Lewis Powell If there was one claim of Hume's that I had a real tough time swallowing this semester, it was Hume's claim that he could resolve the problem of mathematical vs. physical points by
specifiying imbuing (unextended) mathematical points with color.
As I was finishing my term paper, I put a couple of things together that helped me make sense of this seemingly bizarre claim.
1) Most of the time when people are talking about the properties of physical objects, the starting point is that the objects are somewhere in space, and thus, extension is often thought to be the primary characteristic. Since Hume's starting point wasn't objects in space, but instead, as parts of a visual field, and the visual field on his view is an array of colors, it makes sense that the primary visual quality is color rather than extension. It is straightforwardly conceptually impossible to have a colorless visible thing (for Hume), so
saying the points are colored imbuing the points with color saves the day.
2) The best I can figure, Hume is endorsing a view that I've dubbed the Pixel theory of vision. Computer monitors are a good analogy for vision. We have a pixelized colored array. To be unextended but visible is to be one pixel. Extension is the compound visibility property (or the compound tactile property). The reason the minima which is clearly not point-sized in the mathematical sense is extensionless is because there is no reasonable notion, for Hume, of sub-pixel measurements. Anything smaller than a pixel can't register, and so sub-pixel sizes are meaningless. Thus, the minima visibile is not sizeless, it's just one minimal-unit big.
3) This also solves the discontinuity problem Hume has (arising from extension being a finite aggregation of unextended parts), I think, because a pixel-y sort of visual field could possibly have no gaps between pixels, thus allowing continuity. These points wind up being a lot more like physical points than mathematical points, but they aren't extended because they cannot be broken down.