Chap. 1 Ex 1.1 # 1&2

Whether to support or criticize beliefs we use arguments, quarrels, debate, and disputes.  They often are interchangeable but to me appear to be different levels of communicating a disagreement; different parts of an ‘argument’. People in everyday life often use these terms interchangeable because of definition overlap.  For example, an angry disagreement; do they have logical valid deferring statements or is it random?    After comparing the definitions I understand how confusing it can be, they are very similar.
Last year I took philosophy and learned the structure of an argument; the premise (reasons) and conclusion (belief or stand).  Which makes sense when you look at the Latin root(s)1 < clarity or make clear.  An argument doesn’t have to be negative in meaning such as a quarrel generally is, it could be used to support anthers view point or as a tool of persuasion.
A quarrel seems the furthest from a true argument with the Latin root 2< to complain.  It doesn’t seem to have a structure just a dispute or disagreement.  ‘The children quarreled who would be the first in line’, not having any valid reasons or statements, just disagreeing with the purpose of opposition. 
A dispute would be the next level in which it is a reason to debate or to question the truth or validity with the Latin root(s)3 < to examine, to reckons.  It doesn’t necessarily mean angrily but to engage in a discussion about a topic or belief.  It could lead to debate which comes next in line.
Most consider a debate a formal discussion with opposing points of beliefs.  It is not necessary angry but you need opposing points for a debate.  So a debate would be an argument with at least two differing sides.   The Latin root 4 < to beat would lend me to believe one side wanted to convince people their side is the correct side; ‘the politicians debated who would pay the most tax’.  
Content determines which of these words should be applied to a given situation.  But the flow of communication could turn a quarrel into an argument with a valid statement(s) and a conclusion.  ‘The children quarreled who would go first and reminded the teacher she was the line leader today.’  Content of evidence and delivery of information seem to help determine which word should be used to describe the situation.

Latin root, The American Heritage College Dictionary. 3^rd Ed. 1993. Print

1. pg 73, 2. pg 1118, 3. pg 401, 4. pg 357