Etymology
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not (adv.)

negative particle, a word expressing negation, denial, refusal, or prohibition, mid-13c., unstressed variant of noht, naht "in no way" (see naught). As an interjection to negate what was said before or reveal it as sarcasm, it is attested by 1900, popularized 1989 by "Wayne's World" sketches on "Saturday Night Live" TV show.

Not, spoken with emphasis, often stands for the negation of a whole sentence referred to: as, I hope not (that is, I hope that the state of things you describe does not exist). [Century Dictionary, 1895]

To not know X from Y (one's ass from one's elbow, shit from Shinola, etc.) was a construction attested from c. 1930 in modern use; but compare Middle English not know an A from a windmill (c. 1400). Double negative construction not un- was derided by Orwell, but is persistent and ancient in English, popular with Milton and the Anglo-Saxon poets.

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have-not (n.)

"poor person," 1742, from have + not. Have in the sense of "one who 'has,' one of the wealthier class of persons" is from the same source. Earliest in translation of "Don Quixote:

'There are but two families in the world, as my grandmother used to say; "the Have's and the Have-not's," and she stuck to the former; and now-a-days, master Don Quixote, people are more inclined to feel the pulse of Have than of Know.' ["Don Quixote de la Mancha," transl. Charles Jarvis, London, 1742]
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forget-me-not (n.)
the flowering plant (Myosotis palustris), 1530s, translating Old French ne m'oubliez mye; in 15c. the flower was supposed to ensure that those wearing it should never be forgotten by their lovers. Similar loan-translations took the name into other languages: German Vergißmeinnicht, Swedish förgätmigej, Hungarian nefelejcs, Czech nezabudka.
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couldn't 
by 1670s, contraction of could + not.
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cannot (v.)
c. 1400, from can (v.1) + not. Old English expressed the notion by ne cunnan. The typical representation of the Scottish pronunciation is canna.
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whatnot (n.)
also what-not, 1530s, "anything," from what + not. Elliptical for "what may I not say," implying "everything else." As the name of a furniture item, first attested 1808, so named for the objects it is meant to hold.
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notwithstanding (prep.)

a negative present participle used as a quasi-preposition, originally and properly two words, late 14c., notwiþstondynge "in spite of, despite," from not + present participle of the verb withstand. It has the old "against" sense of with. A loan-translation of Medieval Latin non obstante "being no hindrance," literally "not standing in the way," from ablative of obstans, present participle of obstare "stand opposite to" (see obstacle). As an adverb, "nevertheless, however," and as a conjunction, "in spite of the fact that," from early 15c.

Notwithstanding ... calls attention with some emphasis to an obstacle: as, notwithstanding his youth, he made great progress. In spite of and despite, by the strength of the word spite, point primarily to active opposition: as, in spite of his utmost efforts, he was defeated; and, figuratively, to great obstacles of any kind: as, despite all hindrances, he arrived at the time appointed. [Century Dictionary]
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non- 

a prefix used freely in English and meaning "not, lack of," or "sham," giving a negative sense to any word, 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," from Old Latin noenum "not one" (*ne oinom, from PIE root *ne- "not" + PIE root *oi-no- "one, unique"). In some cases perhaps from Middle English non "not" (adj.), from Old English nan (see not). "It differs from un- in that it denotes mere negation or absence of the thing or quality, while un- often denotes the opposite of the thing or quality" [Century Dictionary].

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*ne- 
Proto-Indo-European root meaning "not."

It forms all or part of: a- (3) "not, without;" abnegate; ahimsa; an- (1) privative prefix; annihilate; annul; aught (n.2) "zero, nothing;" deny; hobnob; in- (1) "not, opposite of, without;" ixnay; naught; naughty; nay; nefarious; negate; neglect; negligee; negotiate; neither; nepenthe; nescience; nescient; neuter; never; nice; nihilism; nihility; nil; nill; nimiety; nix; no; non-; none; nonplus; nor; not; nothing; null; nullify; nulliparous; renegade; renege; un- (1) prefix of negation; willy-nilly.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit a-, an- "not;" Avestan na "not;" Greek a-, an-, ne- "not;" Latin in- "not," ne "that not;" Old Church Slavonic and Lithuanian ne "not;" Old Irish an-, ni, Cornish ny "not;" Gothic and Old English un- "not."
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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.

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