Structures and structural realism

Krause, Décio (2003) Structures and structural realism.

Abstract

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.