What Do Symmetries Tell Us About Structure?

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Barrett, Thomas William
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Mathematicians, physicists, and philosophers of physics often look to the symmetries of an object for insight into the structure or constitution of the object. My aim in this paper is to explain why this practice is successful. In order to do so, I prove two theorems that are closely related to (and in a sense, generalizations of) Beth's and Svenonius' theorems.