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Décio Krause, Structures and Structural Realism, Logic Journal of the IGPL, Volume 13, Issue 1, January 2005, Pages 113–126, https://doi.org/10.1093/jigpal/jzi007
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Abstract
The ‘ontic’ form of structural realism (OSR), roughly speaking, admits a complete elimination of the objects in 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 (partial structures), 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 not to correspond adequately the OSR claims. Since OSR is also linked with the semantic approach to theories, the structures to be dealt with are (at least in principle) taken to be 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 complete elimination of the relata is possible, although it would be adequate for characterizing OSR. In this paper we present a definition of a kind of relation that 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 suitable objects. Although there is not a ‘complete’ elimination of relata, 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 within a ‘set-theoretical’ framework.
