The characterisation of structure: Definition versus axiomatisation

Abstract. We argue that neither the set-theoretical nor the category-theoretical conceptions of structure serve the needs of structural realism, in that they cannot clarify what it means to say that being B is or has structure S, which claim is central to structural realism. Such a clarification is warranted by any viable ac-count of reference, which almost any variety of realism needs. There is however a view that can adopt both set-theoretical and category-theoretical conceptions of structure; this is the view that adopts Bas van Fraassen’s extension of Nelson Good-man’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 ‘struc-ture ’ 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 what it means to say that being B is or has structure S in