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.
      [1913 Webster]

   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):

arguing
    n 1: a contentious speech act; a dispute where there is strong
         disagreement; "they were involved in a violent argument"
         [syn: controversy, contention, contestation,
         disputation, disceptation, tilt, argument,
         arguing]