half-wit n.

Old English half, halb (Mercian), healf (W. Saxon) "side, part," not necessarily of equal division (original sense preserved in behalf), from Proto-Germanic *halba- "something divided" (source also of Old Saxon halba, Old Norse halfr, Old Frisian, Middle Dutch half, German halb, Gothic halbs "half"), a word of no certain etymology. Perhaps from PIE root *skel- (1) "to cut," or perhaps a substratum word. Noun, adjective, and adverb all were in Old English.

Used also in Old English phrases, as in modern German, to mean "one half unit less than," for example þridda healf "two and a half," literally "half third." The construction in two and a half, etc., is first recorded c. 1200. Of time, in half past ten, etc., first attested 1750; in Scottish, the half often is prefixed to the following hour (as in German, halb elf = "ten thirty").

To go off half-cocked in the figurative sense "speak or act too hastily" (1833) is in allusion to firearms going off prematurely; half-cocked in a literal sense "with the cock lifted to the first catch, at which position the trigger does not act" is recorded by 1750. In 1770 it was noted as a synonym for "drunk." Bartlett ("Dictionary of Americanisms," 1848) writes that it was "a metaphorical expression borrowed from the language of sportsmen, and is applied to a person who attempts a thing in a hurry without due preparation, and consequently fails."

"mental capacity," Old English wit, witt, more commonly gewit "understanding, intellect, sense; knowledge, consciousness, conscience," from Proto-Germanic *wit- (source also of Old Saxon wit, Old Norse vit, Danish vid, Swedish vett, Old Frisian wit, Old High German wizzi "knowledge, understanding, intelligence, mind," German Witz "wit, witticism, joke," Gothic unwiti "ignorance"), from PIE root *weid- "to see," metaphorically "to know." Related to Old English witan "to know" (source of wit (v.)).

Meaning "ability to connect ideas and express them in an amusing way" is first recorded 1540s; that of "person of wit or learning" is from late 15c. For nuances of usage, see humor (n.). Witjar was old slang (18c.) for "head, skull." Witling (1690s) was "a pretender to wit."

A witty saying proves nothing. [Voltaire, Diner du Comte de Boulainvilliers]

Wit ought to be five or six degrees above the ideas that form the intelligence of an audience. [Stendhal, "Life of Henry Brulard"]