"of or pertaining to controversy," 1640s, from French polémique "disputatious, controversial," or directly from Greek polemikos "of war, warlike, belligerent; skilled in war, fit for service; like an enemy, stirring up hostility," from polemos "war," a word of unknown origin. Related: Polemical (1630s); polemically.
1620s, "the part of the spar-deck of a man-of-war between the poop and the main-mast," originally "a smaller deck above the half-deck," covering about a quarter of the vessel [OED], from quarter (n.1).
"It is used as a promenade by the officers only" [Century Dictionary], hence the colloquial nautical noun quarter-decker (by 1867) "an officer who is more looked upon as a stickler for small points of etiquette than as a thorough seaman."