radicality n.

late 14c., "originating in the root or ground;" of body parts or fluids, "vital to life," from Latin radicalis "of or having roots," from Latin radix (genitive radicis) "root" (from PIE root *wrād- "branch, root"). The basic sense of the word in all meanings is "pertaining or relating to a root or roots," hence "thoroughgoing, extreme."

The figurative meaning "going to the origin, essential" is from 1650s. The political sense of "reformist" is by 1817, of the extreme section of the British Liberal party (radical reform had been a current phrase since 1786), via the notion of "change from the roots" (see radical (n.)). The meaning "unconventional" is from 1921. U.S. youth slang use is from 1983, from 1970s surfer slang meaning "at the limits of control."

The mathematical radical sign, placed before any quantity to denote that its root is to be extracted, is from 1680s; the sign itself is a modification of the letter -r-. Radical chic is attested from 1970; popularized, if not coined, by Tom Wolfe. Radical empiricism was coined 1897 by William James (see empiricism).

word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).

Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]