Pure, absolute, simple, sheer denote free from everything that is foreign to the true nature or the essential character of the thing specified.
Pure distinctively suggests freedom from intermixture. When applied to concrete things, it usually implies lack of contamination, adulteration, or pollution.
When applied to an abstraction or to a concrete example of an abstraction, it implies the absence of everything that would obscure the thing in its essence or in its ideal character.
Absolute implies freedom from relation to or dependence on anything else; it is applied chiefly to abstractions (as space, time, and magnitude) viewed independently of experience and considered in their ultimate ideal character; thus, absolute space, as used in physics, is space conceived of as apart from the things which occupy it, and which limit or determine the ordinary person’s notion of it.
Because of such use, absolute often comes close to real, as opposed to apparent. Absolute music, in theory, is music that depends solely on such distinctive properties of that art as tone, harmony, and rhythm to produce its effects, and avoids, in contrast to program music, all suggestion or characterization of external things.
Absolute is applied to substances less often than is pure, but both are applied to alcohol: pure alcohol is free from other matter except for a modicum of water; absolute alcohol is both pure and completely dehydrated.
Simple stresses singleness of character and is distinguished from what is compound or complex. It can connote homogeneity and incapacity for analysis or further reduction.
Simple, as applied to abstractions or conceptions, often suggests artificial freedom from complexity, and sometimes also unreality or untruth, when the simplicity is attained by eliminating essential factors.
Sheer, more than any of these words, tends to lose its significance and to become a mere intensive.
However, it can distinctively imply such a dissociation from everything else that the pure and essential character of the quality (as a trait, virtue, or power) to which it is applied is clearly displayed.