My thesis looks at structural analogies between symmetries in physics, and phenomena of synonymy and translation in formalised languages. In this context, a symmetry transformation is a transformation of the mathematical structures used in the theory, in such a way that any solution of the theory’s equations is transformed into another solution. First, I look at how model-theoretic notions of homomorphism, translations and equivalence can be fruitfully applied to debates in metaphysics over haecceitism and quidditism. Second, I argue in favour of both anti-haecceitism and anti-quidditism (now understood in this precise fashion). Third, I show that the arguments from these cases can be extended to symmetries in physics; and, hence, that the general commitments to anti-haecceitism and anti-quidditism entail that models related by a symmetry should not be interpreted as representing the same physical possibility. Finally, I look at a specific case (the accelerative shift symmetry of Newtonian gravitation), and consider how the lessons of this symmetry may be formally implemented.
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