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Reduction, Representation and Commensurability of Theories

Published online by Cambridge University Press:  01 April 2022

Peter Schroeder-Heister  and
Frank Schaefer
Peter Schroeder-Heister
Affiliation:
Fachgruppe Philosophie Universität Konstanz
Frank Schaefer
Affiliation:
Fakultät für Mathematik Universität Konstanz
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Abstract

Theories in the usual sense, as characterized by a language and a set of theorems in that language (“statement view”), are related to theories in the structuralist sense, in turn characterized by a set of potential models and a subset thereof as models (“non-statement view”, J. Sneed, W. Stegmüller). It is shown that reductions of theories in the structuralist sense (that is, functions on structures) give rise to so-called “representations” of theories in the statement sense and vice versa, where representations are understood as functions that map sentences of one theory into another theory. It is argued that commensurability between theories should be based on functions on open formulas and open terms so that reducibility does not necessarily imply commensurability. This is in accordance with a central claim by Stegmüller on the compatibility of reducibility and incommensurability that has recently been challenged by D. Pearce.

Type
Research Article
Information
Philosophy of Science , Volume 56 , Issue 1 , March 1989 , pp. 130 - 157
Copyright
Copyright © 1989 by the Philosophy of Science Association

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Footnotes

†

The results reported here were presented in part at the 11th International Wittgenstein Symposium, Kirchberg am Wechsel (Austria), August 4–13, 1986, and at the Department of Philosophy of the University of Helsinki in December 1987. We would like to thank Martin Carrier, Hans Rott and two anonymous referees for many helpful comments on an earlier version of this paper, David Pearce for his stimulating remarks on our abstracted version for the Wittgenstein Symposium, Heinrich Kehl for his literature hints, and Stephen Read and Ron Feemster for revising the English.

Our paper is dedicated to Jürgen Mittelstraß on the occasion of his 50th birthday.

References

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