Conclusion
Even those generally skeptical of propensity interpretations of probability must now grant the following two points. First, the above single-case propensity interpretation meets recognized formal conditions for being a genuine interpretation of probability. Second, this interpretation is not logically reducible to a hypothetical relative frequency interpretation, nor is it only vacuously different from such an interpretation.
The main objection to this propensity interpretation must be not that it is too vague or vacuous, but that it is metaphysically too extravagant. It asserts not only that there are physical possibilities in nature, but further that nature itself contains innate tendencies toward these possibilities, tendencies which have the logical structure of probabilities. Thus the basic dispute between advocates of an actualist relative frequency interpretation and a single-case propensity interpretation is not a matter of epistemology, but metaphysics. The frequency theorist wishes to maintain that claims about physical probabilities are nothing more than claims about relative frequencies that will occur in the actual history of the world, be it infinite or no. It is a substantial, though hardly conclusive, argument for the propensity view that the mathematical structures commonly employed in studies of stochastic processes and statistical inference are richer than can be accommodated by a relative frequency interpretation. Whether it is possible to bridge this gap without going beyond an actualist metaphysics remains to be seen.38
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References
ArbibMichael A.: 1969,Theories of Abstract Automata, Prentice-Hall, Englewood Cliffs, N.J.
BraithwaiteR. B.: 1953,Scientific Explanation, Cambridge University, Cambridge, England.
BubJeffrey: 1975, ‘Popper's Propensity Interpretation of Probability and Quantum Mechanics’, inInduction, Probability and Confirmation: Minnesota Studies in the Philosophy of Science, Vol. VI, R. M.Anderson and GroverMaxwell (eds.), University of Minnesota Press, Minneapolis.
BungeMario: 1967a,Foundations of Physics, Springer Verlag, New York.
BungeMario: 1967b,Scientific Research I, Springer-Verlag, New York.
CarnapRudolf: 1950,Logical Foundations of Probability, University of Chicago Press., 2nd edn., Chicago, 1962.
FineTerrence L.: 1973,Theories of Probability, Academic Press, New York.
deFinettiBruno: 1974,Theory of Probability, Wiley, New York.
FetzerJames H.: 1971, ‘Dispositional Probabilities’, inBoston Studies in the Philosophy of Science, Vol. VIII, Roger C.Buck and Robert S.Cohen (eds.), D. Reidel Publishing Co., Dordrecht, Holland, pp. 473–482.
GiereRonald N.: 1969, ‘Bayesian Statistics and Biased Procedures’,Synthese 20, 371–87.
GiereRonald N.: 1973a, ‘Objective Single Case Probabilities and the Foundations of Statistics’, inLogic, Methodology and Philosophy of Science IV, Proceedings of the 1971 International Congress, Bucharest, P.Suppes, L.Henken, A.Joja and Cr. C.Moisil (eds.), North Holland, Amsterdam, pp. 467–83.
GiereRonald N.: 1973b, Review of D. H. Mellor,The Matter of Chance, Ratio XV, 149–55.
GiereRonald N.: 1976, ‘Empirical Probability, Objective Statistical Methods and Scientific Inquiry’, inFoundations of Probability Theory, Statistical Inference and Statistical Theories of Science, Vol. II: Foundations and Philosophy of Statistical Inference, W. L.Harper and C. A.Hooker (eds.), D. Reidel Publ, Co., Dordrecht, Holland, pp. 63–101.
GiereRonald N.: 1977, ‘Testing vs Information Models of Statistical Inference’, inLogic, Laws and Life: Pittsburgh Series in the Philosophy of Science, Vol VI, R. G.Colodny, (ed.), University of Pittsburgh Press, Pittsburgh.
GillesDonald: 1973,An Objective Theory of Probability, Menthuen, London.
HackingIan: 1965,Logic of Statistical Inference, Cambridge University Press, Cambridge.
HackingIan: 1975,The Emergence of Probability, Cambridge University Press, Cambridge, England.
HintikkaJaakko: 1966, ‘A Two-Dimensional Continuum of Inductive Methods’, inAspects of Inductive Logic, J.Hintikka and P.Suppes, (eds.), North-Holland, Amsterdam, pp. 113–32.
KeynesJohn Maynard: 1921,A Treatise on Probability, Macmillan, London.
KyburgHenry E.Jr.: 1970,Probability and Inductive Logic, Macmillan, London.
Kyburg, Henry E., Jr.: 1974, ‘Propensities and Probabilities’, inThe British Journal for the Philosophy of Science 25, 358–375.
LeviIsaac: 1967,Gambling with Truth, Knopf, New York.
