Etymology
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argue (v.)
c. 1300, "to make reasoned statements to prove or refute a proposition," from Old French arguer "maintain an opinion or view; harry, reproach, accuse, blame" (12c.), ultimately from Latin arguere "make clear, make known, prove, declare, demonstrate," from PIE *argu-yo-, suffixed form of root *arg- "to shine; white." The transmission to French might be via arguere in a Medieval Latin sense of "to argue," or from Latin argutare "to prattle, prate," frequentative of arguere.

De Vaan says arguere is probably "a denominative verb 'to make bright, enlighten' to an adj. *argu- 'bright' as continued in argutus and outside Italic." He cites a closely similar formation in Hittite arkuuae- "to make a plea." Meaning "to oppose, dispute, contend in argument" is from late 14c. Related: Argued; arguing.
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arguable (adj.)
"capable of being argued," 1610s, from argue + -able.
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arguer (n.)
late 14c., agent noun from argue (v.).
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arguendo 
"in the course of argument," 1817, courtroom Latin, from Medieval Latin ablative of arguendum, gerundive of arguere "to argue" (see argue).
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argufy (v.)
"to argue for the sake of controversy, wrangle, worry with arguments," 1751, colloquial, from argue + -fy. Compare speechify.
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argle (v.)
1580s "to argue obstinately, wrangle," "prob. a popular perversion of argue, or confusion of that word with haggle" [OED]. Reduplicated form argle-bargle is from 1822 (sometimes argy-bargy, 1857); As a noun, "wrangling" from 1861.
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argument (n.)
early 14c., "statements and reasoning in support of a proposition or causing belief in a doubtful matter," from Old French arguement "reasoning, opinion; accusation, charge" (13c.), from Latin argumentum "a logical argument; evidence, ground, support, proof," from arguere "make clear, make known, prove" (see argue). Sense passed through "subject of contention" (1590s) to "a quarrel" (by 1911), a sense formerly attached to argumentation.
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*arg- 
Proto-Indo-European root meaning "to shine; white," hence "silver" as the shining or white metal.

It forms all or part of: argent; Argentina; argentine; Argo; argue; Argus; hydrargyrum; litharge.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit rajata-, Avestan erezata-, Old Persian ardata-, Armenian arcat, Greek arguron, Latin argentum, Old Irish argat, Breton arc'hant "silver;" Sanskrit arjuna- "white, shining;" Hittite harki- "white;" Greek argos "white."
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moot (v.)

"to debate, argue for and against" (mid-14c.), from Old English motian "to meet, talk, discuss, argue, plead," from mot "meeting" (see moot (n.)). Meaning "raise or bring forward for discussion" is from 1680s. Related: Mooted; mooting.

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scrap (v.2)

"to fight, brawl, box," 1867, colloquial, from scrap (n.2). Intransitive sense of "argue heatedly, quarrel" is by 1895. Related: Scrapped; scrapping.

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