Etymology
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neither (conj., adv.)

"not one or the other," Middle English neither, naither, nether, from Old English nawþer, contraction of nahwæþer, literally "not of two," from na "no" (from PIE root *ne- "not") + hwæþer "which of two" (see whether). Spelling altered c. 1200 by association with either. Paired with nor from c. 1300; earlier with ne. Meaning "not in any case, in no case, not at all" is from 1550s. Also used in late Old English as a pronoun. As an adjective, "not either," mid-14c.

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nor (conj.)

"and not," mid-13c., from ne (adv.) "no" + or (conj.), or else a contraction of Middle English nauther (see neither) and influenced in form by or. Generally correlative to neither or some other negative.

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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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*kwo- 
also *kwi-, Proto-Indo-European root, stem of relative and interrogative pronouns.

It forms all or part of: cheese (n.2) "a big thing;" cue (n.1) "stage direction;" either; hidalgo; how; kickshaw; neither; neuter; qua; quality; quandary; quantity; quasar; quasi; quasi-; query; quib; quibble; quiddity; quidnunc; quip; quodlibet; quondam; quorum; quote; quotidian; quotient; ubi; ubiquity; what; when; whence; where; whether; which; whither; who; whoever; whom; whose; why.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit kah "who, which;" Avestan ko, Hittite kuish "who;" Latin quis/quid "in what respect, to what extent; how, why," qua "where, which way," qui/quae/quod "who, which;" Lithuanian kas "who;" Old Church Slavonic kuto, Russian kto "who;" Old Irish ce, Welsh pwy "who;" Old English hwa, hwæt, hwær, etc.
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neuter (adj.)

late 14c., neutre, in grammar, of nouns, pronouns, etc., "neither masculine nor feminine in gender," also of verbs, "having middle or reflexive meaning, neither active nor passive," from Latin neuter "of the neuter gender," literally "neither one nor the other," from ne- "not, no" (from PIE root *ne- "not") + uter "either (of two)" (see whether). The Latin word is probably a loan-translation of Greek oudeteros "neither, neuter." From 1520s it also had the sense of "taking neither side" which now generally goes with neutral (adj.).

As a noun from mid-15c., "the neuter gender;" by 1797 of certain animals (among bees, ants, etc.) that are of neither sex and incapable of generation.

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indifferent (adj.)
late 14c., "unbiased, impartial, not preferring one to the other" (of persons), "alike, equal" (of things), from Old French indifferent "impartial" or directly from Latin indifferentem (nominative indifferens) "not differing, not particular, of no consequence, neither good nor evil," from in- "not, opposite of" (see in- (1)) + differens, present participle of differre "set apart" (see differ). Extended sense of "apathetic, no more inclined to one thing than to another" first recorded early 15c.; that of "neither good nor bad" is from 1530s, on notion of "neither more nor less advantageous," but since 17c. it has tended toward "rather bad."
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adiaphorous (adj.)
"indifferent, non-essential, morally neither right nor wrong," 1630s, from Greek adiaphoros "not different; indifferent," from a- "not" (see a- (3)) + diaphoros "different."
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so-so (adv.)
mid-15c., "moderately well," 1520s, "indifferently, neither too poorly nor too well," from so (adv.), which is attested from mid-13c. in the sense "in this state or condition." As an adjective, "mediocre, neither too good nor too bad," 1540s. So-and-so is from 1596 meaning "something unspecified;" first recorded 1897 as a euphemistic term of abuse. In 17c.-18c. So, so also could be colloquially a mere introductory phrase.
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neutral (adj.)

1540s, in alchemy, "composed of contrasting elements which, in proper proportion, neutralize each other," also, of states, rulers, etc., "refraining from taking sides in a fight, not engaged on or interfering with either side" (probably from a similar meaning of neutralis in Medieval Latin), from Latin neutralis, from neuter "neither the one nor the other, neither of two" (see neuter (adj.)).

By 1550s of persons. Chemistry sense of "exhibiting neither acid nor alkaline qualities" is from 1660s. From 1711 in the sense of "of or belonging to a power not taking sides in a war or conflict." Of colors, "of low chroma, without positive quality of color," from 1821. Neutral corner is from boxing (1908), indicating the two corners of the ring not used between rounds by the fighters and their seconds.

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undead (adj.)
"neither dead nor alive," c. 1400, from un- (1) "not" + dead. As a noun meaning "vampires and such," from 1904. Old English undeadlic (adv.) meant "immortal, for all eternity."
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