  The founders of structuralism shared an appreciation of the importance of group theory in the ontology of physics. Cassirer held that the possibility of talking of ‘objects’ in a context is the possibility of individuating invariants (1944). Similarly, Max Born says: “Invariants are the concepts of which science speaks in the same way as ordinary language speaks of ‘things’, and which it provides with names as if they were ordinary things” (1953, 149), and: “The feature which suggests reality is always some kind of invariance of a structure independent of the aspect, the projection” (149). He goes so far as to say: “I think the idea of invariant is the clue to a relational concept of reality, not only in physics but in every aspect of the world.” (144). Eddington says: “What sort of thing is it that I know? The answer is structure. To be quite precise it is structure of the kind defined and investigated in the mathematical theory of groups” (1939, 147). Poincaré understands group structure in Kantian terms as a pure form of the understanding.