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An Axiomatic Foundation for the Logic of Inductive Generalization

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Formal Methods in the Methodology of Empirical Sciences

Part of the book series: Synthese Library ((SYLI,volume 103))

Abstract

One of the most interesting viewpoints from which inductive logic can be looked at is to ask what the different factors are that must be taken into account in singular inductive inference, i.e., in the usual technical jargon, what the arguments of the representative functions of one’s system of inductive methods are. It is well known that Carnap’s λ-continuum of inductive methods can be derived from essentially one single assumption concerning these arguments of the representative function.1 It is shown in this paper that a logic of inductive generalization is obtained if this assumption is weakened in a natural way.

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References

  • J. G. Kemeny, ‘Carnap’s theory of probability and induction’, in P. A. Schilpp (ed.), The Philosophy of Rudolf Carnap, Open Court, LaSalle, Ill., 1963, pp. 711–738

    Google Scholar 

  • R. Carnap and W. Stegmüller, Induktive Logik und Wahrscheinlichkeit, Springer-Verlag, Wien, 1958, pp. 242–249;

    Google Scholar 

  • R. Carnap, ‘Notes on probability and induction’, Synthese 25 (1973), pp. 286–292.

    Article  Google Scholar 

  • B. de Finetti, ‘Foresight: Its logical laws, its subjective sources’, in H. E. Kyburg and H. E. Smokier (eds.), Studies in Subjective Probability, John Wiley, New York, 1964, pp. 93–158.

    Google Scholar 

  • R. Hilpinen, ‘Carnap’s new system of inductive logic’, Synthese 25 (1973), pp. 311–313.

    Article  Google Scholar 

  • J. Hintikka, ‘A two-dimensional continuum of inductive methods’, in J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, North-Holland, Amsterdam 1966, pp. 113–132.

    Chapter  Google Scholar 

  • J. Hintikka, ‘On a combined system of inductive logic’, in Studia Logico-Mathematica et Philosophica in Honorem Rolf Nevanlinna, Acta Philosophica Fennica 18 (1965), pp. 21–30.

    Google Scholar 

  • H. Gaifman, ‘Concerning measures on first-order calculi’, Israel Journal of Mathematics 2 (1964), 1–18

    Article  Google Scholar 

  • D. Scott and P. Krauss, ‘Assigning probabilities to logical formulas’, in J. Hintikka and P. Suppes (eds.), Aspects of Inductive Logic, North-Holland, Amsterdam, 1966, p. 224.

    Google Scholar 

  • J. Hintikka, ‘Unknown probabilities, Bayesianism, and de Finetti’s Representation Theorem’, in R. C. Buck and R. S. Cohen (eds.), Boston Studies in the Philosophy of Science VIII, D. Reidel, Dordrecht, 1971, pp. 325–341.

    Google Scholar 

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Authors

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Marian Przełęcki Klemens Szaniawski Ryszard Wójcicki Grzegorz Malinowski

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© 1976 D. Reidel Publishing Company, Dordrecht, Holland

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Hintikka, J., Niiniluoto, I. (1976). An Axiomatic Foundation for the Logic of Inductive Generalization. In: Przełęcki, M., Szaniawski, K., Wójcicki, R., Malinowski, G. (eds) Formal Methods in the Methodology of Empirical Sciences. Synthese Library, vol 103. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1135-8_4

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  • DOI: https://doi.org/10.1007/978-94-010-1135-8_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1137-2

  • Online ISBN: 978-94-010-1135-8

  • eBook Packages: Springer Book Archive

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