1550s, from un- (1) "not" + past participle of finish (v.).
Entries linking to unfinished
un- 1
prefix of negation, Old English un-, from Proto-Germanic *un- (source also of Old Saxon, Old Frisian, Old High German, German un-, Gothic un-, Dutch on-), from PIE *n- (source of Sanskrit a-, an- "not," Greek a-, an-, Old Irish an-, Latin in-), combining form of PIE root *ne- "not." Often euphemistic (such as untruth for "lie").
The most prolific of English prefixes, freely and widely used in Old English, where it forms more than 1,000 compounds. It underwent a mass extinction in early Middle English, but emerged with renewed vigor 16c. to form compounds with native and imported words. It disputes with Latin-derived cognate in- (1) the right to form the negation of certain words (indigestable/undigestable, etc.), and though both might be deployed in cooperation to indicate shades of meaning (unfamous/infamous), typically they are not.
It also makes words from phrases (such as uncalled-for, c. 1600; undreamed-of, 1630s; uncome-at-able, 1690s; unputdownable, 1947, of a book; un-in-one-breath-utterable, Ben Jonson; etc., but the habit is not restricted to un-; such as put-up-able-with, 1812). As a prefix in telegramese to replace not and save the cost of a word, it is attested by 1936.
finish v.
late 14c., "to bring to an end;" mid-15c., "to come to an end" (intransitive), from Old French finiss-, present participle stem of fenir "stop, finish, come to an end; die" (13c.), from Latin finire "to limit, set bounds; put an end to; come to an end," from finis "that which divides, a boundary, border," figuratively "a limit, an end, close, conclusion; an extremity, highest point; greatest degree," which is of unknown origin, perhaps related to figere "to fasten, fix" (see fix (v.)). Meaning "to kill, terminate the existence of" is from 1755.