mid-15c., "presentation of formal arguments," from Old French argumentacion (14c.), from Latin argumentationem (nominative argumentatio) "the bringing forth of a proof," noun of action from past-participle stem of argumentari "adduce proof, draw a conclusion," from argumentum (see argument). Meaning "debate, wrangling, argument back and forth" is from 1530s.
1540s, refutacion, "act of disproving; overthrowing of an argument" (by countervailing argument or proof), from French réfutation (16c.) and directly from Latin refutationem (nominative refutatio) "disproof of a claim or argument," noun of action from past-participle stem of refutare ""drive back; rebut, disprove" (see refute).
c. 1600, "dispute (something), oppose by argument" (a sense now obsolete); 1610s, "to make the subject of verbal contention, debate, discuss; contend against (someone) in argument," probably a back-formation from controversy. Related: Controverted; controverting; controvertible.