The North American songbird (Cardinalis virginianus) is attested from 1670s, so named for its fine red color, resembling the cardinals in their red robes.
"chief, pivotal," early 14c., from Latin cardinalis "principal, chief, essential," a figurative use, literally "pertaining to a hinge," from cardo (genitive cardinis) "that on which something turns or depends; pole of the sky," originally "door hinge," which is of unknown origin. Related: Cardinally.
The cardinal numbers (1590s) are "one, two, three," etc. as opposed to ordinal numbers "first, second, third," etc.; they are so called because they are the principal numbers and the ordinals depend on them.
The cardinal points (1540s) are north, south, east, west. The cardinal sins (c. 1600) are too well known to require rehearsal. The cardinal virtues (c. 1300) were divided into natural (justice, prudence, temperance, fortitude) and theological (faith, hope, charity). The natural ones were the original classical ones, which were amended by Christians. But typically in Middle English only the first four were counted as the cardinal virtues:
Of þe uour uirtues cardinales spekeþ moche þe yealde philosofes. ["Ayenbite of Inwyt," c. 1340]
By analogy of this, and cardinal winds (late 14c.), cardinal signs (four zodiacal signs marking the equinoxes and the solstices, late 14c.), etc., the adjective in Middle English acquired an association with the number four.
late 14c., "moral strength (as a cardinal virtue); courage," from Latin fortitudo "strength, force, firmness, manliness," from fortis "strong, brave" (see fort). From early 15c. as "physical strength."
"a region, district, land, country," late 14c., from Old French plage (13c.) and directly from Late Latin plagia "a plain, shore," noun use of adjective (plagia regio), from plaga "a region, stretch of country" (see pelagic). From early 15c. as "one of the four cardinal directions of the compass." Astronomical use in reference to a region of the sun's chromosphere is from 1949.
1767, "explain in a rational way, make conformable to reason," from rational + -ize. The psychological sense of "to give an explanation that conceals true motives" dates from 1922, on the notion of "cause to appear reasonable or socially acceptable." In 19c. Newman and Browning also used it with an intransitive sense of "think for oneself, employ one's reason as the supreme test." Related: Rationalized; rationalizer; rationalizing.
mid-14c. (c. 1200 as a surname), "intelligence; discretion, foresight; practical wisdom to see what is suitable or profitable;" also one of the four cardinal virtues, "wisdom to see what is virtuous;" from Old French prudence (13c.) and directly from Latin prudentia "a foreseeing, foresight, sagacity, practical judgment," contraction of providentia "foresight" (see providence, which is a doublet). The secondary sense of "knowledge, science" (late 14c.) is preserved in jurisprudence.