Abstract
This paper is a first step in a larger enterprise. The ultimate aim of my enterprise is to uncover the logical structures, in a strict sense of the word “logic”, typically involved in scientific enterprise, not just in the justification of already obtained results but in the acquisition of new information.
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Notes
See T.S. Kuhn, The Structure of Scientific Revolutions, second ed., The University of Chicago Press, 1970;
T.S. Kuhn, The Essential Tension: Selected Studies in Scientific Tradition and Change, The University of Chicago Press, 1977;
Gary Cutting, editor, Paradigms and Revolutions; Applications and Appraisals of Science, University of Notre Dama Press, Notre Dame, 1980;
Ian Hacking, editor, Scientific Revolutions (Oxford Readings in Philosophy), Oxford U.P., 1981.
See J.D. Sneed, The Logical Structure of Mathematical Physics, D. Reidel, Dordrecht, 1971;
Wolfgang Stegmüller, Theorienstruktur und Theoriendynamik, Springer-Verlag, Berlin-Heidelberg-New York, 1973;
Wolfgang Stegmüller, Theory Construction, Structure, and Rationality, Springer-Verlag, 1979. Useful surveys of the tradition Sneed and Stegmüller started are Ilkka Niiniluoto, The Growth of Theories: Comments on the Structuralist Approach in Jaakko Hintikka et al., editors, Theory Change Ancient Axiomatics, and Galileo’s Methodology, D. Reidel, Dordrecht, 1980, pp. 3–47; and Ilkka Niiniluoto, “Scientific Progress”, Synthese vol. 45 (1980), pp. 427–462.
See Erkenntnis vol. 10, no 2 (July 1976), with contributions by Sneed, Stegmüller, and Kuhn.
Cf. Dana Scott and Peter Krauss, “Assigning Probabilities to Logical Formulas” in Jaakko Hintikka and Patrick Suppes, editors, Aspects of Indicative Logic, North-Holland, Amsterdam, 1966, pp. 219–264.
See David Pearce and Veikko Rantala, “On a New Approach to Metascience”, Reports from the Department of Philosophy, University of Helsinki, no. 1 (1981), pp. 1–42 (with further references).
Karl R. Popper, The Logic of Scientific Discovery, Hutchinson, London, 1959;
Karl R. Popper, Conjectures and Refutations, Routledge and Kegan Paul, London 1963;
Karl Popper, Objective Knowledge, Oxford U.P., 1972;
P.A. Schilpp, editor, The Philosophy of Karl Popper I–II, Open Court, La Salle, Ill., 1974.
See Jaakko Hintikka and Juhani Pictarinen, “Semantic Information and Inductive Logic” in Jaakko Hintikka and Patrick Suppes, editors, Aspects of Inductive Logic, North-Holland, Amsterdam, 1966, pp. 96–112; Jaakko Hintikka, “Varieties of Information and Scientific Explanation”, in B. van Rootselaar and J.F. Staal, editors, Logic, Methodology, and Philosophy of Science III: Proceedings of the 1967 Congress, North-Holland, Amsterdam, 1968. Of course we have to restrict our attention to a relevant range of hypotheses, but there is nothing ad hoc about such restrictions.
Cf., e.g., Lester E. Dubins and Leonard J. Savage, How To Gamble If You Must: Inequalities for Stochastic Processes, McGraw-Hill, New York, 1965.
Larry Laudan, Progress and Its Problems: Towards a Theory of Scientific Growth, University of California Press, Berkeley, 1977;
Larry Laudan, Science and Hypothesis, D. Reidel, Dordrecht, 1981;Larry Laudan, “A Problem-solving Approach to Scientific Progress” in Ian Hacking, editor (note 1 above).
Jaakko Hintikka, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, vol. 28, no. 4), Helsinki, 1976; “New Foundations for a Theory of Questions and Answers”, forthcoming; “Questions with Outside Quantifiers” in Robinson Schneider et al., editors, Papers from the Parasession on Nondeclaratives, Chicago Linguistics Society, Chicago, 1982, pp. 83–92.
E. W. Beth, “Semantic Entailment and Formal Derivability”, Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde, N.R. vol. 18, no. 13, Amsterdam, 1955, pp. 309–342; reprinted in Jaakko Hintikka, editor, Philosophy of Mathematics, Oxford U.P., 1969, pp. 9–41.
One can construe a tableau construction as an attempt to construct a model set in which the entries in the left tableau column are all included but which does not contain any entries in the right tableau column. If you turn a closed tableau upside down you obtain a Gentzen-type proof of the desired sequent.
Richard Robinson, “Begging the Question 1971”, Analysis, vol. 31 (1971), pp. 113–117.
If my questioning games are thought of as research games against nature, the motivation of this restriction is clear. Nature can directly tell us what is true or false in particular cases, not whether some complicated sentence involving nested quantifiers is true or false.
Cf. R. G. Collingwood, An Essay on Metaphysics, Clarendon Press, Oxford, 1940;
R. G. Collingwood, An Autobiography, Clarendon Press, Oxford, 1939;
Michael Krausz, “The Logic of Absolute Presuppositions” in Michael Krausz, editor, Critical Essays on the Philosophy of R. G. Collingwood, Clarendon Press, Oxford, 1972, pp. 222–240.
This is shown by the existence of theories which are model-complete but not complete. Cf., e.g. Abraham Robinson, Introduction to Model Theory and to the Metamathematics of Algebra, North-Holland, Amsterdam, 1963.
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Hintikka, J. (1999). True and False Logics of Scientific Discovery. In: Inquiry as Inquiry: A Logic of Scientific Discovery. Jaakko Hintikka Selected Papers, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9313-7_5
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