Hostname: page-component-84b7d79bbc-7nlkj Total loading time: 0 Render date: 2024-07-31T18:22:26.092Z Has data issue: false hasContentIssue false

A Logic of Induction

Published online by Cambridge University Press:  01 April 2022

Colin Howson*
Affiliation:
Department of Philosophy, Logic, and Scientific Method, London School of Economics and Political Science
*
Send reprint requests to the author, Department of Philosophy, Logic, and Scientific Method, London School of Economics and Political Science, Houghton St., London WC2A 2AE.

Extract

1. Probabilism. Statistics is probably the last discipline the ordinary person would associate with ideological wars, but one has been raging there for the last thirty years and more. Until recently the Classical, also known as Frequentist, theory of statistical inference dominated. But gradually a quite different approach has attracted adherents. This, named the Bayesian theory after the eighteenth-century English clergyman, Thomas Bayes, is a phoenix, reborn from the theory of inductive inference dominant from the mid-eighteenth to the late nineteenth century, which said that the measure of confidence proper to employ in an uncertain proposition is its probability (the idea goes back well beyond Bayes; in his great Ars Conjectandi, published posthumously in 1715, James Bernoulli stated that probability is degree of certainty (Part IV, Chapter II)).

Type
Research Article
Copyright
Copyright © 1997 by the Philosophy of Science Association

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.)

References

Armendt, B. (1980), “Is there a Dutch Book argument for probability kinematics?”, Philosophy of Science 47:583–589.CrossRefGoogle Scholar
Bayes, T. (1763), “An essay towards solving a problem in the doctrine of chances”, Philosophical Transactions of the Royal Society 53:370–418.Google Scholar
Blackwell, , and Dubins, L. (1962), “Merging of opinions with increasing information”, Annals of Mathematical Statistics 33:882–887.CrossRefGoogle Scholar
Dawid, A. P., Stone, M., and Zidek, J. V. (1973), “Marginalization paradoxes in Bayesian and structural inference”, Journal of the Royal Statistical Society B: 189223.Google Scholar
Earman, J. (1992), Bayes or bust? A critical examination of Bayesian confirmation theory. Cambridge, MA: MIT Press.Google Scholar
Fisher, R. A. (1947) The design of experiments, 4th edition. Edinburgh: Oliver and Boyd.Google Scholar
Gaifman, H. and Snir, M. (1980), “Probabilities over rich languages, testing and randomness”, Journal of Symbolic Logic 47:495–548.Google Scholar
Gärdenfors, P. and Sahlin, N-E (1988), Decision, probability and utility. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Giere, R. (1984), Understanding scientific reasoning, 2nd edition. New York: Holt, Rinehart and Winston.Google Scholar
Hacking, I. (1967), “Slightly more realistic personal probability”, Philosophy of Science 34, 311325.CrossRefGoogle Scholar
Halmos, P. (1950), Measure theory. New York: van Nostrand-Reinhold.CrossRefGoogle Scholar
Hellman, G. (1997), “Bayes and beyond”, this volume.CrossRefGoogle Scholar
Howson, C. and Urbach, P. (1993), Scientific reasoning: the Bayesian approach, 2nd edition. Chicago: Open Court.Google Scholar
Jaynes, E. T. (1968), “Prior probabilities”, IEEE Transactions on Systems Science and Cybernetics SSC-4: 227241.CrossRefGoogle Scholar
Jaynes, E. T. (1973), “The well-posed problem”, Foundations of Physics 3:477–493.CrossRefGoogle Scholar
Jeffrey, R. C. (1983), The logic of decision. Chicago: University of Chicago Press.Google Scholar
Jeffreys, H. (1961), Theory of Probability, 3rd edition. Oxford: Clarendon Press.Google Scholar
Kolmogorov, A. N. (1950), Foundations of the theory of probability (translation for the German of 1933 by N. Morrison). New York: Chelsea.Google Scholar
Laplace, P. S. de (1951), Philosophical essay on probabilities. New York: Dover. (English translation of Essai philosophique sur les proabilités, 1820).Google Scholar
Lindley, D. (1982), “Scoring rules and the inevitability of probability”, International Statistical Review 50: 126.CrossRefGoogle Scholar
Maher, P. (1997), “Depragmatized Dutch Book Arguments”, this volume.CrossRefGoogle Scholar
Mayo, D. (1996), Error and the growth of experimental knowledge. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Milne, P. M. (1983), “A note on scale invariance”, British Journal for the Philosophy of Science 34: 4955.CrossRefGoogle Scholar
Neyman, J. (1952), Lectures and conferences on mathematical statistics, 2nd edition. Washington, D.C.: Graduate School of U.S. Dept. of Agriculture.Google Scholar
Ramsey, F. P. (1931), “Truth and probability”, in The foundations of mathematics and other logical essays. London: Routledge and Kegan Paul.Google Scholar
Savage, L. J. (1954), The foundations of statistics. New York: John Wiley.Google Scholar
Teller, P. (1973), “Conditionalisation and observation”, Synthese 26:218–258.CrossRefGoogle Scholar
van Fraassen, B. C. (1984), “Belief and the will”, Journal of Philosophy LXXXI: 235256.CrossRefGoogle Scholar
van Fraassen, B. C. (1989), Laws and symmetry. Oxford: Oxford University Press.CrossRefGoogle Scholar
Walley, P. (1991), Statistical reasoning with imprecise probabilities. London: Chapman and Hall.CrossRefGoogle Scholar
Williams, P. M. (1980), “Bayesian conditionalisation and the principle of minimum information”, British Journal for the Philosophy of Science 31: 131144.CrossRefGoogle Scholar