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Crucial to structural realism is the Central Claim that entity B is or has structure S. We argue that neither the set-theoretical nor the category-theoretical conceptions of structure clarify the Claim in a way that serves the needs of structural realism. One of these needs is to have a viable account of reference, which almost any variety of realism needs. There is also a view of structure that can adopt both set-theoretical and category-theoretical conceptions of structure; this is the view that adopts B.C. van Fraassen's extension of Nelson Goodman's concept of representation-as from art to science. Yet the ensuing fountain of perspectives is a move away from realism, structural realism included. We then suggest that a new theory of structure is needed, one that takes the word 'structure" to express a primitive fundamental concept; the concept of structure should be axiomatised rather than defined in terms of other concepts. We sketch how such a theory can clarify the Central Claim in a manner that serves a descriptivist account of reference, and thereby structural realism.

DOI: 10.1007/978-90-481-9115-4_28

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