David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Philosophy of Science 75 (2):178-200 (2008)
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, e. g., for the discovery of new analogies.
|Keywords||Analogical reasoning Mathematical reasoning|
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References found in this work BETA
George Lakoff (1980). Metaphors We Live By. University of Chicago Press.
Ernest Nagel (1961). The Structure of Science: Problems in the Logic of Scientific Explanation. Harcourt, Brace & World.
Carl Hempel (1965). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. The Free Press.
Mary B. Hesse (1966). Models and Analogies in Science. University of Notre Dame Press.
Dedre Gentner (1983). Structure‐Mapping: A Theoretical Framework for Analogy. Cognitive Science 7 (2):155-170.
Citations of this work BETA
Dirk Schlimm (2011). On the Creative Role of Axiomatics. The Discovery of Lattices by Schröder, Dedekind, Birkhoff, and Others. Synthese 183 (1):47-68.
Alison Pease, Markus Guhe & Alan Smaill (2013). Developments in Research on Mathematical Practice and Cognition. Topics in Cognitive Science 5 (2):224-230.
Dirk Schlimm (2012). A New Look at Analogical Reasoning. Metascience 21 (1):197-201.
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