Longman Dictionary of Contemporary English - argue

~ v 1 »DISAGREE« to disagree with someone in words, often in an angry way  (Did you hear the couple next door arguing last night?)  (I'm not going to argue with you, but I think you're wrong.) + abou  (They were arguing about how to spend the money.) + over  (The family argued bitterly over who should inherit the house. (=argue about something, especially about who should have something)) 2 »STATE« to state, giving clear reasons, that something is true, should be done etc  (a well-argued case | argue that)  (Croft argued that a date should be set for the withdrawal of troops. | argue for/against (=argue that something should or should not be done))  (You can argue against extending the airport on the grounds of cost. | argue the point (=discuss something))  (We could argue this point for hours without reaching any sensible conclusions.) 3 argue sb into/out of sth especially BrE to persuade someone to do or not do something  (Joyce argued me into buying a new jacket.) 4 »SHOW CLEARLY« formal to show that something clearly exists or is true  (The commissioner's statement argues a high level of police involvement.) 5 argue the toss BrE informal to continue to argue about a decision that has been made and cannot be changed  (How stupid of me to argue the toss with the traffic policeman.)