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English "counters" are in some way worse because they aren't consistent. Slice of bread, slice of cheese but not slice paper.

To be fair, Japanese has "everday use" counters and "trivia TV show" counters.

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Not going to defend the consistency of English for a second but for that particular example: paper isn’t sliced, so it wouldn’t make sense to refer to “a slice of paper”.

Obviously the standard usage of a “piece of paper” is pretty arbitrary, but slice is clearly wrong.

On the other hand, all 3 of those can be used with "piece of". Slice describes something that was done to it, and sheet describes its form. (As opposed to scrap or some such term.)

I don't see how that's inconsistent. Slice is used to describe things that are cut from a larger whole, particularly for food, while paper is manufactured as sheets.

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