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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References
Balzer, W., C. U. Moulines, and J. D. Sneed: 1987,An Architectonic for Science, The Structuralist Program, D. Reidel, Dordrecht.
DiSalle, R.: 1992, ‘Einstein, Newton and the Empirical Foundations of Spacetime Geometry’,International Studies in the Philosophy of Science 6(3), 181–9.
Earman, J.: 1989,World Enough and Space-Time, Absolute versus Relational Theories of Space and Time, MIT Press, Cambridge, MA.
Ehlers, J.: 1973, ‘The Nature and Structure of Spacetime’, in J. Mehra (Ed.),The Physicist's Conception of Nature, D. Reidel, Dordrecht.
Friedman, M.: 1983,The Foundations of Space-Time Theories, Princeton University Press, Princeton.
Herschel, W.: 1912 [1783], ‘On the Proper Motion of the Sun and Solar System’, inThe Scientific Papers of Sir William Herschel, London.
Ishigaki, T.: 1994, ‘Newton'sPrincipia from a Logical Point of View’,The Annals of the Japan Association for Philosophy of Science 8(4), 221–36.
Kant, I.: 1973 [1755], ‘Allgemeine Naturgeschichte und Theorie des Himmels’, in A. Buchenau (Ed.),Immanuel Kants Werke, Band 1, Gerstenberg, Hildesheim.
Lambert, J. H.: 1929 [1761], ‘Concerning Systems of Systems (from ‘Kosmologischen Briefe’)’, in H. Shapley and K. E. Howarth (eds.),A Source Book in Astronomy, McGraw-Hill, New York.
Newton, I.: 1966a [1726],Sir Isaac Newton PRINCIPIA, Motte's Translation Revised by Cajori, University of California Press, Berkeley.
Newton, I.: 1966b [1728], ‘The System of the World’, inSir Isaac Newton PRINCIPIA, Motte's Translation Revised by Cajori, University of California Press, Berkeley.
Pannekoek, A.: 1989 [1961],A History of Astronomy, Dover, New York.
Sneed, J. D.: 1979,The Logical Structure of Mathematical Physics, the second edition, D. Reidel, Dordrecht.
Stegmüller, W.: 1976,The Structure and Dynamics of Theories, Springer, New York.
Stegmüller, W.: 1979,The Structuralist View of Theories, A Possible Analogue of the Bourbaki Programme in Physical Science, Springer, Berlin.
Trautman, A.: 1973, ‘Theory of Gravitation’, in J. Mehra (Ed.),The Physicist's Conception of Nature, D. Reidel, Dordrecht.
Wright, T.: 1929 [1750], ‘Speculation on the Structure of the Milky Way (from ‘An Original Theory of the Universe’)’, in H. Shapley and K. E. Howarth (Eds.),A Source Book in Astronomy, McGraw-Hill, New York.
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Ishigaki, T. A formal system for classical particle mechanics, its model-theoretic applications and space-time structure. Synthese 102, 267–292 (1995). https://doi.org/10.1007/BF01089803
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DOI: https://doi.org/10.1007/BF01089803