Coordinate-free Thinking

Thinking outside the box is a nice metaphor, but we are so used to putting things in boxes that it may seem essential to our way of thinking. This idea is enforced by the standard view of relations that says that relata always come in a certain order. There is, however, an alternative view on relations, the antipositionalist view, according to which the constituents of the complexes of a relation neither come in a certain order, nor do they occupy positions. Instead, a relation is conceived as a network of interrelated complexes. We show that this view facilitates a coordinate-free way of thinking and that it may thus have a heuristic value.