David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Synthese 67 (3):391 - 437 (1986)
The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: the assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories.
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References found in this work BETA
Hartry Field (1980). Science Without Numbers. Princeton University Press.
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Rudolf Carnap (1966). Philosophical Foundations of Physics;. New York,Basic Books, Inc..
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Citations of this work BETA
Roman Frigg & Ioannis Votsis (2011). Everything You Always Wanted to Know About Structural Realism but Were Afraid to Ask. European Journal for Philosophy of Science 1 (2):227-276.
Mauricio Suárez & Nancy Cartwright (2007). Theories: Tools Versus Models. Studies in History and Philosophy of Science Part B 39 (1):62-81.
Anjan Chakravatty (2010). Informational Versus Functional Theories of Scientific Representation. Synthese 172 (2):197 - 213.
Chris Swoyer (1991). Structural Representation and Surrogative Reasoning. Synthese 87 (3):449 - 508.
Joseph Berkovitz (2015). The Propensity Interpretation of Probability: A Re-Evaluation. Erkenntnis 80 (3):629-711.
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