Geometrical and other properties that may be labelled ‘structural’ are held up as examples of properties that are not potencies, but are categorical properties. The debate between Mellor and Prior is examined in order to shed light on this question. The problem is then related to the question of whether a true physical theory should be background-free, on the grounds that it is the presence of spacetime as a background in intuitive physical theories that is responsible for the appearance that spatial properties are categorical, whereas advanced physical theories tend to be background-free.
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