Thinking in a coordinate-free way about relations

Abstract

How we talk about relations has a great influence on how we think about relations. By saying that Spain defeated the Netherlands we obviously say something entirely different from saying that the Netherlands defeated Spain. This makes many of us think that in the underlying relation itself one of the relata comes first and the other comes second. However, there are good reasons to view the order as a representational artifact. In this paper I present a new logic that allows us to think and talk about relations in a coordinate-free manner. The logic is minimalistic in the sense that it has no predicates except equality, but its expressive power is the same as that of first-order predicate logic.