• Journal for History of Mathematics
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• v.28 no.4
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• pp.181-190
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• 2015

In spite of various attempts to characterize the ontological status of space-time, Newtonian substantivalism and Leibnizian relationism, what is really at issue in the controversy between the two parties is by no means clear. This essay argues that from the perspective of space-time symmetries, classical space-time can be unambiguously classified as substantival space-time and relational space-time. The symmetries of space-time theories distinguish the invariant geometric relationships between events. The essential difference between the two space-times stems from whether or not there exists the affine structure that distinguishes the inertial trajectories of a given body.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.87-100
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• 2017

The ontological status of Newtonian space-time has been debated under the name of substantivalism-relationism controversy. The debates between the two parties are concerned with the nature of existence of space-time. Substantivalism maintains that the points of space-time have existence analogous to material substance. Relationism claims that space-time should be understood as the framework of possible spatio-temporal relations between bodies. Newtonian space is considered as a three dimensional entity in accordance with our geometric common sense. Yet given that the concept of motion is defined as the change of position throughout time, it is possible to interpret space-time as a 4 dimensional entity. In this essay, substantivalist-relationist debate is considered within the context of non-relativistic 4 dimensional space-time theory. This essay attempts to clarify the dispute over the ontology of space-time by elucidating the relationship between the ontology of space-time, motion, and space-time symmetry.