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Spielman and Lewis on Inductive Immodesty

Published online by Cambridge University Press:  14 March 2022

David Lewis*
Affiliation:
Princeton University

Extract

An inductive method Cλ in the λ-system of Carnap [1] is immodest, on evidence e, iff its estimate, on e, of its own accuracy is higher than its estimate, on e, of the accuracy of any rival method Cλ. Immodesty seems to be a condition of stable trust: if you trusted a modest Cλ, you should start by trusting its advice to replace it by a rival that it estimates to be more accurate. One might guess that any Cλ would be immodest on any evidence. But in [2] I proved that, under a certain accuracy measure taken from Carnap [1], §§ 20–21, there would be exactly one immodest Cλ. Unfortunately, that one sometimes turns out to be C0 (the straight rule); and since nobody in his right mind would trust C0 we are then left with no acceptable Cλ. Stephen Spielman [3] has proposed a remedy: an estimate of accuracy, on evidence e, should disregard accuracy under circumstances that are ruled out by e. Spielman proves that if this change is made, any Cλ is immodest on any evidence.

Type
Discussion
Copyright
Copyright © 1974 by The Philosophy of Science Association

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References

REFERENCES

[1] Carnap, R. The Continuum of Inductive Methods. Chicago: University of Chicago Press, 1952.Google Scholar
[2] Lewis, D.Immodest Inductive Methods.” Philosophy of Science 38 (1971): 5463.CrossRefGoogle Scholar
[3] Spielman, S.Lewis on Immodest Inductive Models.” Philosophy of Science 39 (1972): 375377.CrossRefGoogle Scholar