LewisDavid: 1973,Counterfactuals, Harvard University Press, Cambridge, Massachusetts.
MellorD. H.: 1971,The Matter of Chance, Cambridge Press, Cambridge, England.
NeutsMarcel F.: 1973,Probability, Allen & Bacon, Inc., Boston.
PaduloLouis and ArbibMichael: 1974,System Theory, W. B. Saunders, Philadelphia.
ParkJ.: 1968, ‘Quantum Theoretical Concept of Measurement’,Philosophy of Science 35, 205–31.
ParzanE.: 1960,Modern Probability Theory and its Applications, Wiley, New York.
ParzenE.: 1962,Stochastic Processes, Holden-Day, San Francisco.
PeirceC. S.: 1934–58,Collected Papers of Charles Sanders Peirce, 8 Vols., Cambridge, Harvard University Press, Massachusetts.
PopperKarl R.: 1957, ‘The Propensity Interpretation of the Calculus of Probability and the Quantum Theory’, inObservation and Interpretation in the Philosophy of Physics, S.Korner (ed.), Butterworth, London.
PopperKarl R.: 1959, ‘The Propensity Interpretation of Probability’,British Journal of the Philosophy of Science 10, 25–42.
PopperKarl R.: 1967, ‘Quantum Mechanics Without “The Observer”’, inQuantum Theory and Reality, M.Bunge (ed.), Springer, New York.
RamseyFrank P.: 1926, ‘Truth and Probability’, inThe Foundations of Mathematics, R. B.Braithwaite (ed.), Routledge and Kegan Paul, London.
ReichenbachHans: 1949,The Theory of Probability, University of California, Berkeley.
RenyiAlfred: 1970,Foundations of Probability, Holden-Day, San Francisco.
RobinsonAbraham: 1966,Non-Standard Analysis, North-Holland, Amsterdam.
SalmonWesley C.: 1967,The Foundations of Scientific Inference, University of Pittsburgh, Pittsburgh.
SavageLeonard J.: 1954,The Foundations of Statistics, Wiley, 2nd ed., 1972, New York.
SchilppP. A., ed.: 1974,The Philosophy of Karl Popper, Open Court, La Salle, Ill.
SettleTom: 1974, ‘Induction and Probability Unfused’, inThe Philosophy of Karl Popper, P. A.Schilpp (ed.), Open Court, La Salle, Ill.
SettleTom: 1975, ‘Presuppositions of Propensity Theories of Probability’, inInduction, Probability, and Confirmation: Minnesota Studies in the Philosophy of Science, Vol. VI, GroverMaxwell and R. M.Anderson (eds.), University of Minnesota Press, Minneapolis.
Sklar, Lawrence: 1970, ‘Is Probability a Dispositional Property?’, inJournal of Philosophy 67, 355–66.
SklarLawrence: 1974, Review of D. H. Mellor:The Matter of Chance, inJournal of Philosophy 71, 418–23.
SuppesPatrick: 1970,Set-Theoretical Structures in Science, Institute for Mathematical Studies in the Social Sciences, Stanford, California.
SuppesPatrick: 1973, ‘New Foundations of Objective Probability: Axioms for Propensities’, inLogic, Methodology and Philosophy of Science IV, Proceedings of the 1971 International Congress, Bucharest, P.Suppes, A.Joja, and Gr. C.Moisil (eds.), North-Holland, Amsterdam.
SuppesPatrick: 1974, ‘Popper's Analysis of Probability in Quantum Mechanis’, inThe Philosophy of Karl Popper, P. A.Schilpp (ed.), Open Court, La Salle, Ill.
van Fraassen, Bas C.: 1970, ‘On the Extension of Beth's Semantics of Physical Theories’, inPhilossophy of Science 37, 325–339.
vanFraassenBas C.: 1974, ‘The Labyrinth of Quantum Logics’, inBoston Studies in the Philosophy of Science, Vol. XIII, R. S.Cohen and M. W.Wartofsky (eds.), D. Reidel Publ. Co., Dordrecht.
van Fraasen, Bas C.: [forthcoming] ‘Relative Frequencies’,Synthese.
Veen, John: 1866,The Logic of Chance, London.
vonMisesRichard: 1957,Probability, Statistics and Truth, Allen & Unwin, London.
White, Alan R.: 1972, ‘The Propensity Theory of Probability’, inBritish Journal for the Philosophy of Science 23, 35–43.
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Giere, R.N. A laplacean formal semantics for single-case propensities. J Philos Logic 5, 321–353 (1976). https://doi.org/10.1007/BF00649395
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DOI: https://doi.org/10.1007/BF00649395