ar·gue / ˈärgyoō/ • v. (-gues, -gued, -gu·ing) 1. [tr.] give reasons or cite evidence in support of an idea, action, or theory, typically with the aim of persuading others to share one's view: defense attorneys argue that the police lacked “probable cause” to arrest the driver. ∎  (argue someone into/out of) persuade someone to do or not to do (something) by giving reasons: I tried to argue him out of it.2. [intr.] exchange or express diverging or opposite views, typically in a heated or angry way: don't argue with me. [tr.] she was too tired to argue the point. DERIVATIVES: ar·gu·er n.

argue XIV. (O)F. arguer :- L. argūtāre babble, f. arguere make clear, prove.
So argument XIV, argumentation XV.