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Two Ways of Analogy: Extending the Study of Analogies to Mathematical Domains

Published online by Cambridge University Press:  01 January 2022

Dirk Schlimm
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Abstract

The structure-mapping theory has become the de facto standard account of analogies in cognitive science and philosophy of science. In this paper I propose a distinction between two kinds of domains and I show how the account of analogies based on structure-preserving mappings fails in certain (object-rich) domains, which are very common in mathematics, and how the axiomatic approach to analogies, which is based on a common linguistic description of the analogs in terms of laws or axioms, can be used successfully to explicate analogies of this kind. Thus, the two accounts of analogies should be regarded as complementary, since each of them is adequate for explicating analogies that are drawn between different kinds of domains. In addition, I illustrate how the account of analogies based on axioms has also considerable practical advantages, for example, for the discovery of new analogies.

Type
Research Article
Information
Philosophy of Science , Volume 75 , Issue 2 , April 2008 , pp. 178 - 200
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

I would like to thank Brian van den Broek, Clark Glymour, Michael Hallett, Brigitte Pientka, and an anonymous reviewer for many discussions and comments. Earlier versions of this paper were presented at the 2004 meeting of the Canadian Philosophical Association in Winnipeg, MB, and at the conference on Philosophical Perspectives on Scientific Understanding, held in August 2005 in Amsterdam, the Netherlands. I am grateful to the various participants for discussions and comments. Work on this paper was supported by the Social Sciences and Humanities Research Council of Canada.

References

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