Past Probabilities
Sven Ove Hansson
Source: Notre Dame J. Formal Logic Volume 51, Number 2
(2010), 207-223.
Abstract
The probability that a fair coin tossed yesterday landed heads is either 0 or 1, but the probability that it would land heads was 0.5. In order to account for the latter type of probabilities, past probabilities, a temporal restriction operator is introduced and axiomatically characterized. It is used to construct a representation of conditional past probabilities. The logic of past probabilities turns out to be strictly weaker than the logic of standard probabilities.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1276284783
Digital Object Identifier: doi:10.1215/00294527-2010-013
Zentralblatt MATH identifier: 05758438
Mathematical Reviews number (MathSciNet): MR2667933
References
[1] Blackburn, S., Reason and Prediction, Cambridge University Press, Cambridge, 1973.
[2] Carnap, R., "The two concepts of probability", Philosophy and Phenomenological Research, vol. 5 (1945), pp. 513--32.
Mathematical Reviews (MathSciNet): MR0013730
Zentralblatt MATH: 0063.00710
Digital Object Identifier: doi:10.2307/2102817
[3] Cooper, N., "The concept of probability", British Journal for the Philosophy of Science, vol. 16 (1965), pp. 226--38.
Zentralblatt MATH: 0199.00201
[4] Eagle, A., "Twenty-one arguments against propensity analyses of probability", Erkenntnis, vol. 60 (2004), pp. 371--416.
Mathematical Reviews (MathSciNet): MR2055243
Zentralblatt MATH: 1093.03504
Digital Object Identifier: doi:10.1023/B:ERKE.0000023408.61887.6a
[5] Hall, N., "Correcting the guide to objective chance", Mind, vol. 103 (1994), pp. 505--17.
Mathematical Reviews (MathSciNet): MR1463409
Digital Object Identifier: doi:10.1093/mind/103.412.505
JSTOR: links.jstor.org
[6] Hall, N., "Two mistakes about credence and chance", Australasian Journal of Philosophy, vol. 82 (2004), pp. 93--111.
[7] Hansson, S. O., ``Do we need second-order probabilities?'' Dialectica, vol. 62 (2008), pp. 525--33.
Mathematical Reviews (MathSciNet): MR2491353
Digital Object Identifier: doi:10.1111/j.1746-8361.2008.01163.x
[8] Hansson, S. O., "Specified meet contraction", Erkenntnis, vol. 69 (2008), pp. 31--54.
Mathematical Reviews (MathSciNet): MR2415566
Zentralblatt MATH: 1155.03010
Digital Object Identifier: doi:10.1007/s10670-007-9088-4
[9] Hansson, S. O., "Measuring uncertainty", Studia Logica, vol. 93 (2009), pp. 21--40.
Mathematical Reviews (MathSciNet): MR2546677
Zentralblatt MATH: 1182.03043
Digital Object Identifier: doi:10.1007/s11225-009-9207-0
[10] Humphreys, P., "Some considerations on conditional chances", The British Journal for the Philosophy of Science, vol. 55 (2004), pp. 667--80.
Mathematical Reviews (MathSciNet): MR2115528
Digital Object Identifier: doi:10.1093/bjps/55.4.667
[11] Keynes, J. M., A Treatise on Probability, Macmillan, London, 1921.
Zentralblatt MATH: 0121.34903
[12] Lewis, D., "A subjectivist's guide to objective chance", pp. 263--93 in Studies in Inductive Logic and Probability, Vol. II, edited by R. C. Jeffrey, University of California Press, Berkeley, 1980.
Mathematical Reviews (MathSciNet): MR587995
[13] Lichtenstein, S., B. Fischhoff, and L. Phillips, "Calibration of probabilities: The state of the art to 1980", pp. 306--34 in Judgment under Uncertainty, Heuristics and Biases, edited by D. Kahneman, P. Slovic, and A. Tversky, Cambridge University Press, Cambridge, 1982.
[14] Stalnaker, R. C., "Probability and conditionals", Philosophy of Science, vol. 37 (1970), pp. 64--80.
Mathematical Reviews (MathSciNet): MR0285345
Digital Object Identifier: doi:10.1086/288280
JSTOR: links.jstor.org
[15] Stoll, R. R., Sets, Logic and Axiomatic Theories, 2d edition, W. H. Freeman and Co., San Francisco, 1974.
Mathematical Reviews (MathSciNet): MR0345780
Zentralblatt MATH: 0292.02002
[16] Swinburne, R., An Introduction to Confirmation Theory, Methuen & Co., London, 1973.
[17] Toulmin, S. E., "Probability", Proceedings of the Aristotelian Society, Supplementary Volumes, vol. 24 (1950), pp. 27--62.
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