 This takes us to a further possible response to the above metaphysical underdetermination which urges realism to retreat from a metaphysics of objects and develop an ontology of structure compatible with the physics (Ladyman 1998 and 2014). An early attempt to do this in the quantum context can be seen in the work of Cassirer who noted the implications of the new physics for the standard notion of individual objects and concluded that quantum objects were describable only as ‘“points of intersection” of certain relations’ (1937, p. 180) Setting aside the neo-Kantian elements in Cassirer’s structuralism, this view of quantum entities has been developed in the context of a form of ‘ontic’ structural realism (Ladyman and Ross 2007). Drawing on the views of both Weyl and Wigner, quantum objects are here understood as ontologically constituted, group theoretically, in terms of sets of invariants, such as rest mass, charge, spin, and so on (Castellani 1998a). From this perspective, both the individuality and non-individuality packages get off on the wrong feet, as it were, by assuming that the way the world is, according to physics, is a world of objects, which can either be regarded as individuals, whether primitively or via weak discernibility, or as non-individuals, whether formally represented through quasi-set theory or not.   How, then, should we regard the ‘Indistinguishability Postulate’ with which we began this discussion of identity and individuality in the quantum context? Both the above packages rest upon a certain understanding of particle permutations, as encapsulated in that  Postulate, namely that these are to be conceived in terms of swapping the particles  between states, or boxes in our illustrative sketch. However, we can also think of the ‘Indistinguishability Postulate’ as expressing a fundamental symmetry constraint on quantum mechanics, to the effect that the relevant states should be invariant under particle permutations. An alternative way of regarding this ‘permutation invariance’ that aligns with a widely accepted view of symmetry principles in general is that it expresses a certain representational redundancy in the formalism. Thus, referring to our sketch above, the permuted arrangement of one particle in each box, which is counted in classical statistical mechanics but not in the quantum form, can be considered as ‘representationally redundant’ in this sense. This casts ‘permutation invariance’ as one of a number of such symmetry principles that have acquired a fundamental role in modern physics (Huggett 1999b; French and Rickles 2003). Not surprisingly perhaps, such a re-casting may also have metaphysical implications in that when applied to certain systems obeying Fermi-Dirac statistics – that is, systems of ‘material’ particles – the composition of such systems (in the sense that they may be regarded as composed or made up of sub-systems considered as ‘parts’) violates standard mereological principles (Caulton 2015; for some possible responses see Bigaj 2016). More generally it has been argued that ‘permutation invariance’ is incompatible with a particle ontology understood even in a metaphysically minimal sense (Jantzen 2011). Given the fundamental significance of the former, it has been suggested that the latter must then be jettisoned. A possible alternative is to adopt a form of space-time substantivalism and take property-bearing regions of space-time to provide the appropriate ontological basis (Jantzen 2011). However that runs into the sorts of problems touched on above.  More radically, perhaps, dropping the above ‘object-oriented’ assumption would undercut the metaphysical underdetermination entirely and open up space for an alternative ontology in terms of which quantum entities are conceived of as nothing more than features of ‘the structure of the world’ (see French and Ladyman 2003). This can then be articulated in terms of the relevant laws and symmetries with the properties of such putative entities understood as the determinate aspects of this structure (see French 2014; for further consideration of such an ontology in the context of ‘structural realism’, see Ladyman 2014).