Abstract
When is it possible to decide that a theory is confirmed by the available evidence? Probabilities seem first to be the good framework for addressing this question. But the philosophers of science did not succeed in building any probabilistic criterion of confirmation beyond dispute. We examine two of the main reasons for this failure. First, the principles of adequacy used by philosophers are often logically inconsistent with each other. We show in the paper how to build consistent subsets of these principles. We identify three main subsets which embody the principles of adequacy for two main kinds of confirmation, namely the relative confirmation and the absolute confirmation. Second, we prove the impossibility of building any probabilistic criterion for absolute confirmation.
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References
Achinstein, P.: 1962–3, ‘The Identity Hypothesis’,B.J.P.S. 13, 167.
Ayer, A.J.: 1965, ‘Le problème de la confirmation’,Logique et analyse,32, 238–264.
Baillie, P.: 1969, ‘That Confirmation May Yet Be a Probability’,B.J.P.S.,20, 41.
Bar-Hillel, Y.: 1955–6, ‘Comment on Degree of Confirmation by Professor K.R. Popper’,B.J.P.S. 6, 155.
Bar-Hillel, Y.: 1956–7, ‘Further Comments on Probability and Confirmation. A Rejoinder to Professor Popper’,B.J.P.S. 7, 245.
Bar-Hillel, Y.: 1974, ‘Popper's Theory of Corroboration’, inThe Philosophy of Karl Popper, The Library of Living Philosophers, P.A. Schilpp (Ed.).
Barwise, J. and Cooper, R.: 1981, ‘Generalized Quantifiers and Natural Language’,Linguistics and Philosophy,IV, 159–219.
Benthem, J. van: 1984, ‘Foundations of Conditional Logic’Journal of Philosophical Logic,XIII, 303–349.
Boudot, M.: 1972, ‘Logique inductive et probabilité’, Colin.
Boyer, A.: 1990, ‘atUne logique inductive probabiliste est elle seulement possible?’,Les Cahiers du CREA: No. 14 (Boyer, A.ed), 121–145.
Campbell, R. and Vinci, Th.: 1983, ‘Novel Confirmation’,B.J.P.S.,34, 315–341.
Carnap, R.: (1956–7), ‘Remarks on Popper's Note on Content and Degree of Confirmation’,B.J.P.S.,7, 243.
Carnap, R.: 1950,Logical Foundations of Probability, Chicago, (2d ed., 1962).
Cohen, L.J..: 1966a, ‘What has Confirmation to do with Probabilities’,Mind,75 (300) 463.
Cohen, L.J.: 1966b, ‘A Logic for Evidential Support’,B.J.P.S. 17, 23.
Cohen, L.J.: 1966c, ‘A Logic for Evidential Support II’,B.J.P.S. 17, 105–126.
Crocco, G. and Lamarre, P.: 1991, ‘Conditional Logic a Powerful Tool for Non- Monotonicity’,Tech. Report IRIT/92-2-T.
Dubois, D. and Prade, H.: 1985,Théorie des possibilités, Masson.
Dubois, D. and Prade, H.: 1991, ‘Possibilistic Logic, Preferential Models, Non-Monotonicity and Related Issues’,Proc. 12th Inter. Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, Aug 24–30.
Dubucs, J.: 1992, ‘Inductive Logic Revisited’,Philosophy of Probabilities, Philosophical Studies Series, Dordrecht-Boston: Kluwer Academic Publishers.
Gabay, D.M.: 1985, ‘Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems’,Proc. NATO Advanced Study Institute on Logics and Models of Concurrent Systems, pp. 439–457, La Colle sur Loup, France, (KR Apt, Ed), Berlin, Springer Verlag.
Good, I.J.: 1950,Probability and the Weighting of Evidence, New York and London.
Good, I.J.: 1955, ‘Popper Degree of Confirmation’,Mathematical Reviews,16, 376.
Good, I.J.: 1987, ‘A Reinstatement, in Response to Gillies, of Readhead's Argument in Support of Induction’,Philosophy of Science,54, 470–472.
Goodman, N.: 1955,Fact, Fiction and Forecast, Harvard: University Press.
Hempel, C.G.: 1943, ‘A Purely Syntactical Definition of Confirmation’,J. Symbolic Logic,8(4), 121–143.
Hempel, C.G.: 1945, ‘Studies in the Logic of Confirmation’,Mind,54 (213), 1–26 and (214) 97–121. Reprinted inAspects of Scientific Explanation, New York (1965).
