IngentaConnect Shared structure need not be shared set-structure

Abstract:

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.

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