Reviewing Reduction in a Preferential Model‐Theoretic Context

Abstract

In this article, we redefine classical notions of theory reduction in such a way that model‐theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model‐theoretic reconstruction of science in which theory succession or reduction is often better—or at a finer level of analysis—interpreted as the result of model succession or reduction. This analysis leads to ‘defeasible reduction’, defined as follows: The conjunction of the assumptions of a reducing theory T with the definitions translating the vocabulary of a reduced theory T′ to the vocabulary of T, defeasibly entails the assumptions of reduced T′. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science.

Acknowledgements

We would like to thank the editor of this journal, James W. McAllister, and the two referees who originally evaluated our manuscript for their suggestions and comments to improve this article.

Notes

[1] See any textbook on non‐monotonic logic, such as Shoham (1988), or Reiter (1980) for formal definitions.

[2] Thus, we may try to determine whether there is an empirical model of T′ which cannot be embedded into any empirical reduct of T ∧ D.

[3] ‘In some cases, the solution thus obtained may even be equally satisfactory from the empirical point of view’ (Balzer, Moulines, and Sneed 1987, 254).

[4] Structural realism is one of the most vibrant species of realism at the moment. It has been advocated by, among others, Poincaré (1900, 1902, 1905), Maxwell (1970), Worrall (1989, 1990), and also Psillos (1999). For a good overview of the field, see Psillos (1999).