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Interpolation as Explanation

Published online by Cambridge University Press:  01 April 2022

Jaakko Hintikka  and
Ilpo Halonen
Jaakko Hintikka
Affiliation:
Boston University
Ilpo Halonen*
Affiliation:
University of Helsinki
*
†Hintikka: Department of Philosophy, 745 Commonwealth Avenue, Boston University, Boston, MA 02215; Halonen: Department of Philosophy, P.O. Box 24 (Unioninkatu 40), University of Helsinki, Helsinki Finland.
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Abstract

A (normalized) interpolant I in Craig's theorem is a kind of explanation why the consequence relation (from F to G) holds. This is because I is a summary of the interaction of the configurations specified by F and G, respectively, that shows how G follows from F. If explaining E means deriving it from a background theory T plus situational information A and if among the concepts of E we can separate those occurring only in T or only in A, then the interpolation theorem applies in two different ways yielding two different explanations and two different covering laws.

Type
Explanation, Confirmation, and Scientific Inference
Information
Philosophy of Science , Volume 66 , Issue S3: Supplement. Proceedings of the 1998 Biennial Meetings of the Philosophy of Science Association. Part I: Contributed Papers Sep., 1999 , 1999 , pp. S414 - S423
Copyright
Copyright © 1999 by the Philosophy of Science Association

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References

Craig, William (1957), “Three Uses of the Herbrand-Gentzen Theorem in Relating Model Theory and Proof Theory”, Journal of Symbolic Logic 22: 269–285.CrossRefGoogle Scholar
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