Abstract
In this paper I discuss the heuristic role which mathematics plays in physical discovery: first through the surplus structure which mathematics injects into physical principles which are given a mathematical formulation; secondly, through the realist interpretation of certain mathematical entities which appear at first sight to be devoid of any physical meaning. I then try to account for this dual role of mathematics in terms of a single philosophical principle, namely Meyerson's principle of identity. I finally apply these considerations to the study of two important questions; the questions namely of the continuity between STR and GTR (STR = Special Theory of Relativity, GTR = General Theory of Relativity) and of the emergence both of General Relativity and of the Unified Field Theories of Weyl, Eddington and Schrödinger-Einstein.
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Notes
Cf. “Geometrie and Erfahrung” in: Einstein, Mein Weltbild, p. 119.
Cf. Oskar Becker, Grundlagen der Mathematik, pp. 144–167.
For the role which mathematical surplus structure plays in physics, cf. M. L. G. Redhead, “Symmetry in Intertheory Relations”, in: Synthese 32 (1975).
Cf. Bernhard Riemann, Collected Works, (Dover) pp. 272–273.
As above, p. 286.
Cf. Mach, Mechanics, Introduction. Also: Erkenntnis and Irrtum, pp. 164–182.
H. Weyl, Raum Zeit Materie, § 40.
Eddington, The mathematical Theory of Relativity, § 97.
Schrödinger, Space-Time Structure, Chapter XII.
Duhem, Aim and Structure of Physical Theory, Part 2,.Chapter 1.
For the important role which philosophical realism plays in the logic of discovery, cf. Popper, “Three Views Concerning Human Knowledge” in: ‘Conjectures and Refutations’ (Section 3).
For the fruitfulness of these equivalent reformulations, cf. Feynman, The Character of Physical Law, p. 168.
E. Meyerson, Identité et Réalité, Chapter I. Also: De L'Explication das Les Sciences, Chapter V.
Cf. Popper, “The Aim of Science”, in: Objective Knowledge, p. 191.
Identité et Réalité, Chapter III.
Weyl, Philosophy of Mathematics and Natural Science, p. 5.
Meyerson, La Déduction Relativiste, Chapter XX.
Weyl, Philosophy of Mathematics and Natural Science, pp. 87–88.
Mach, The History and the Root of the Principle of the Conservation of Energy, Notes.
Eddington, The Mathematical Theory of Relativity, p. 120.
“Prinzipielles zur allgemeinen Relativitätstheorie”, Annalen der Physik, Band 55, 1918. Also see Appendix 1.
For this point I am indebted to Professor J. Stachel.
Cf. above, see I.1.
Mathematical Theory of Relativity, p. 212.
Mathematical Theory of Relativity, p. 213.
Mathematical Theory of Relativity, p. 206.
Schrödinger, Space-Time Structure, p. 112.
Cf. my "Why did Einstein's programme supersede Lorentz's?, Brit. J. Phil. Sci. 24 (1973) pp 95–123 and 223–62.
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Zahar, E.G. (1979). The mathematical origins of general relativity and of unified field theories. In: Nelkowski, H., Hermann, A., Poser, H., Schrader, R., Seiler, R. (eds) Einstein Symposion Berlin. Lecture Notes in Physics, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09718-X_84
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DOI: https://doi.org/10.1007/3-540-09718-X_84
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