Abstract
In this paper it is shown, firstly, that physical theories contain not completely formalizable elements, the most significant being meaning assignments to formal components, approximations, unspecified elements fixed by suitable determination in specific models, and the scope (or region of validity) of the theories; secondly, that the importance of these elements depends on the type of theory as specified by a number of characteristics; and thirdly, that theories can — and must — contain various kinds of inconsistencies that are amenable to rational manipulation but preclude axiomatization within the framework of formal logic. Finally a number of aims for the axiomatic approach are outlined which are compatible with these non-formalizable elements and moreover do not exist for axiomatic methods in mathematics.
First published in: Rev. Mex. Fís. 27, 583 (1981)
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References
Bhaskar, R. (1978): A Realist Theory of Science ( Harvester Press, Sussex )
Bohr, A., Mottelson, B.R. (1969/75): Nuclear Structure 2 Vol. (Benjamin, New York)
Brown, G.E. (1971): Unified Theory of Nuclear Models and Forces 3rd edn. ( North-Holland, Amsterdam )
Bunge, M. (1968) in I. Lakatos & A. Musgrave (eds.) Problems in the Philosophy of Physics ( North-Holland, Amsterdam ) p. 120
Bunge, M. (1973): Philosophy of Science ( Reidel, Dordrecht )
Claverie, P, Diner, S. (1976): in O. Chalvet et al. (eds.) Localization and Delocalization in Quantum Chemistry Vol. II (Reidel, Dordrecht) pp. 395, 449, 461
Carathéodory, C. (1909): Math. Annalen 67, 355
Falk, G., Jung, H. (1959) in S. Flügge (ed.) Handbuch der Physik, Vol. III/2 ( Springer, Berlin Heidelberg New York ), p. 119
Farquhar, I. (1964): Ergodic Theory in Statistical Mechanics ( Wiley, New York )
Gudder, S.P. (1977) in W.O. Price & S.S. Chissick (eds.) The Uncertainty Principle and Foundations of Quantum Mechanics ( Wiley, London ), p. 247
Hao Wang (1963): A Survey of Mathematical Logic Chapt. I II ( North-Holland, Amsterdam )
Heyting, A. (1930): Sitzber. preuss. Akad. Wiss., phys. math. Kl. (Göttingen) p. 42, 57, 158
Hilbert, D. (1900): Nachr. K. Ges. Wiss., math-phys. Kl., 253
Hilbert, D., Bernays, P. (1934/39): Grundlagen der Mathematik (J. Springer, Berlin)
Jaynes, E.T. (1957): Phys. Rev. 106, 171
Jost, R. (1960) in M. Fierz, V.F. Weisskopf (eds.) Theoretical Physics in the Twentieth Century (Interscience) p. 107
Kneebone, G.T. (1963): Mathematical Logic and the Foundations of Mathematics ( Van Nostrand, London )
Mehra, J., Sudarshan, E.C.G. (1972): Nuovo Cimento 11B, 215
Neumann, J. von (1932): Mathematische Grundlagen der Quantenmechanik ( Springer, Berlin Heidelberg New York )
Penrose, O. (1970): Foundations of Statistical Mechanics (Wiley, New York)
Rosenfeld, L. (1968): Nucl. Phys. A108 (1954), 241
Scheibe, E. (1973): The Logical Analysis of Quantum Mechanics ( Pergamon Press, Oxford ) p. 14
Suppes, P. (1954): Philos. Sci. 21, 242
Tisza, L. (1963): Rev. Mod. Phys. 35, 151
Tolman, R.C. (1938): The Principles of Statistical Mechanics ( Oxford University Press, Oxford )
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Brody, T.A. (1993). The Axiomatic Approach in Physics. In: de la Peña, L., Hodgson, P.E. (eds) The Philosophy Behind Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78978-6_26
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DOI: https://doi.org/10.1007/978-3-642-78978-6_26
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