Next we can introduce structure by opening our eyes, gazing at a lit lamp bulb, and closing our eyes again. An after-image (AI) appears. This possesses some intrinsic properties—i.e. extension, shape, and colour—and extrinsic properties i.e. location at a particular position in the visual field, as well as topological and geometrical relations with other after-images in the same field. For example, one AI can be spatially BETWEEN two other AIs. Three AIs can form a triangle: four AIs can form a square, etc.. The edge of an AI can form a Jordan curve. Moreover, when we move our eyes we notice that the AIs move too to stay in the focus of attention.
These simple observations establish the important point that visual (phenomenal) space is a genuine space. A genuine space may be defined as that in which an entitiy can move about in. Tennis balls move in physical space A. After-images, as well as the eyes of the body-image, move about in phenomenal space B.
Two different genuine spaces in a cosmos can be related in three ways;—
i. A and B are different cross-sections in a higher-dimensional space C (Broad’s 1923 theory: since elaborated by others).
ii. B is a subset of A (as in the Identity Theory).
iii. A and B have no spatial relations and only causal ones (Price’s 1953 theory)
iv. Nevertheless, in all three cases, we are dealing with real spaces, and not imaginary, mathematical, phase spaces, etc.