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[In this paper I offer an answer to a question raised in (Psillos, 2006): How can one speak of structures without objects? Specifically, I use category theory to show that, mathematically speaking, structures do not need objects. Next, I argue that, scientifically speaking, this category-theoretic answer is silly because it does not speak to the scientific structuralist’s appeal to the appropriate kind of morphism to make precise the concept of shared structure. Against French et al.’s approach,1 I note that to account for the scientific structuralist’s uses of shared structure we do not need to formally frame either the structure of a scientific theory or the concept of shared structure. Here I restate my (Landry, 2007) claim that the concept of shared structure can be made precise by appealing to a kind of morphism, but, in science, it is methodological contexts (and not any category or set-theoretic framework) that determine the appropriate kind. Returning to my aim, I reconsider French’s example of the role of group theory in quantum mechanics to show that French already has an answer to Psillos’ question but this answer is not found in either his set-theoretic formal framework or his ontic structural realism. The answer to Psillos is found both by recognizing that it is the context that determines what the appropriate kind of morphism is and, as Psillos himself suggests,2 by adopting a methodological approach to scientific structuralism.Brading, KatherineChakravartty, AnjanRickles, DeanNounou, AntigonePsillos, StathisFrench, StevenLandry, Elaine]
Published: Jan 27, 2011
Keywords: Category Theory; Abstract System; Shared Structure; Ontic Structural Realism; Scientific Structuralism
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