63. Geometrical Figures. 63.1 The generalisation which introduces geometrical figures is an extreme instance of the sort of generalisation already considered. Namely, instead of generalising from a dark-blue figure to a sight-figure, we pass to the concept of the relation of any sense-object to the volumes of its situation. This concept of a figure, in which any particular sense has been lost sight of, would be entirely without any counterpart in perception, if it were not for the fact of perceptual objects. A perceptual object is the association in one situation of a set of sense-objects, in general ‘conveyed’ by the normal perception of one of them. The high perceptive capacity of sense-figures leads to their association in a generalised figure, which is the geometrical figure of the object. Indeed, the insistent obviousness of the geometrical figure is one reason for the perception of perceptual objects. The object is not the figure, but our awareness of it is derived from our awareness of the figure. The reason for discriminating the perceptual object from its figure in that situation is that the physical object persists while its figure changes. For example, a sock can be twisted into all sorts of figures.
63.2 The current doctrine of different kinds of space — tactual space, visual space, and so on — arises entirely from the error of deducing space from the relations between figures. With such a procedure, since there are different types of figures for different types of sense, evidently there must be different types of space for different types of sense. And the demand created the supply.
63.3 If however the modern assimilation of space and time is to hold, we must then go further and admit
