Etymology
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vindication (n.)

late 15c., "act of avenging, revenge," from Old French vindicacion "vengeance, revenge" and directly from Latin vindicationem (nominative vindicatio) "act of claiming or avenging," noun of action from past participle stem of vindicare "lay claim to, assert; claim for freedom, set free; protect, defend; avenge" (related to vindicta "revenge"), probably from vim dicare "to show authority," from vim, accusative of vis "force" (see vim) + dicare "to proclaim" (from PIE root *deik- "to show," also "pronounce solemnly," and see diction). Meaning "justification by proof, defense against censure" is attested from 1640s.

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venge (v.)
"avenge," c. 1300, from Old French vengier "revenge, avenge, punish," from Latin vindicare "avenge, vindicate" (see vindication). Related: Venged; venging.
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vendetta (n.)
"a private war in which a kinsman wreaks vengeance on the slayer of a relative," 1846, from Italian vendetta "a feud, blood feud," from Latin vindicta "vengeance, revenge" (see vindication). Especially associated with Corsica.
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vindictive (adj.)
1610s, "vengeful," from Latin vindicta "revenge" (see vindication) + -ive; or perhaps a shortening of vindicative based on the Latin word. From 1620s as "punitive, retributive," rather than personally vengeful or deliberately cruel. Related: Vindictively.
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Deo vindice 

Latin, "(with) God (as our) defender," national motto of the Confederate States of America, from ablative of Deus "God" (see Zeus) + ablative of present participle of  vindicare "to liberate; to act as avenger; protect, defend" (see vindication).

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vindicate (v.)
1620s, "to avenge or revenge," from Latin vindicatus, past participle of vindicare "to stake a claim; to liberate; to act as avenger" (see vindication). Meaning "to clear from censure or doubt, by means of demonstration" is recorded from 1630s. Related: Vindicated, vindicating.
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avenge (v.)
"vindicate by inflicting pain or evil on the wrongdoer," late 14c., from Anglo-French avenger, Old French avengier, from a- "to" (see ad-) + vengier "take revenge" (Modern French venger), from Latin vindicare "to claim, avenge, punish" (see vindication). See revenge (v.) for distinction of use. Related: Avenged; avenging. As a noun to go with it, 16c. English tried avenge, avengeance, avengement, avenging.
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revenge (v.)

late 14c., revengen, "avenge oneself," from Old French revengier, revenger, variants of revenchier "take revenge, avenge" (13c., Modern French revancher), from re-, here perhaps an intensive prefix (see re-), + vengier "take revenge," from Latin vindicare "to lay claim to, avenge, punish" (see vindication). Transitive sense of "take vengeance on account of" is from early 15c. Related: Revenged; revenging; revengement.

To avenge is "to get revenge" or "to take vengeance"; it suggests the administration of just punishment for a criminal or immoral act. Revenge seems to stress the idea of retaliation a bit more strongly and implies real hatred as its motivation. ["The Columbia Guide to Standard American English," 1993]
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exculpation (n.)

"the act of exonerating from a charge of fault or crime; vindication," 1715, noun of action from exculpate.

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theodicy (n.)
"vindication of divine justice," 1771, from French théodicée, title of a 1710 work by Leibniz to prove the justice of God in a world with much moral and physical evil, from Greek theos "god" (from PIE root *dhes-, forming words for religious concepts) + dike "custom, usage; justice, right; court case" (see Eurydice). Related: Theodicean.
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