word-forming element used in English from c. 1300 and meaning "against, in opposition; in return; corresponding," from Anglo-French countre-, French contre-, from Latin contra "opposite, contrary to, against, in return," also used as a prefix (see contra (prep., adv.)). A doublet of contra-. In some cases it probably represents a purely English use of counter (adv.).
1640s, "perceiving directly and immediately," from French intuitif or directly from Medieval Latin intuitivus, from intuit-, past-participle stem of Latin intueri "look at, consider," from in- "into" (from PIE root *en "in") + tueri "to look at, watch over," a word of uncertain origin. Meaning "self-evident" is from 1833. Related: Intuitively; intuitiveness.