Equivalent theories (or statements, or models, or representations) represent the very same state of the world; any differences are merely conventional or notational. Our question is the metaphysics of equivalence, what it is to be equivalent.
The Tools of Metaphysics and the Metaphysics of Science. Theodore Sider
The Tools of Metaphysics and the Metaphysics of Science. Theodore Sider
One naturally or naively wants out of a notion of equivalence a weapon to silence anyone who wants to think about absurd questions such as whether a 1 kg object is really 1 or 1,000 in mass.
On the philosophical front: we might want to consider a structure, W, whose domain is the set of all living wombats. In order to work out which sentences are true in W using Robinson’s own proposal, we would have to treat each wombat as a name for itself, and so imagine a language whose syntactic parts are live wombats. This stretches the ordinary notion of a language to breaking point.
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