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As an English learner(I'm Chinese), I've always been confused by the concept of countable and uncountable nouns.

For example, I totally understand why "water" is uncountable, but why does “paper” also uncountable? I mean water can't be counted, yet by all means I think "paper” is indeed countable.

Though I wouldn't argue that when "paper” is used to describe the material on which we write in general, it is uncountable, a mass noun, yet I still think it can be count when we specify it to one piece, two pieces... like the specific page in a book.

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    The literal answer to how native speakers (learn to) distinguish them is by hearing them used. So if you are five years old and you hear your teacher say "here's a piece of paper", you're going to learn (maybe not immediately) that you can't just say "here's a paper". – legatrix Dec 13 '20 at 12:09
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    There is no strict logical reasoning for which nouns are countable and which are not. There are only tendencies (as you have understood for 'water'). But the language itself doesn't force any nouns to be countable or not---you can see this from the fact that people often say "I'll have a coffee" or "I'll have a beer", depite the fact that coffee and beer are often taught in introductory grammar as uncountable. – legatrix Dec 13 '20 at 12:12
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    Actually, you can see the arbitrariness of what is countable and uncountable if you look at Classical Chinese and modern Mandarin. In CC you could say 一樹 but now you have to use a counter, 一顆樹 (I think this is accurate, anyway). But presumably the trees are the same! – legatrix Dec 13 '20 at 12:15
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We distinguish between them in much the same way that a French speaker distinguishes between masculine and feminine. They are learned. As with real grammatical gender in French, sometimes it is easy to guess whether a noun is countable or not. It is easy to guess that "femme" is a feminine word, just as it is easy to guess that "water" is (usually) uncountable. But in other cases it just has to be learned: "chip" is countable, "rice" is uncountable. "Bread" is non-count, but "loaf" is countable.

However being countable or not is not a proper gender system, because many nouns can be used as both count or non-count with a change in meaning. "A paper" means "a short report, usually scientific" (and it doesn't mean a leaf of paper in book). On the other hand, "paper" is the substance that is written on, and substances are normally non-count. Similarly "A water" is a single serving of water, whereas "water" is the substance that is drunk.

When a word has a basic meaning of "type of substance" it is non-countable. The countable form often means a specific form and not just any countable piece of that substance. So "a glass" is a cup made from glass, and not just a sheet of glass. There is no way to guess that "a glass" means a type of cup. You just have to learn it.

In the same way, you just learn that "a paper" means "a scientific report" and not any piece of paper.

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