Origin and history of cardinality

early 12c., "one of the ecclesiastical princes who constitute the sacred college," from Medieval Latin cardinalis, originally as a noun "one of the presbyters of the chief (cardinal) churches of Rome," short for cardinalis ecclesiae Romanae or episcopus cardinalis, from Latin cardinalis (adj.) "principal, chief, essential" (see cardinal (adj.)).

The North American songbird (Cardinalis virginianus) is attested from 1670s, so named for its fine red color, resembling the cardinals in their red robes.

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]