Etymology
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carp (v.)

early 13c., "to talk, speak, tell," from Old Norse karpa "to brag," which is of unknown origin. The meaning turned toward "find fault with, complain," particularly without reason or petulantly (late 14c.) probably by influence of Latin carpere "to slander, revile," literally "to pluck" (which is from PIE root *kerp- "to gather, pluck, harvest"). Related: Carped; carping.

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blatant (adj.)

coined 1596 by Edmund Spenser in "The Faerie Queen," in blatant beast, a thousand-tongued monster representing slander; perhaps primarily an alliterative word, but perhaps suggested by Latin blatire "to babble." It entered general use by 1650s as "noisy in an offensive and vulgar way;" the sense of "obvious, glaringly conspicuous" is from 1889. Related: Blatantly; blatancy.

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lacerate (v.)

"to tear roughly," early 15c., from Latin laceratus, past participle of lacerare "tear to pieces, mangle," figuratively, "to slander, censure, abuse," from lacer "torn, mangled," from PIE root *lek- "to rend, tear" (source also of Greek lakis "tatter, rag," lakizein "to tear to pieces;" Latin lacinia "flap of a garment," lancinare "to pierce, stab;" Russian lochma "rag, tatter, scrap;" Albanian l'akur "naked"). Figurative sense in English is from 1640s. Related: Lacerated; lacerating.

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challenge (v.)
Origin and meaning of challenge

c. 1200, "to rebuke," from Old French chalongier "complain, protest; haggle, quibble," from Vulgar Latin *calumniare "to accuse falsely," from Latin calumniari "to accuse falsely, misrepresent, slander," from calumnia "trickery" (see calumny).

From late 13c. as "to object to, take exception to;" c. 1300 as "to accuse," especially "to accuse falsely," also "to call to account;" late 14c. as "to call to fight." Also used in Middle English with a sense of "claim, take to oneself." Related: Challenged; challenging.

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defamation (n.)
Origin and meaning of defamation

c. 1300, defamacioun, "disgrace, dishonor, ill repute" (senses now obsolete), from Old French diffamacion and directly from Medieval Latin deffamation, from Latin diffamationem (nominative diffamatio), noun of action from past-participle stem of diffamare "to spread abroad by ill report, make a scandal of," from dis-, here probably suggestive of ruination, + fama "a report, rumor" (from PIE root *bha- (2) "to speak, tell, say").

From late 14c. as "the wrong of injuring another's reputation without justification." From early 15c. as "calumny, slander, an instance of defaming."

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belie (v.)

Middle English bilien, "tell a lie about, accuse falsely, slander," from Old English beleogan "to deceive by lies," from be- + lie (v.1) "to lie, tell lies." The  sense of "to contradict as a lie, give the lie to, show to be false" is attested by 1640s.

The other verb lie once also had an identical variant form, from Old English belicgan, which meant "to encompass, beleaguer," and in Middle English (bilien) was a euphemism for "to have sex with" (i.e. "to lie with carnally").

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blaspheme (v.)

"to speak impiously or irreverently of God and sacred things," mid-14c., blasfemen, from Old French blasfemer "to blaspheme" (14c., Modern French blasphémer), from Church Latin blasphemare (which in Late Latin also meant "revile, reproach," hence blame (v.)), from Greek blasphēmein "to speak lightly or amiss of sacred things, to slander," from blasphēmos "evil-speaking" (see blasphemy).

A classical reintroduction in English after the original word, taken from vernacular Old French, had been worn down and sense-shifted to blame. Related: Blasphemed; blasphemer; blaspheming.

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challenge (n.)
Origin and meaning of challenge

early 14c., chalenge, "something one can be accused of, a fault, blemish;" mid-14c., "false accusation, malicious charge; accusation of wrong-doing," also "act of laying claim" (to something), from Anglo-French chalenge, Old French chalonge "calumny, slander; demand, opposition," in legal use, "accusation, claim, dispute," from Anglo-French chalengier, Old French chalongier "to accuse, to dispute" (see challenge (v.)). The accusatory connotations faded 17c. The meanings "an objection" in law, etc.; "a calling to fight" are from mid-15c. The sense of "difficult task" is by 1954.

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traduce (v.)

1530s, "alter, change over, transport," from Latin traducere "change over, convert," also "lead in parade, make a show of, dishonor, disgrace," originally "lead along or across, bring through, transfer" (source also of French traduire, Spanish traducir, Italian tradurre), from trans "across, beyond" (see trans-) + ducere "to lead" (from PIE root *deuk- "to lead"). Sense of "defame, slander" in English is from 1580s, from Latin traducere in the sense of "scorn or disgrace," a figurative use from the notion of "to lead along as a spectacle." Related: Traduced; traducing.

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*mel- (3)

Proto-Indo-European root meaning "false, bad, wrong." The exact sense of the root remains uncertain, "since it concerns a collection of largely isolated words in different IE branches" [de Vaan].

It forms all or part of: blame; blaspheme; blasphemous; blasphemy; ‌‌dismal; mal-; malady; malaise; malaria; malediction; malefactor; malefic; malevolence; malevolent; malice; malicious; malign; malison; malversation; mauvais.

It is the hypothetical source of/evidence for its existence is provided by: Avestan mairiia‑, "treacherous;" Greek meleos "idle; unhappy;" Latin male (adv.) "badly," malus (adj.) "bad, evil;" Old Irish mell "destruction;" Armenian mel "sin;" Lithuanian melas "lie," Latvian malds "mistake," possbily also Greek blasphemein "to slander." 

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