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John Dougherty
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conference paper description
Much of the philosophical literature on classical Yang--Mills theories is concerned with the differences between interpretations that represent the state of the world in terms of fields and those that represent the state of the world in terms of properties assigned to curves in spacetime. In the philosophical literature on Yang-Mills theories, field formulations are taken to have more structure and to be local in a particular sense, while the alternative curve-based formulations are taken to have less structure at the cost of nonlocality. I formalize the notion of locality at issue and show that theories with less structure are indeed nonlocal. However, the amount of structure had by some formulation is independent of whether it uses fields or curves. This leads to a general lesson about structure in mathematized theories. The difference in structure corresponding to the difference in locality is not a difference in set-theoretic structure. Rather, it is a difference in the structure of the collection of models of the theory considered as a category.

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