  However, Barcan Marcus has offered an alternative perspective, insisting on ‘No identity without entity.’ (Marcus 1993) and arguing that although ‘… all terms may “refer” to objects… not all objects are things, where a thing is at least that about which it is appropriate to assert the identity relation.’ (ibid., p. 25) Object-reference then becomes a wider notion than thing-reference. Within such a framework, we can then begin to get a formal grip on the notion of objects which are not self-identical through so-called ‘Schrödinger logics’, introduced by da Costa (da Costa and Krause 1994) These are many-sorted logics in which the expression x = y is not a well-formed formula in general; it is where x and y are one sort of term, but not for the other sort corresponding to quantum objects. A semantics for such logics can be given in terms of ‘quasi-sets’ (da Costa and Krause 1997). The motivation behind such developments is the idea that collections of quantum objects cannot be considered as sets in the usual Cantorian sense of ‘… collections into a whole of definite, distinct objects of our intuition or of our thought.’ (Cantor 1955, p. 85). Quasi-set theory incorporates two kinds of basic posits or ‘Urelemente’: m-atoms, whose intended interpretation are the quantal objects and M-atoms, which stand for the ‘everyday’ objects, and which fall within the remit of classical set theory with Ur-elements. Quasi-sets are then the collections obtained by applying the usual Zermelo-Fraenkel framework plus Ur-element ZFU-like axioms to a basic domain composed of m-atoms, M-atoms and aggregates of them (Krause 1992; for a comparison of qua-set theory with quasi-set theory, see Dalla Chiara, Giuntini and Krause 1998).