1550s, "not having necessary qualifications, from un- (1) "not" + past participle of qualify (v.). Meaning "not modified or limited" is recorded from 1796. As a verb, unqualify "disqualify" is from 1650s.
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.
mid-15c., qualifien, transitive, "to invest with (a quality), impart a certain quality to," from French qualifier (15c.) and directly from Medieval Latin qualificare "attribute a quality to; make of a certain quality," from Latin qualis "of what sort?," correlative pronominal adjective (see quality) + combining form of facere "to make" (from PIE root *dhe- "to set, put").
Meaning "to limit, modify by a limitation or reservation, restrict" is from 1530s, as is the sense of "to have or have taken the necessary steps for rendering oneself capable of holding an office, etc." The sense of "to be or become fit for an employment, office, etc." is by 1580s. Related: Qualified; qualifying.
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Definitions of unqualified from WordNet
not limited or restricted;
an unqualified denial
not meeting the proper standards and requirements and training;
having no right or entitlement;
legally not qualified or sufficient;
a wife is usually considered unqualified to testify against her husband