Newman’s Objection is Dead; Long Live Newman’s Objection!
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There are two ways of reading Newman’s objection to Russell’s structuralism. One assumes that according to Russell, our knowledge of a theory about the external world is captured by an existential generalization on all non-logical symbols of the theory. Under this reading, our knowledge amounts to a cardinality claim. Another reading assumes that our knowledge singles out a structure in Russell’s (and Newman’s) sense: a model theoretic structure that is determined up to isomorphism. Under this reading, our knowledge is far from trivial, for it amounts to knowledge of the structure of the relations between objects, but not their identity. Newman’s objection is then but an expression of structural realism. Since therefore the content of theories is described by classes of structures closed under isomorphism, the most natural description of a theory in structural realism is syntactic.