A formal system for classical particle mechanics, its model-theoretic applications and space-time structure

Synthese 102 (2):267 - 292 (1995)
Abstract
In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time.
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DOI 10.1007/BF01089803
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The logical structure of mathematical physics.J. D. Sneed - 1975 - Tijdschrift Voor Filosofie 37 (1):151-152.
Einstein, Newton and the Empirical Foundations of Space Time Geometry.Robert DiSalle - 1992 - International Studies in the Philosophy of Science 6 (3):181 – 189.

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