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Metainduction over Unboundedly Many Prediction Methods: A Reply to Arnold and Sterkenburg

Published online by Cambridge University Press:  01 January 2022

Gerhard Schurz
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Abstract

The universal optimality theorem for metainduction works for epistemic agents faced with a choice among finitely many prediction methods. Eckhart Arnold and Tom Sterkenburg objected that it breaks down for infinite or unboundedly growing sets of methods. In this article the metainductive approach is defended against this challenge by extending the optimality theorem (i) to unboundedly growing sets of methods whose number grows less than exponentially in time, (ii) to sequences of methods with an application to Goodman's problem, and (iii) to infinite sets of methods whose number of predictive equivalence classes grows less than linearly in time.

Type
Research Article
Information
Philosophy of Science , Volume 88 , Issue 2 , April 2021 , pp. 320 - 340
Copyright
Copyright © The Philosophy of Science Association

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