The objects of perception which I take to be ‘external’ to me, such as coloured surfaces that I see, are only ‘external’ in my private space . . . When on a common-sense basis, people talk of the gulf between mind and matter, what they really have in mind is the gulf between a tactual percept, and a ‘thought’—e.g. a memory, a pleasure, or a volition. But this, as we have seen, is a division within the mental world; the percept is as mental as the ‘thought’. (Simon and Schuster edition, p. 228)The second excerpt is from the previous chapter, “Space in Psychology”:
All this [the physiological account of perception], I say, has long been a commonplace, but it has a consequence that has not been adequately recognised, namely that the space in which the physical table is located must be different from the space we know by experience. (p. 222)
In these two passages Russell does not refer to the theory of perception as such, that is, the “physical theory of perception” as he calls it in the chapter “Physics and Experience,” or “causal theory of perception” in his book The Analysis of Matter, devoting a chapter to it under that name. Russell makes explicit reference once again to the proverbial table which so often serves as an example in these armchair exegeses (perhaps being a pedagogical tradition dating from medieval scholasticism?):
The colored surface that I see when I look at a table has a spatial position in the space of my visual field; it exists only where eyes and nerves and brain exist to cause the energy of photons to undergo certain transformations. (The ‘where’ in this sentence is a ‘where’ in physical space.) The table as a physical object, consisting of electrons, positrons, and neutrons, lies outside my experience, and if there is a space which contains both it and my perceptual space, then in that space the physical table must be wholly external to my perceptual space. This conclusion is inevitable if we accept the view as to the physical causation of sensations which is forced on us by physiology . . . . (p. 220f)In saying that the conclusion “is inevitable,” I would refer to my recent remarks about data “demanding” one theory over another, because the inevitability of the conclusion (= theory) here not only depends upon but is in a sense "demanded" by the causal chain of empirical events, all save the last, arguably, as at most a percipient can only report that he indeed “sees the light” (pun intended), but no observer can also see his visual space and independently verify that it exists (yes, just the sort of argument that behaviorists used to use against what they miscalled "introspection"). Of course Russell was an avowed monist so it is reasonable to assume that dualism plays no part in the “physical causation of sensations” to which he refers.
Russell is at pains to say that confusion has resulted from conflating different senses of the word “space.” (p. 201), but assures us that percepts are nonetheless in the brain: “Percepts, considered causally, are between events in afferent nerves (stimulus) and events in efferent nerves (reaction); their location in the causal chains is the same as that of certain events in the brain.” (p. 209)
So without evidence to the contrary, it seems reasonable to assume that when Russell refers to two different spaces (physical and perceptual) he means space not in the cosmological sense, but in sense 11 of the word space in OED, “Specific or limited extent,” because he is claiming that perceptual space is “private,” or conversely, that it is separate from external physical space, i.e., external to the body.
In spite of that, I suspect that Russell may have conflated two senses of “space,” because merely in separating perceptual space from physical space he seems to be using sense 11 of “space,” yet elsewhere in the context of his argument seems to be employing OED sense 7, “Physical extent or area; extent in two or three dimensions.” They are not synonymous senses of the word.
Lord Brain basically just restates Russell’s main point, and while Broad (1923) says it is “possible” to have “a space-like whole of more than three dimensions, in which sensa of all kinds, and scientific objects literally have places,” and that “scientific space would be one kind of section of such a quasi-space, and e.g. a visual field would be another kind of section of the same quasi-space,” he does not seem to explain (1) the necessity of such a “space-like whole” nor (2) how it is “possible.” By referring to "places," again Broad seems to be using sense 11, not sense 7 of the word "space."
Where then does this leave us, as other than Broad’s imaginative proposal, what compelling evidence is there to support it since he put forth the idea 1923?