White paper appears white when light from the sun or a light bulb illuminates it because white paper reflects most of the visible wavelengths of the spectrum.
However, paper, we ordinarily call white, would not necessarily appear white under all illuminations. For example, if a red spot light illuminates a piece of white paper that paper will appear red. If you think about it, you already know this. For example, a screen on which movies or slides are projected is usually white. Yet, we see a bevy of colors that make up the images projected on the screen.