Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T08:16:37.983Z Has data issue: false hasContentIssue false
  • English
  • Français

The Infinite Ballot Box of Nature: De Morgan, Boole, and Jevons on Probability and the Logic of Induction

Published online by Cambridge University Press:  28 February 2022

John V. Strong
John V. Strong*
Affiliation:
Boston College
Get access Rights & Permissions [Opens in a new window]

Extract

Nature is to us like an infinite ballot box, the contents of which are being continually drawn, ball after ball, and exhibited to us. Science is but the careful observation of the succession in which balls of various character present themselves ([12], p. 150).

The project of formulating an account of scientific inference in terms of concepts drawn from probability theory, and based on the programmatic belief that inductive logic (that is, the theory of the principles of inductive reasoning) is the same as probability logic, is one usually associated in our own day with the names of such twentieth-century philosophers of science as John Maynard Keynes, Hans Reichenbach and Rudolf Carnap ([13], [27], [3]).

Type
Part VI. Induction and Probability
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1976 , Issue 1: Volume One: Contributed Papers 1976 , 1976 , pp. 197 - 211
Copyright
Copyright © 1976 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.)

Footnotes

1

An earlier version of this paper was presented at the Third Hunt Foundation Workshop in History and Philosophy of Science, Morgantown, West Virginia, April 10-13, 1975. I am grateful to the other participants in the workshop, and in particular to Larry Laudan and Edward Madden, for their suggestions and criticisms.

References

Boole, G. “On the Theory of Probabilities, and in Particular on Mitchell's Problem of Distribution of the Fixed Stars.” (1851). (Reprinted in G. Boole, Studies in Logic and Probability. London:: Watts, 1952. Pages 247-259.).Google Scholar
Boole, G. An Investigation of the Laws of Thought. London: Macmillan, 1854. (References are to the reprint edition. New York: Dover, 1951.).Google Scholar
Carnap, R. Logical Foundations of Probability. (2nd ed.). Chicago: University of Chicago Press, 1962.Google Scholar
De Morgan, A. “Theory of Probabilities.” In Encyclopaedia Metropolitana. London: B. Fellowes, 1817-1845.Google Scholar
De Morgan, A. An Essay on Probabilities. London: Longman and Taylor, 1838.Google Scholar
De Morgan, A. Formal Logic. London: Taylor and Walton, 1847.Google Scholar
De Morgan, A. A Budget of Paradoxes. (2nd ed.). Chicago: Open Court, 1915.Google Scholar
Ellis, R.L. “On the Foundations of the Theory of Probabilities”, Trans. Camb. Phil. Soc. 8 (1843): 1-6.Google Scholar
Fisher, R.A. Statistical Methods and Scientific Inference. (2nd ed.). New York: Hafner, 1959.Google Scholar
Graunt, J. Natural and Political Observations….Made Upon the Bills of Morality. London: M. Martin, 1662.Google Scholar
Hacking, I. “Equiposslbility Theories of Probability.” British Journal for the Philosophy of Science 22 (1971): 339-355.CrossRefGoogle Scholar
Jevons, W.S. The Principles Of Science. A Treatise on Logic and Scientific Method. (2nd ed.). London: Macmillan, 1877.Google Scholar
Keynes, J.M. A Treatise on Probability. London: Macmillan, 1921.Google Scholar
Kries, J. von. Die Principien der Wahrscheinlichkeitsrechnung. Eine logische Untersuchung. Freiburg: Mohr, 1886.Google Scholar
Kyburg, H. Probability and Inductive Logic. New York: Macmillan, 1970.Google Scholar
Laplace, P.S. “Memoire sur la probabilité des causes par les événements.” In Oeuvres de Laplace. Paris: Gauthier-Villars, 1878-1912, t. 8 ème. Pages 27-65.Google Scholar
Laplace, P.S. Essai Philosophique sur les Probabilities [=“Introduction' to Theorie Analytique des Probabilities]. In Laplace Ouevres de Laplace. Paris: Gauthier-Villars, 1878-1912, t. 7ème.. Pages VL-CLIII.Google Scholar
Laudan, L. “The Nature and Sources of Locke's Views on Hypotheses.” Journal of the History of Ideas. 23 (1967): 211-223.CrossRefGoogle Scholar
Laudan, L. “Theories of Scientific Method from Plato to Mach.” History of Science. 7 (1968): 1-63.CrossRefGoogle Scholar
Laudan, L. “Peirce and the Trivialization of the Self-Correcting Thesis.” In Foundations of Scientific Method: The Nineteenth Century. Edited by Giere, R. and Westfall, R.. Bloomington, Indiana: Indiana University Press, 1973. Pages 275-306.Google Scholar
Laudan, L. “Induction and Probability in the Nineteenth Century.” . In Logic, Methodology and Philosophy of Science IV. Edited by Suppe, P. et al. Amsterdam: North-Holland, 1973. Pages 429-438.Google Scholar
Macaulay, T. Critical and Historical Essays. London: M.M. Dent, 1907. (Everyman's Library).Google Scholar
Madden, E.H. (ed.). Theories of Scientific Method: The Renaissance Through the Nineteenth Century. Seattle and London: University of Washington Press, 1966.Google Scholar
Mays, W. “Jevons's Conception of Scientific Method.” The Manchester School of Economic and Social Studies 30 (1962): 223-249.CrossRefGoogle Scholar
Mill, J.S. A System of Logic Ratiocinative and Inductive. Toronto: University of Toronto Press, 1973. (This edition includes the variants from all eight editions of the Logic which appeared during Mill's lifetime.)Google Scholar
Mises, R. von. Wahrscheinlichkeit, Statistik und Wahrheit, 1928. (Translated as Probability, Statistics, and Truth. New York: Macmillan, 1957.).CrossRefGoogle Scholar
Reichenbach, H. Wahrscheinlichkeitslehre, 1935. (Translated and revised as The Theory of Probability. Berkeley and Los Angeles: University of California Press, 1949.).Google Scholar
Salmon, W. The Foundations of Scientific Inference. Pittsburgh: University of Pittsburgh Press, 1967.CrossRefGoogle Scholar
Uspensky, J.V. Introduction to Mathematical Probability. New York: McGraw-Hill, 1937.Google Scholar
Venn, J. The Logic of Chance. London: Macmillan, 1866.((3rd ed.). London: Macmillan, 1888.)Google Scholar
Wright, G. von. A Treatise on Induction and Probability. Patterson, N.J.: Littlefteld, Adams, 1960.Google Scholar