Abstract
The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different “scientific mentalities’ in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion of a “scientific theory” in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4).
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References
Arbib, M. and Padulo, L.: 1974, System Theory, Saunders, Philadelphia.
Ashby, W. R.: 1976, Introduction to Cybernetics, Methuen, London.
Balzer, W. and Sneed, J. D.: 1977/8, Generalized Net Structures of Empirical Theories’, Studia Logica 36, 195–211, and 37, 167–177.
Barwise, J. (ed.): 1977, Handbook of Mathematical Logic, North-Holland, Amsterdam.
Benthem, J. F. A. K. van: 1978, ‘Ramsey Eliminability’, Studia Logica 37, 321–336.
Benthem, J. F. A. K. van: 1980, The Logic of Time’, Filosofisch Instituut, Rijksuniversiteit, Groningen.
Benthem, J. F. A. K. van: 1980a, Modeltheorie voor Wetenschapsfilosofen’, Filosofisch Instituut, Rijksuniversiteit, Groningen.
Benthem Jutting, L. S. van: 1979, ‘Checking Landau's ‘Grundlagen’ in the AUTOMATH System’, Mathematical Centre Tracts 83, Amsterdam.
Beth, E. W.: 1949, ‘Towards an Up-to-date Philosophy of the Natural Sciences’, Methodos 1, 178–185.
Beth, E. W. and Piaget, J.: 1966, Mathematical Epistemology and Psychology, D. Reidel, Dordrecht.
Chang, C. C. and Keisler, H. J.: 1973, Model Theory, North-Holland, Amsterdam.
Craig, W. and Vaught, R. L.: 1958, ‘Finite Axiomatizability using Additional Predicates’, Journal of Symbolic Logic 23, 289–308.
Chomsky, N.: 1957, Syntactic Structures, Mouton, Den Haag.
Fine, K.: 1975, ‘Vagueness, Truth and Logic’, Synthese 30, 265–300.
Giedymin, J. (ed): 1978, K. Ajdukiewicz — The Scientific World-Perspective and Other Essays’, Reidel, Dordrecht.
Giles, R.: 1979, ‘Formal Languages and Physics’, in Hooker (ed.) 1979, pp.
Henkin, L., Suppes, P. and Tarski, A. (eds.): 1959, ‘The Axiomatic Method: with Special Reference to Geometry and Physics, North-Holland, Amsterdam.
Hilbert, D.: 1899, Grundlagen der Geometrie, Teubner, Leipzig.
Hintikka, J. and Remes, U.: 1974, The Method of Analysis, Its Philosophical Significance and Geometrical Origins, D. Reidel, Dordrecht.
Hooker, C. A. (ed.): 1979, Physical Theory as Logico-Operational Structure, D. Reidel, Dordrecht.
Kochen, S. and Specker, E.: 1967, ‘The Problem of Hidden Variables in Quantum Mechanics’, Journal of Mathematics and Mechanics 17, 59–67.
Lakatos, I. M.: 1976, Proofs and Refutations, Cambridge University Press, Cambridge.
Lindström, P.: 1979, ‘Some Results on Interpretability’, Department of Philosophy, University of Göteborg.
Lorenzen, P. and Lorenz, K.: 1978, Dialogische Logik, Wissenschaftliche Buchgesellschaft, Darmstadt.
Montague, R.: 1974, Formal Philosophy, Yale University Press, New Haven.
Nagel, E.: 1961, The Structure of Science, Harcourt, Brace & World, New York.
Pearce, D.: 1980, ‘Logical Properties of the Structuralist Concept of Reduction’ Erkenntnis (forthcoming) (referred to as 1980A).
Pearce, D.: 1980, ‘A Mathematical Characterization of Interpretation, Reduction and Definitional Equivalence’, to appear in Studia Logica (referred to as 1980B).
Pearce, D.: 1981, ‘Some Relations between Empirical Systems’, Epistemologia 4, 363–380.
Perelman, C.: 1976, Logique Juridique, Jurisprudence Générale Dalloz, Paris.
Piaget, J.: 1973, Principles of Genetic Epistemology, Routledge and Kegan Paul, London.
Przełçcki, M.: 1969, The Logic of Empirical Theories, Routledge and Kegan Paul, London.
Przełçcki, M.: 1974, ‘A Set-theoretic versus a Model-theoretic Approach to the Logical Structure of Physical Theories’, Studia Logica 33, 91–105.
Przełçcki, M., Szaniowski, K. and Wójcicki, R. (eds.): 1976, Formal Methods in the Methodology of Empirical Sciences, D. Reidel, Dordrecht.
Quine, W. V. O.: 1951, ‘Two Dogmas of Empiricism’, in Quine 1963, pp
Quine, W. V. O.: 1963, From a Logical Point of View, Harper and Row, New York.
Ramsey, F. P.: 1978, Foundations: Essays in Philosophy, Logic, Mathematics and Economics, Routledge and Kegan Paul, London.
Rantala, V.: 1977, ‘Definability in Empirical Sciences’, Acta Philosophica Fennica 29, 213–222.
Rantala, V.: 1977, Aspects of Definability, North-Holland, Amsterdam (referred to as 1977a).
Rantala, V.: 1980, ‘On the Logical Basis of the Structuralist Philosophy of Science’, Erkenntnis 15, 33–53.
Reichenbach, H.: 1956, The Philosophy of Space and Time, Dover, New York.
Saarinen, E. (ed.): 1979, Game-theoretical Semantics, D. Reidel, Dordrecht.
Segerberg, K.: 1971, An Essay in Classical Modal Logic, Filosofiska Studier 13, Uppsala.
Smorynski, C.: 1977, ‘The Incompleteness Theorems’, in Barwise 1977, pp. 821–865.
Smullyan, R. M.: 1977, The Tao Is Silent, Harper and Row, New York.
Sneed, J. D.: 1971, The Logical Structure of Mathematical Physics, D. Reidel, Dordrecht (2nd ed. rev. 1979).
Stegmüller, W.: 1979, The Structuralist View of Theories, Springer, Berlin.
Suppe, F.: 1976, ‘Theoretical Laws’, in Przełçcki, Szaniowski, and Wójcicki (eds.) 1976, pp 247–267.
Suppes, P.: 1957, Introduction to Logic, Van Nostrand, New York.
Suppes, P.: 1960, ‘A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences’, Synthese 12, 287–301.
Suppes, P. (ed.): 1973, Space, Time and Geometry, D. Reidel, Dordrecht.
Tarski, A.: 1959, ‘What is Elementary Geometry?’, in Henkin, Suppes and Tarski (eds.) 1959, pp.
Toulmin, S. E.: 1958, The Uses of Argument, Cambridge University Press, Cambridge.
Vaught, R. L.: 1960, ‘Sentences True in All Constructive Models’, Journal of Symbolic Logic 25, 39–53.
Wessel, H. (ed.): 1977, Logik und empirische Wissenschaften, Akademie Verlag, Berlin (DDR).
Weyl, H.: 1963, Philosophy of Mathematics and Natural Science, Atheneum, New York.
Zeeman, E. C.: 1964, ‘Causality Implies the Lorentz Group’, Journal of Mathematical Physics 5, 490–493.
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I would like to thank David Pearce and Veikko Rantala for their helpful comments.
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van Benthem, J. The logical study of science. Synthese 51, 431–472 (1982). https://doi.org/10.1007/BF00485263
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DOI: https://doi.org/10.1007/BF00485263