Structures and structural realism

The 'ontic' form of structural realism (OSR), roughly speaking, aims at a complete elimination of objects of the discourse of scientific theories, leaving us with structures only. As put by the defenders of such a claim, the idea is that all there is are structures and, if the relevant structures are to be set theoretical constructs, as it has also been claimed, then the relations which appear in such structures should be taken to be 'relations without the relata'. As far as we know, there is not a definition of structure in standard mathematics which fits their intuitions, and even category theory seems do not correspond adequately to the OSR claims. Since OSR is also linked to the semantic approach to theories, the structures to be dealt with are (at least in principle) to be taken as set theoretical constructs. But these are 'relational' structures where the involved relations are built from basic objects (in short, the rank of the relation is greater than the rank of the relata), and so no elimination of the relata is possible, although it would be interesting for characterizing OSR. In this paper we present a definition of a relation which does not depend on the particular objects being related in the sense that the 'relation' continues to hold even if the relata are exchanged by other suitable ones. Although there is not a 'complete' elimination of the relata, there is an elimination of 'particular' relata, and so our definition might be viewed as an alternative way of finding adequate mathematical 'set-theoretical' frameworks for describing at least some of the intuitions regarding OSR.
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