The Collaborative International Dictionary of English v.0.48:

Argue \Ar"gue\, v. t.
   1. To debate or discuss; to treat by reasoning; as, the
      counsel argued the cause before a full court; the cause
      was well argued.
      [1913 Webster]

   2. To prove or evince; too manifest or exhibit by inference,
      deduction, or reasoning.
      [1913 Webster]

            So many laws argue so many sins.      --Milton.
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   3. To persuade by reasons; as, to argue a man into a
      different opinion.
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   4. To blame; to accuse; to charge with. [Obs.]
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            Thoughts and expressions . . . which can be truly
            argued of obscenity, profaneness, or immorality.
                                                  --Dryden.
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   Syn: to reason; evince; discuss; debate; expostulate;
        remonstrate; controvert.

   Usage: To Argue, Dispute, Debate. These words, as here
          compared, suppose a contest between two parties in
          respect to some point at issue. To argue is to adduce
          arguments or reasons in support of one's cause or
          position. To dispute is to call in question or deny
          the statements or arguments of the opposing party. To
          debate is to strive for or against in a somewhat
          formal manner by arguments.
          [1913 Webster]

                Men of many words sometimes argue for the sake
                of talking; men of ready tongues frequently
                dispute for the sake of victory; men in public
                life often debate for the sake of opposing the
                ruling party, or from any other motive than the
                love of truth.                    --Crabb.
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                Unskilled to argue, in dispute yet loud,
                Bold without caution, without honors proud.
                                                  --Falconer.
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                Betwixt the dearest friends to raise debate.
                                                  --Dryden.
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The Collaborative International Dictionary of English v.0.48:

Argue \Ar"gue\, v. i. [imp. & p. p. Argued; p. pr. & vb. n.
   Arguing.] [OE. arguen, F. arguer, fr. L. argutare, freq. of
   arguere to make clear; from the same root as E. argent.]
   1. To invent and offer reasons to support or overthrow a
      proposition, opinion, or measure; to use arguments; to
      reason.
      [1913 Webster]

            I argue not
            Against Heaven's hand or will.        --Milton.
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   2. To contend in argument; to dispute; to reason; -- followed
      by with; as, you may argue with your friend without
      convincing him.
      [1913 Webster]

WordNet (r) 3.0 (2006):

argue
    v 1: present reasons and arguments [syn: argue, reason]
    2: have an argument about something [syn: argue, contend,
       debate, fence]
    3: give evidence of; "The evidence argues for your claim"; "The
       results indicate the need for more work" [syn: argue,
       indicate]

Moby Thesaurus II by Grady Ward, 1.0:

163 Moby Thesaurus words for "argue":
   affirm, agitate, allege, altercate, analyze, announce, annunciate,
   approve, argufy, assert, assever, asseverate, attest, aver, avouch,
   avow, balk, bandy words, be construed as, be indicative of,
   be significant of, be symptomatic of, bespeak, betoken, bicker,
   breathe, canvass, cavil, characterize, choplogic, claim, clash,
   conflict, connote, contend, contest, convince, cross swords,
   cut and thrust, debate, declare, defend, demonstrate, demur,
   denominate, denote, differ, differentiate, disaccord, disagree,
   discept, disclose, discuss, display, dispute, dissent, dissuade,
   entail, enunciate, establish, evidence, evince, exhibit,
   expostulate, express, fight, furnish evidence, give and take,
   give evidence, give indication of, give token, go to show, hassle,
   have, have it out, highlight, hint, hold, identify, illustrate,
   imply, import, indicate, insist, investigate, involve,
   issue a manifesto, jib, join issue, justify, lay down, lock horns,
   logomachize, maintain, manifest, manifesto, mark, mean, moot, note,
   object, persuade, pettifog, plead, point to, polemicize, polemize,
   predicate, prevail upon, proclaim, profess, pronounce, protest,
   prove, put, put it, quarrel, quibble, reason, refer to,
   remonstrate, reveal, review, row, say, scrap, set down, set forth,
   show, show signs of, sift, signalize, signify, spar, speak,
   speak for itself, speak out, speak up, speak volumes, spell,
   squabble, stand for, stand on, state, study, submit, suggest,
   symbolize, symptomatize, symptomize, take sides, talk, talk out of,
   tell, tend to show, testify, thrash out, try conclusions,
   ventilate, vindicate, warrant, witness, wrangle