworth - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (1):50-57.

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