Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-06-07T13:49:43.350Z Has data issue: false hasContentIssue false

Slightly More Realistic Personal Probability

Published online by Cambridge University Press:  14 March 2022

Ian Hacking*
Affiliation:
Makerere University College

Abstract

A person required to risk money on a remote digit of π would, in order to comply fully with the theory [of personal probability] have to compute that digit, though this would really be wasteful if the cost of computation were more than the prize involved. For the postulates of the theory imply that you should behave in accordance with the logical implications of all that you know. Is it possible to improve the theory in this respect, making allowance within it for the cost of thinking, or would that entail paradox?

Type
A Panel Discussion of Personal Probability
Copyright
Copyright © Philosophy of Science Association 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

L. J. Savage, “Difficulties in the Theory of Personal Probability,” in this issue of Philosophy of Science. Unless otherwise specified all references to Savage's work are to this article.

References

REFERENCES

[1] Carnap, R., Meaning and Necessity, Chicago, 1947.Google Scholar
[2] Carnap, R., Logical Foundations of Probability, Chicago, 1950.Google Scholar
[3] Carroll, Lewis, “What the tortoise said to Achilles,” Mind IV (1895) 278280.10.1093/mind/IV.14.278CrossRefGoogle Scholar
[4] Courant, R., What is Mathematics? New York, 1941.Google Scholar
[5] Cox, R. T., The Algebra of Probable Inference, Baltimore, 1961.Google Scholar
[6] David, F. N., Gods, Games and Scholars, London, 1962.Google Scholar
[7] de Finetti, B., “Foresight, its logical laws, its subjective sources,” Studies in Subjective Probability, ed. H. E. Kyburg Jr., and Howard Smokier, New York, 1964. Translated by Kyburg from the French of 1937.Google Scholar
[8] Good, I. J., “On the principle of total evidence,” British Journal for the Philosophy of Science XVIII (1967) 319321.10.1093/bjps/17.4.319CrossRefGoogle Scholar
[9] Hacking, I., Logic of Statistical Inference, Cambridge, 1965.10.1017/CBO9781316534960CrossRefGoogle Scholar
[10] Hacking, I., “Possibility,” Philosophical Review LXXVI (1967) 143168.10.2307/2183640CrossRefGoogle Scholar
[11] Hintikka, J., Knowledge and Belief, Ithaca, 1962.Google Scholar
[12] Jeffrey, R., The Logic of Decision, New York, 1965.10.2307/2023748CrossRefGoogle Scholar
[13] Jeffreys, H., The Theory of Probability, Oxford, 1939.Google Scholar
[14] Lewis, C. I., and Langford, C. H., Symbolic Logic, New York, 1932.Google Scholar
[15] Lindley, D. V., Introduction to Probability and Statistics from a Bayesian Viewpoint, Cambridge, 1965.10.1017/CBO9780511662973CrossRefGoogle Scholar
[16] Quine, W. V. O., From a Logical Point of View, New York, 1950.Google Scholar
[17] Ramsey, F. P., “Truth and Probability,” The Foundations of Mathematics, London, 1931.Google Scholar
[18] Ryle, G., “‘If’, ‘so’, and ‘because’,” Philosophical Analysis, ed. M. Black, Ithaca, 1950.Google Scholar
[19] Savage, L. J., The Foundations of Statistics, New York, 1954.Google Scholar
[20] Savage, L. J., and others, , The Foundations of Statistical Inference, London, 1962.Google Scholar
[21] Shimony, A., “Coherence and the axioms of confirmation,” Journal of Symbolic Logic XX (1955) 128.CrossRefGoogle Scholar
[22] Suppes, P., “Concepts Formation and Bayesian Decision,” Aspects of Inductive Logic, ed. J. Hintikka and P. Suppes, Amsterdam, 1966.CrossRefGoogle Scholar
[23] Suppes, P., “Probabilistic Inference and the Concept of Total Evidence,” Ibid.Google Scholar
[24] Vickers, J., “Coherence and the axioms of confirmation,” Philosophy of Science XXXII (1965) 3238.CrossRefGoogle Scholar
[25] Williams, J. S., “The role of probability in fiducial inference,” Sankhyä, A, XXVIII (1966) 271296.Google Scholar