No, if anything you have it completely backwards. Once again, pixel density is measured in
dots-per-inch (or pixels-per-inch). It's a linear measurement, not an area -- it's NOT
dots-per-square-inch or pixels-per-square-inch. I wish people would take the time to at least glance at the reference links that are given to them rather than just immediately firing off a response. Look on wikipedia, it couldn't be clearer:
http://en.wikipedia.org/wiki/Pixel_density
fpnc is right about pixel density, at least in terms of using ppi as pixel density. It's a bit odd that this is often the convention, since density occurs in two dimensions. With ppi, which uses the hypotenuse, the density in two dimensions is implied. I guess it's easier to use a smaller number like 132 ppi than something like 17424 pixels per *square* inch, which is what we are really talking about.
Still, when you double the ppi, the reality is that 4 times as many pixels are contained within each square inch, so no matter how you abbreviate it, that's 4 times the density.
But yes, if ppi is used, we'll have to call 2048x1536 "double" the density.
As for resolution, resolution is more commonly measured in two dimensions and reflects pixel count. For example, 1024x768 is a resolution. Only on macrumors have I seen resolution also being treated as a one dimensional number, suggesting that 2048x1536 is a doubling of 1024x768. Since screen resolutions must be determined by pixel counts in both dimensions, we should call it quadrupling, since pixel count is quadrupled.
If you go to 2048x1536 on the iPad, you double the density (using ppi), but quadruple the resolution (using pixel count), as fpnc suggested.