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  • Cited by 2
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    This chapter has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Simandan, Dragos 2011. Is engaged pluralism the best way ahead for economic geography? Commentary on Barnes and Sheppard (2009). Progress in Human Geography, Vol. 35, Issue. 4, p. 568.

    Crupi, Vincenzo 2015. Inductive Logic. Journal of Philosophical Logic, Vol. 44, Issue. 6, p. 641.

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  • Print publication year: 2008
  • Online publication date: June 2012

15 - Inductive Logic and Inductive Reasoning

Summary

In days of yore, logic was neatly divided into two parts, Deductive Logic and Inductive Logic (Mill 1949/1843). The two parts were often taught as parts of a single course. Inductive logic has faded away, and now the very term has acquired a slightly antiquated patina. It has also acquired a number of quite specific modern meanings.

One very narrow and very specific meaning is that inductive inference is the inference from a set of observations or observation sentences (crow #1 is black; crow #2 is black; …; crow #n is black) to their universal generalization (all crows are black). There is not much logic here, but there is a big problem: to determine when, if ever, such an inference is “justified.”

A somewhat less ambitious construal of “induction” is as the inference from a statistical sample to a statistical generalization, or an approximate statistical generalization: from “51% of the first 10,000 tosses of this coin yielded heads,” to “Roughly half of the tosses of the coin will, in the long run, yield heads.” So construed (as by Baird 1992), the line between the logic of induction and the mathematics of statistics is a bit vague. This has been of little help to inductive logic, since the logic of statistical inference has itself been controversial.

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  • Online ISBN: 9780511814273
  • Book DOI: https://doi.org/10.1017/CBO9780511814273
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References
Ernest, W. Adams. The Logic of Conditionals. Reidel, Dordrecht, 1975.
Baird, Davis. Inductive Logic: Probability and Statistics. Prentice-Hall, Englewood Cliffs, NJ, 1992.
Boole, George. An Investigation into the Laws of Thought. Dover Publications, New York, 1854 (orig).
Broad, C. D.. The principles of demonstrative induction. Mind, 39:302–317; 426–439, 1930.
Broad, C. D.. Induction, Probability and Causation: Selected Papers. Humanities Press, New York, 1968.
Carnap, Rudolf. The Logical Foundations of Probability. Chicago: University of Chicago Press, 1950.
Rudolf Carnap. A basic system of inductive logic, part i. In Jeffrey, Richard and Carnap, Rudolf, editors, Studies in Inductive Logic and ProbabilityI, pages 33–165. University of California, Berkley, 1971.
Frege, Gottlob. The Foundations of Arithmetic. Basil Blackwell, Oxford, 1950 (1893).
Harman, Gilbert and Kulkarni, Sanjeev. The problem of induction. Philosophy and Phenomenological Research, 72:559–75.
John, Maynard Keynes. A Treatise on Probability. Macmillan and Co., London, 1952.
Henry, E. Kyburg Jr. and Choh, Man Teng. Uncertain Inference. Cambridge University Press, New York, 2001.
Henry, E. Kyburg Jr.Probability and the Logic of Rational Belief. Wesleyan University Press, Middletown, CT, 1961.
Henry E. Kyburg, Jr. Conjunctivitis. In Swain, Marshall, editor, Induction, Acceptance and Rational Belief, volume 5, pages 55–82. Reidel, Dordrecht, 1970.
Henry, E. Kyburg Jr.Full belief. Theory and Decision, 25:137–162, 1988.
Henry, E. Kyburg Jr.The rule of adjunction and reasonable inference. Journal of Philosophy, 94:109–125, 1997.
Clarence, Irving Lewis. A Survey of Symbolic Logic. University of California Press, Berkeley, 1918.
David Lewis. Probabilities of conditionals and conditional probability. In Harper, W., Stalnaker, R., and Pearce, G., editors, Ifs, pages 129–147. Reidel, Dordrecht, 1981.
McGee, Vann. Conditional probabilities and compounds of conditionals. The Philosophical Review, 48:485–541, 1989.
John, Stuart Mill. A System of Logic. Longmans Greene and Co., London, 1949, 1843.
Robert, C. Moore. Semantical considerations on nonmonotonic logic. Artificial Intelligence, 25:75–94, 1985.
Pearl, Judea. Causality. Cambridge University Press, New York, 2000.
Quine, W. V. O.. Mathematical Logic. Harvard University Press, Cambridge, MA, 1951.
Quine, W. V. O.. Word and Object. John Wiley and Sons, New York, 1960.
Reiter, Raymond. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.
Patrick Suppes. Subjective probability as a measure of a non-measurable set. In Nagel, Suppes and Tarski, , editors, Logic, Methodology and Philosophy of Science, pages 319–329. University of California Press, Berkeley, 1962.