Here's a language puzzle a friend posed to me and I posed to Scott: You have an apple. Imagine it sitting on the table in front of you. Now, you hit it with a hammer once. Is it still an apple? (Most listeners say "yes".) Then you hit it hundreds of times until it's all over the table. Is it still an apple? (Most listeners say "no," Scott says, "no, then it's just apple.")
The puzzle is supposed to interrogate the point at which something loses identity, but we became fascinated with the fact that this whole distinction can be encapsulated by the difference between "an apple," "the apple," and "apple."
I've just encountered tips for ESL speakers page that explains it this way: the indefinite articles (a, an) are only appropriate if the noun in question is "countable." As in "I had three apples, now I only have an apple." But "apple" is uncountable because it's just the material, and not any sort of totality. Consider the distinction between "glass" and "a glass," or between some bodily materials ("crap," others that shall remain nameless) and their countable counterparts. I learned from the above site that some nouns are considered countable in some languages and not in others, and I think this is evidence for the fact that the distinction between "apple" and "an apple" is more conventional than natural.
Additionally, we've had some great laughs totalizing and de-totalizing common nouns, like: "ugh, who got phone all over the place!?" "hold on, i've got a sand in my eye" "would you pass me a celery?" "eww, i'm covered in chair!" (It's more fun than you'd think! Feel free to send us your results.)
Finally, we noticed that the definite article doesn't bow to the totalized/untotalized distinction. "The apple is on the table" can mean either "an apple is on the table, and we both know which apple it is" or "there's apple on the table, and we both know which apple mush i'm talking about." Either way, use of the definite article is not licensed by any quality, such as countablility, of the noun, but by the speaker's and listener's shared knowledge of the noun in question.