Model Selection and the Problem of Language Invariance

This page was last edited on 02/07/02 by Malcolm R Forster

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Publication Data

Forster, Malcolm R. (1999): "Model Selection in Science: The Problem of Language Variance." British Journal for the Philosophy of Science 50: 83-102.

Abstract

 Recent solutions to the model selection problem, described in Forster and Sober (1994), trade off the simplicity and fit of hypotheses by defining simplicity as the paucity of adjustable parameters. Scott De Vito (1997) charges that these solutions are "conventional" because he thinks that the number of adjustable parameters may change when the hypotheses are described differently. This he believes is exactly what is illustrated in Goodman’s new riddle of induction, otherwise known as the grue problem. However, the "number of adjustable parameters" is actually a loose way of referring to a quantity that is not language dependent. The quantity arises out of Akaike’s theorem in a way that ensures its language invariance.

Main References

DeVito, Scott [1997]: "A Gruesome Problem for the Curve Fitting Solution," British Journal for the Philosophy of Science 48, pp. 391- 396.

Forster, M.  R. and E. Sober [1994]:  “How to Tell when Simpler, More Unified, or Less Ad Hoc Theories will Provide More Accurate Predictions.” British Journal for the Philosophy of Science 45: 1 - 35.

Contents
  1. Introduction
  2. A methodological puzzle redescribed
  3. The curve-fitting problem redefined
  4. Akaike’s theorem revisited
  5. The grue problem as a curve-fitting problem
  6. Language invariance restored