Philosophy of Science 49 (4):575-590 (1982)

In the correspondence with Clarke, Leibniz proposes to construe physical theory in terms of physical (spatio-temporal) relations between physical objects, thus avoiding incorporation of infinite totalities of abstract entities (such as Newtonian space) in physical ontology. It has generally been felt that this proposal cannot be carried out. I demonstrate an equivalence between formulations postulating space-time as an infinite totality and formulations allowing only possible spatio-temporal relations of physical (point-) objects. The resulting rigorous formulations of physical theory may be seen to follow Leibniz' suggestion quite closely. On the other hand, physical assumptions implicit in the postulation of space-time totalities are made explicit in the reconstruction of the space-time versions from the physical-relation versions
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DOI 10.1086/289078
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References found in this work BETA

Newtonian Space-Time.Howard Stein - 1967 - Texas Quarterly 10 (3):174--200.
Mathematics Without Foundations.Hilary Putnam - 1967 - Journal of Philosophy 64 (1):5-22.
The Leibniz-Clarke Correspondence.H. G. Alexander - 1956 - Philosophy 32 (123):365-366.
A Theory of Time and Space.Alfred A. Robb - 1915 - Mind 24 (96):555-561.
Euclid's Elements and the Axiomatic Method.Ian Mueller - 1969 - British Journal for the Philosophy of Science 20 (4):289-309.

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