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In ordinary representations of relations the order of the relata plays a structural
role, but in the states of affairs or the facts themselves such an order
often does not seem to be intrinsically present. An alternative way to represent
relations makes use of positions for the arguments. This is no problem
for the love relation, but for relations like the adjacency relation and cyclic
relations, different assignments of objects to the positions can give exactly
the same states. This is a puzzling situation. The question is, what is the
ontological status of the positions, and, more generally, what is the internal
structure of relations? In this thesis mathematical models for relations are
developed, which provide more insight into the structure of relations “out
there” in the real world
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