Abstract
The purpose of this paper is to make a simple observation regarding the Johnson-Carnap continuum of inductive methods (see Johnson 1932, carnap 1952). From the outset, a common criticism of this continuum was its failure to permit the confirmation of universal generalizations: that is, if an event has unfailingly occurred in the past, the failure of the continuum to give some weight to the possibility that the event will continue to occur without fail in the future. The Johnson-Carnap continuum is the mathematical consequence of an axiom termed “Johnson's sufficientness postulate”, the thesis of this paper is that, properly viewed, the failure of the Johnson-Carnap continuum to confirm universal generalizations is not a deep fact, but rather an immediate consequence of the sufficientness postulate; and that if this postulate is modified in the minimal manner necessary to eliminate such an entailment, then the result is a new continuum that differs from the old one in precisely one respect: it enjoys the desideratum of confirming universal generalizations.
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References
AyerA. J.: 1972, Probability and Evidence, Macmillan, London.
Barker, S. F.: 1957, Induction and Hypothesis, Cornell University Press.
CarnapR.: 1952, The Continuum of Inductive Methods, The University of Chicago Press, Chicago.
CostantiniD.: 1979, ‘The Relevance Quotient’, Erkenntnis 14, 149–157.
CostantiniD. and GalavottiM. C.: 1987, ‘Johnson e l'interpretazione degli enunciati probabilistici’, in R.Simili (ed.), L'Epistemologia di Cambridge 1850–1950 (Società Editrice il Mulino, Bologna), 245–262.
EarmanJ.: 1992, Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory, MIT Press, Cambridge, MA.
GoodI. J.: 1992, Introductory remarks for the article in Biometrika 66 (1979), in J. L.Britton (ed.), The Collected Works of A. M. Turing: Pure Mathematics, North-Holland, Amsterdam, pp. 211–223.
HintikkaJ.: 1966, ‘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.
HintikkaJ. and NiiniluotoI.: 1980, ‘An Axiomatic Foundation for the Logic of Inductive Generalization’, in R. C.Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume 2, University of California Press, Berkeley, CA, pp. 157–181.
JeffreysH. and WrinchD.: 1919, ‘On Certain Aspects of the Theory of Probability’, Philosophical Magazine 38, 715–731.
JohnsonW. E.: 1932, ‘Probability: The Deductive and Inductive Problems’, Mind 49, 409–423. [Appendix on pages 421–423 edited by R. B. Braithwaite.]
KuipersT. A. F.: 1978, Studies in Inductive Probability and Rational Expectation, D. Reidel Publishing Company, Dordrecht.
ZabellS. L.: 1982, ‘W. E. Johnson's Sufficientness Postulate’, Annals of Statistics 10, 1091–1099.
ZabellS. L.: 1989, ‘The Rule of Succession’, Erkenntnis 31, 283–321.
ZabellS. L.: 1992, ‘Predicting the Unpredictable’, Synthese 90, 205–232.
Zabell, S. L.: 1996, ‘The Continuum of Inductive Methods Revisited’, in J. Earman and J. Norton (eds.), The Cosmos of Science, University of Pittsburgh Series in the History and Philosophy of Science.
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Zabell, S.L. Confirming universal generalizations. Erkenntnis 45, 267–283 (1996). https://doi.org/10.1007/BF00276794
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DOI: https://doi.org/10.1007/BF00276794