Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-08T22:23:45.027Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Extension of Beth's Semantics of Physical Theories

Published online by Cambridge University Press:  14 March 2022

Bas C. Van fraassen
Bas C. Van fraassen*
Affiliation:
University of Toronto
Get access Rights & Permissions [Opens in a new window]

Abstract

A basic aim of E. Beth's work in philosophy of science was to explore the use of formal semantic methods in the analysis of physical theories. We hope to show that a general framework for Beth's semantic analysis is provided by the theory of semi-interpreted languages, introduced in a previous paper. After developing Beth's analysis of nonrelativistic physical theories in a more general form, we turn to the notion of the ‘logic’ of a physical theory. Here we prove a result concerning the conditions under which semantic entailment in such a theory is finitary. We argue, finally, that Beth's approach provides a characterization of physical theory which is more faithful to current practice in foundational research in the sciences than the familiar picture of a partly interpreted axiomatic theory.

Type
Research Article
Information
Philosophy of Science , Volume 37 , Issue 3 , September 1970 , pp. 325 - 339
Copyright
Copyright © 1970 by The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

This study was supported in part by NSF grant GS-1566. I also wish to express my debt to Dr. F. Suppe, University of Illinois, for stimulating discussion. His doctoral thesis [27] develops a point of view closely related to Beth's.

References

REFERENCES

[1] Bednarek, A. R. and Wallace, A. D., “Finite Approximants of Compact Totally Disconnected Machines,” Mathematical Systems Theory, vol. 1, 1967, pp. 209–224.CrossRefGoogle Scholar
[2] Beth, E. W., “Analyse Sémantique des Théories Physiques,” Synthese, vol. 7,1948/49, pp. 206–207.Google Scholar
[3] Beth, E. W., Naturphilosophie, Noorduyn, Gorinchem; 1948.Google Scholar
[4] Beth, E. W., “Semantics of Physical Theories,” Synthese, vol. 12, 1960, pp. 172–175.CrossRefGoogle Scholar
[5] Beth, E. W., “Towards an Up-to-date Philosophy of the Natural Sciences,” Methodos, vol. 1, 1949, pp. 178–185.Google Scholar
[6] Carnap, R., Meaning and Necessity, 2nd edit., University of Chicago Press, Chicago, 1956.Google Scholar
[7] d'Abro, A., The Rise of the New Physics, Dover, New York, 1951.Google Scholar
[8] Ginsberg, S., “Some Remarks on Abstract Machines,” Transactions of the American Mathematical Society, vol. 96, 1960, pp. 400–444.CrossRefGoogle Scholar
[9] Green, H. S., Matrix Mechanics, Noordhoff, Groningen, 1965.Google Scholar
[10] Grünbaum, A., Philosophical Problems of Space and Time, Knopf, New York, 1963.Google Scholar
[11] Hall, G. G., Applied Group Theory, American Elsevier, New York, 1967.Google Scholar
[12] Hanson, N. R., “Are Wave Mechanics and Matrix Mechanics Equivalent Theories?,” in Current Issues in the Philosophy of Science (eds. Feigl, H. and Maxwell, G.), Holt, Rinehart and Winston, New York, 1961, pp. 401–425.Google Scholar
[13] Hutten, E. H., “On Semantics and Physics,” Proceedings of the Aristotelian Society, vol. 49, 1948/49, pp. 115–132.CrossRefGoogle Scholar
[14] Kaempffer, F. A., Concepts in Quantum Mechanics, Academic Press, New York, 1965.Google Scholar
[15] Lax, P. D. and Phillips, R. S., Scattering Theory, Academic Press, New York, 1967.Google Scholar
[16] Mackey, G. W., The Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963.Google Scholar
[17] Mandl, F., Quantum Mechanics, Academic Press, New York, 1957.Google Scholar
[18] Moore, E. F., “Gedanken—Experiments on Sequential Machines,” Automata Studies, Annals of Mathematics Studies, no. 34, pp. 129–153.CrossRefGoogle Scholar
[19] Morse, P. M., “Markow Processes,” in Notes on Operations Research 1959, M.I.T. Press, Cambridge (Mass.), 1959, pp. 84–105.Google Scholar
[20] Nemyckii, V. V., Topological Problems of the Theory of Dynamical Systems, American Mathematical Society Translation no. 103 (1954); reprinted in American Mathematical Society Translations, Series 1, vol. 5, 1962.Google Scholar
[21] Putnam, H., “A Philosopher Looks at Quantum Mechanics,” in Beyond the Edge of Certainty (ed. Colodny, R. G.), Prentice-Hall, Englewood Cliffs, 1965, pp. 75–101.Google Scholar
[22] Reichenbach, H., The Direction of Time, University of California Press, Berkeley, 1956.CrossRefGoogle Scholar
[23] Rescher, N., “On the Logic of Chronological Propositions,” Mind, vol. 75 (N.S.), 1966, pp. 75–96.CrossRefGoogle Scholar
[24] Sellars, W., “Counterfactuals, Dispositions, and the Causal Modalities,” Minnesota Studies in the Philosophy of Science, vol. II, 1957, pp. 225–308.Google Scholar
[25] Sellars, W., Science, Perception and Reality, Humanities Press, New York, 1963.Google Scholar
[26] Spector, M., “Models and Theories,” British Journal for the Philosophy of Science, vol. 16, 1965, pp. 121–142.CrossRefGoogle Scholar
[27] Suppe, F., Meaning and Use of Models in Mathematics and the Exact Sciences, Dissertation, University of Michigan, 1967.Google Scholar
[28] Suppes, P., “What is a Scientific Theory ?,” in Philosophy of Science Today, (ed. Morgenbesser, S.), Basic Books, New York, 1967, pp. 55–67.Google Scholar
[29] Suppes, P., Set-Theoretical Structures in Science, forthcoming (mimeographed, Stanford University, 1967).Google Scholar
[30] van Fraassen, B. C., “The Labyrinth of Quantum Logic,” presented at the Philosophy of Science Association First Biennial Meeting, Pittsburgh, October 1968.Google Scholar
[31] van Fraassen, B. C., “Meaning Relations among Predicates,” Nous, vol. 1, 1967, pp. 161–179.CrossRefGoogle Scholar
[32] van Fraassen, B. C., “Meaning Relations and Modalities” Nous, vol. 3, 1969, pp. 155–167.CrossRefGoogle Scholar
[33] van Fraassen, B. C., “A Topological Proof of the Löwenheim-Skolem, Compactness, and Strong Completeness Theorems for Free Logic,” Zeitschrift für math. Logik und Grundlagen der Math., vol. 14, 1968, pp. 245–254.CrossRefGoogle Scholar
[34] Weyl, H., The Theory of Groups and Quantum Mechanics (tr. H. P. Robertson), Methuen, London, 1931.Google Scholar