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

Thestructure‐mapping theoryhas 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‐...

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Bibliographic Details
Published in:Philosophy of science 2008-04, Vol.75 (2), p.178-200
Main Author: Schlimm, Dirk
Format: Article
Language:English
Subjects:
Analog
Analogies
Analogy
Astronomical objects
Axioms
Cognition
Cognition & reasoning
Conceptualization
Epistemology. Philosophy of science. Theory of knowledge
Homomorphisms
Linguistics
Mapping
Mathematical relations
Mathematics
Metaphors
Morphisms
Philosophical axioms
Philosophy
Philosophy of science
Reasoning
Structural analysis
Theory
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Summary:Thestructure‐mapping theoryhas 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 theaxiomaticapproach 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.
ISSN:0031-8248
1539-767X
DOI:10.1086/590198