Specific articles are used with nouns which have been identified previously. (The speaker and the listener both know which thing/person/substance/idea is being referred to.)
The teacher is coming up the stairs.
(Both listener and speaker know which teacher and which stairs.)
Give me the red shirt. (I know which one you are talking about.)
Non-specific articles are used with nouns that have not been identified previously (by both the speaker and the listener.) They are used with items that have not been singled-out yet. (Note: As soon as the items are identified, they require a specific article.)
I want a candy bar. (Any candy bar will do.)
Which one do you want? (Asking for specification)
The one on the right. (I choose that one.)
Give me some milk. (Any milk is fine.)
I need some new shoes. (But I haven't decided which ones to buy yet.)
I bought some shoes at Valmart. (I know which shoes, but you don't.)
These are the shoes that I bought. (Now we both know which ones.)
Non-count and plural nouns are used without articles in the generic sense.
Cats are afraid of dogs. (in general)
Water is necessary for survival.
*However, singular count nouns cannot stand alone in a sentence, so an article (usually a or an) is used.
Oranges contain Vitamin C. (generally)
Orange contains Vitamin C. (incorrect)
An orange contains Vitamin C. (okay)
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