A Semantics for Articles: I don't know if this is at all original or correct. Let me know what you think. Articles tell us whether the speaker is using a noun to refer to a class or an individual.
Ex 1. Joe yells at Sue, Sue cries, Jim white knights to her rescue and slaps Joe. Joe shrugs and says "A woman in tears is a powerful thing."
'A woman' refers to a class.
Ex 2. Sue gets angry at Joe for slapping Jim and says "The man is crazy."
'The man' refers to an individual.