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Immodest Inductive Methods

Published online by Cambridge University Press:  14 March 2022

David Lewis
David Lewis*
Affiliation:
Princeton University
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Abstract

Inductive methods can be used to estimate the accuracies of inductive methods. Call a method immodest if it estimates that it is at least as accurate as any of its rivals. It would be unreasonable to adopt any but an immodest method. Under certain assumptions, exactly one of Carnap's lambda-methods is immodest. This may seem to solve the problem of choosing among the lambda-methods; but sometimes the immodest lambda-method is λ = 0, which it would not be reasonable to adopt. We should therefore reconsider the assumptions that led to this conclusion: for instance, the measure of accuracy.

Type
Research Article
Information
Philosophy of Science , Volume 38 , Issue 1 , March 1971 , pp. 54 - 63
Copyright
Copyright © 1971 by The Philosophy of Science Association

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Footnotes

1

I am grateful to Robert L. Goble for many valuable comments; to the University of California for a Faculty Fellowship supporting the work reported in this paper; to the U.C.L.A. Campus Computing Network for an allocation of computer time used to prepare the numerical examples shown in Figures 1 and 2; to Diane Wells for drawing the figures; and to an anonymous referee for Philosophy of Science who suggested certain improvements in exposition.

References

REFERENCES

[1] Barker, S. F., Induction and Hypothesis, Cornell University Press, Ithaca, New York, 1957.Google Scholar
[2] Carnap, R., The Continuum of Inductive Methods, University of Chicago Press, Chicago, 1952.Google Scholar