Hilpinen, R.: 1968, ‘Rules of Acceptance and Inductive Logic’,Acta Philosophica Fennica 22, Amsterdam: North Holland Publ.
Kraus, S., Lehmann, D., and Magidor, M.: 1990, ‘Non-Monotonic Reasoning, Preferential Models and Cumulative Logics’,Artificial Intelligence,44, 167–207.
Kyburg, H.E. Jr: 1961,Probability and the Logic of Rational Belief, Middletown, Conn.: Wesleyan University Press.
Levi, I.: 1963, ‘Corroboration and Rules of Acceptance’,B.J.P.S. 13, 307–313. Reprinted inDecisions and Revisions, Cambridge: University Press (1984).
Levi, I.: 1986, ‘Probabilistic Pettifoggery’,Erkenntnis XXV, 133–140.
Makinson, D.: 1991, ‘General Patterns in Nonmonotonic Reasoning’,Handbook of Logic in Artificial Intelligence and Logic Programming, Vol II: Non Monotonic and Uncertain Reasoning, Oxford: University Press.
Makinson, D. and Gardenfors, P.: 1990,The Logic of Theory Change, (Fuhrman, A. and Morreau, M. Eds.),Lecture Notes in Artificial Intelligence No. 465, pp. 185–205, Berlin: Springer Verlag.
Miller, D.: 1990, ‘Reply to Zwirn & Zwirn’,Les Cahiers du CREA No. 14 (Boyer, A. ed.), 149–153.
Nicod, J.: 1930,Foundations of Geometry and Induction, London.
Nicod, J.: 1961,Le problème logique de l'induction, Paris, 2nd ed.
Popper, K.R.: 1954, ‘Degrees of Confirmation’,B.J.P.S.,5, 143.
Popper, K.R.: 1955–6, ‘Content and Degree of Confirmation: A Reply to Dr Bar-Hillel’,B.J.P.S.,6, 157.
Popper, K.R.: 1956–7a, ‘Reply to Professor Carnap’,B.J.P.S.,7, 244.
Popper, K.R.: 1956–7b, ‘Adequacy and Consistency: A Second Reply to Dr Bar-Hillel’,B.J.P.S.,7, 249.
Popper, K.R.: 1956–7c, ‘A Second Note on Degree of Confirmation’,B.J.P.S.,7, 359.
Popper, K.R.: 1958, ‘A Third Note on Degree of Corroboration or Confirmation’,B.J.P.S.,8, 294.
Popper, K.R.: 1959,The Logic of Scientific Discovery, London.
Popper, K.R. and Miller, D.: 1983, ‘A Proof of the Impossibility of Inductive Probability’,Nature,302, (April 21), 687–688.
Popper, K.R. and Miller, D.: 1987, ‘Why Probabilistic Support Is Not Inductive’,Philosophical Transactions of the Royal Society of London,A321, 59–81.
Redhead, J.L.G.: 1985, ‘On the Impossibility of Inductive Probability’,B.J.P.S.,36 185–191.
Settle, T.W.: 1970, ‘Confirmation as a Probability: Dead But It Won't Lie Down’,B.J.P.S.,21, 200.
Shoham, Y.: 1988,Reasoning about Change - Time and Causation from the Standpoint of Artificial Intelligence, Cambridge, Mass.: MIT Press.
Stopes-Roy, H.V.: 1968,J. Symbolic Logic,33(1), 142.
Zwirn, D. and Zwirn H.P.: 1989, ‘L'argument de Popper et Miller contre la justification probabiliste de l'induction’,L'Age de la Science,2,Epistémologie, 59–81.
Zwirn, D. and Zwirn, H.P.: 1993, ‘Logique inductive et soutien probabiliste’,Dialogue,XXXII(2).
Zwirn, D. and Zwirn, H.P.: 1995, ‘Confirmation non probabiliste’,Methodes logiques pour les sciences cognitives, Dubucs, J. and Lepage, F. (eds.), Hermes.
Zwirn, D. and Zwirn, H.P.: (mimeo) ‘On some Probabilistic Confirmation Criteria’.
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Zwirn, D., Zwirn, H.P. Metaconfirmation. Theor Decis 41, 195–228 (1996). https://doi.org/10.1007/BF00136126
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DOI: https://doi.org/10.1007/BF00136126