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In this paper I assess the 'Invariance Principle', which states that only quantities that are invariant under the symmetries of our theories are physically real. I argue, contrary to current orthodoxy, that the variance of a quantity under a theory's symmetries is not a sufficient basis for interpreting that theory as being uncommitted to the reality of that quantity. Rather, I argue, the variance of a quantity under symmetries only ever serves as a motivation to refrain from any commitment to the quantity in question. In the process of this discussion, I address the related but importantly distinct issue of when symmetries can be said to prompt a mathematical reformulation of the relevant theory.

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In this paper I argue that the focus of much contemporary discussion concerning the proper role and philosophical significance of weak discernibility in the context of quantum mechanics (and other physical theories) is misplaced. In particular, I claim that metaphysicians' criticism of weak discernibility on the basis of its alleged inability to ground objects' numerical distinctness is orthogonal to Saunders's (2003a) main concern in his original paper, which is to use the notion of weak discernibility as part of a broader "logical aid" for interpreting physical theories. How exactly this "methodological" (as opposed to "metaphysical") construal of weak discernibility is supposed to work, however, is not immediately transparent. This paper therefore serves both as an attempt to gain a better understanding of Saunders's interpretational program, and also seeks to encourage a renewed emphasis on the set of issues and questions that such a program-at least on my understanding of it-would appear to raise.