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.
Keywords
Statistical Mechanic Physical Theory Theoretical Structure Axiomatic Approach Primitive ConceptPreview
Unable to display preview. Download preview PDF.
References
- Bhaskar, R. (1978): A Realist Theory of Science ( Harvester Press, Sussex )Google Scholar
- Bohr, A., Mottelson, B.R. (1969/75): Nuclear Structure 2 Vol. (Benjamin, New York)Google Scholar
- Brown, G.E. (1971): Unified Theory of Nuclear Models and Forces 3rd edn. ( North-Holland, Amsterdam )Google Scholar
- Bunge, M. (1968) in I. Lakatos & A. Musgrave (eds.) Problems in the Philosophy of Physics ( North-Holland, Amsterdam ) p. 120CrossRefGoogle Scholar
- Bunge, M. (1973): Philosophy of Science ( Reidel, Dordrecht )Google Scholar
- Claverie, P, Diner, S. (1976): in O. Chalvet et al. (eds.) Localization and Delocalization in Quantum Chemistry Vol. II (Reidel, Dordrecht) pp. 395, 449, 461CrossRefGoogle Scholar
- Carathéodory, C. (1909): Math. Annalen 67, 355CrossRefGoogle Scholar
- Falk, G., Jung, H. (1959) in S. Flügge (ed.) Handbuch der Physik, Vol. III/2 ( Springer, Berlin Heidelberg New York ), p. 119Google Scholar
- Farquhar, I. (1964): Ergodic Theory in Statistical Mechanics ( Wiley, New York )Google Scholar
- Gudder, S.P. (1977) in W.O. Price & S.S. Chissick (eds.) The Uncertainty Principle and Foundations of Quantum Mechanics ( Wiley, London ), p. 247Google Scholar
- Hao Wang (1963): A Survey of Mathematical Logic Chapt. I II ( North-Holland, Amsterdam )MATHGoogle Scholar
- Heyting, A. (1930): Sitzber. preuss. Akad. Wiss., phys. math. Kl. (Göttingen) p. 42, 57, 158Google Scholar
- Hilbert, D. (1900): Nachr. K. Ges. Wiss., math-phys. Kl., 253Google Scholar
- Hilbert, D., Bernays, P. (1934/39): Grundlagen der Mathematik (J. Springer, Berlin)Google Scholar
- Jaynes, E.T. (1957): Phys. Rev. 106, 171ADSCrossRefGoogle Scholar
- Jost, R. (1960) in M. Fierz, V.F. Weisskopf (eds.) Theoretical Physics in the Twentieth Century (Interscience) p. 107Google Scholar
- Kneebone, G.T. (1963): Mathematical Logic and the Foundations of Mathematics ( Van Nostrand, London )MATHGoogle Scholar
- Mehra, J., Sudarshan, E.C.G. (1972): Nuovo Cimento 11B, 215MathSciNetCrossRefGoogle Scholar
- Neumann, J. von (1932): Mathematische Grundlagen der Quantenmechanik ( Springer, Berlin Heidelberg New York )MATHGoogle Scholar
- Penrose, O. (1970): Foundations of Statistical Mechanics (Wiley, New York)MATHGoogle Scholar
- Rosenfeld, L. (1968): Nucl. Phys. A108 (1954), 241MATHCrossRefGoogle Scholar
- Scheibe, E. (1973): The Logical Analysis of Quantum Mechanics ( Pergamon Press, Oxford ) p. 14Google Scholar
- Suppes, P. (1954): Philos. Sci. 21, 242CrossRefGoogle Scholar
- Tisza, L. (1963): Rev. Mod. Phys. 35, 151ADSCrossRefGoogle Scholar
- Tolman, R.C. (1938): The Principles of Statistical Mechanics ( Oxford University Press, Oxford )Google Scholar