2.0131 The spatial object must be in infinite space. (A spatial point is an argument-place.)
The speck in a visual field of course need not be red, but it must have a color: it has, so to speak, color-space around it. The note must have a pitch, the object of the sense of touch a degree of hardness, etc.
Black (p. 50) suggests that perhaps the space must be infinite because it must be boundless, otherwise objects on a boundary might have a privileged position. This seems doubtful to me. But what other reason could there be? Black also says ‘speck’ should be ‘patch’. I think ‘spot’ is the closest to a literal translation.
The reference to the object of the sense of touch is interesting here since such objects are especially problematic for sense data theorists such as Russell. What are such objects? Surely just material objects of a very familiar kind. Wittgenstein does not say this here, but perhaps he wants to intimate it. What does he say? There is not one but many spaces of possible states of affairs: the space of (three-dimensional) space, the space of color, the space of pitch, the space of hardness, and so on. Each can be thought of as a dimension or set of dimensions. Is there some über-space of spaces in which these dimensions exist? Is that what logic would be? Presumably not because: a) see above, and b) this has all been presented as mere metaphor. But perhaps we presume too much here. We must go on.