David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 158 (1):1 - 17 (2007)
Recent semantic approaches to scientific structuralism, aiming to make precise the concept of shared structure between models, formally frame a model as a type of set-structure. This framework is then used to provide a semantic account of (a) the structure of a scientific theory, (b) the applicability of a mathematical theory to a physical theory, and (c) the structural realist’s appeal to the structural continuity between successive physical theories. In this paper, I challenge the idea that, to be so used, the concept of a model and so the concept of shared structure between models must be formally framed within a single unified framework, set-theoretic or other. I first investigate the Bourbaki-inspired assumption that structures are types of set-structured systems and next consider the extent to which this problematic assumption underpins both Suppes’ and recent semantic views of the structure of a scientific theory. I then use this investigation to show that, when it comes to using the concept of shared structure, there is no need to agree with French that “without a formal framework for explicating this concept of ‘structure-similarity’ it remains vague, just as Giere’s concept of similarity between models does ...” (French, 2000, Synthese, 125, pp. 103–120, p. 114). Neither concept is vague; either can be made precise by appealing to the concept of a morphism, but it is the context (and not any set-theoretic type) that determines the appropriate kind of morphism. I make use of French’s (1999, From physics to philosophy (pp. 187–207). Cambridge: Cambridge University Press) own example from the development of quantum theory to show that, for both Weyl and Wigner’s programmes, it was the context of considering the ‘relevant symmetries’ that determined that the appropriate kind of morphism was the one that preserved the shared Lie-group structure of both the theoretical and phenomenological models.
|Keywords||Semantic view of scientific theories Structural realism Scientific structuralism Suppes Bourbaki structuralism Shared structure Mathematical applicability|
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References found in this work BETA
Peter Achinstein (1968). Concepts of Science. Baltimore, Johns Hopkins Press.
Tian Yu Cao (2003). Can We Dissolve Physical Entities Into Mathematical Structures? Synthese 136 (1):57 - 71.
Tian Yu Cao (2003). Structural Realism and the Interpretation of Quantum Field Theory. Synthese 136 (1):3 - 24.
Newton C. A. Da Costa, Otávio Bueno & Steven French (1997). Suppes Predicates for Space-Time. Synthese 112 (2):271-279.
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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.
Steven French (2011). Shifting to Structures in Physics and Biology: A Prophylactic for Promiscuous Realism. Studies in History and Philosophy of Science Part C 42 (2):164-173.
Steven French (2012). Unitary Inequivalence as a Problem for Structural Realism. Studies in History and Philosophy of Science Part B 43 (2):121-136.
Steven French (2011). Metaphysical Underdetermination: Why Worry? Synthese 180 (2):205 - 221.
Steven French (2010). Keeping Quiet on the Ontology of Models. Synthese 172 (2):231 - 249.
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