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Why are counters (助数詞) necessary to describe the numerical quantity of objects
in Japanese?

I'm interested in the linguistic explanation specifically, but also curious as
to how strict those who are fluent tend to be about it in colloquial
conversation.
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counters comparative-linguistics
Why are counters necessary to describe the quantity of objects?
Counters aren't necessary any more in Japanese than gendered nouns are in
romance languages, e.g. _la_ vache vs. _le_ chat.

English has something extremely similar to counters called [Collective
Nouns](http://users.tinyonline.co.uk/gswithenbank/collnoun.htm). When you see
several fish, you call it a "school of fish". You wouldn't say a "school of
wolves", you'd say a "pack of wolves".

Are these necessary? Anyone could just say a "group of fish/wolves", but it
simply wouldn't sound right to our ears. That's the same way it works in
Japanese, to say 一枚のペン simply wouldn't sound right, even though you could
easily say 一つのペン.
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Adding to @bcioutier's great answer, it is somewhat wrong to assume there are
counters only in Japanese or there are no counters in English as @Eiríkr
Útlendi commented. I am not saying you are assuming so.

English uses a couple to indicate two. And there are a half a dozen to mean
six, a dozen for twelve, a score for 20, a gross (12 dozens) for 144, etc.

There are also special words for people using prefixes for each number.

> Soloist, duet, trio, quartet, quintet, sextet, septet, octet.

Your question,

> Why are counters (助数詞) necessary to describe the numerical quantity of
> objects in Japanese?

Japanese needs counters to describe quantity of objects, some are complicated,
some are not. But that's the way the language has evolved for thousands of
years as English has on its own way. If someone asks why English uses _duet_
and _trio_ instead of just 'two people' and 'three people', you will answer
because they have specific meaning to indicate the number of people in music
or entertainment.

> how strict those who are fluent tend to be about it in colloquial
> conversation.

It will depend on each native speaker. There are some counters which are
strictly followed and some are not.

For more information, you can read the link on [Words for numbers in
English](http://gwydir.demon.co.uk/jo/numbers/words/intro.htm) and [Japanese
counter word](https://en.wikipedia.org/wiki/Japanese_counter_word).
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Counter words are not necessary, but many languages do use them. My favourite
counter in English for illustrative purposes is "sheet(s)", as in "two sheets
of paper". With other counters like "two _bottles_ of beer", you can sometimes
get away with "two beers", but "two papers" doesn't mean "two sheets of paper"
(although it can now mean "two publications").

While in English counter words
("[classifiers](https://en.wikipedia.org/wiki/Classifier_\(linguistics\))")
are usually only used for [mass
nouns](https://en.wikipedia.org/wiki/Mass_nouns) (i.e. things where it is
unclear what "one [thing]" is), in Japanese counting items/people/days/etc. is
_always_ done using [Japanese counter
words](https://en.wikipedia.org/wiki/Japanese_counter_word). (One could say
that Japanese has no [count nouns](https://en.wikipedia.org/wiki/Count_noun),
so that all nouns are mass nouns/non-count nouns.)

There is some level of flexibility in what counter to choose for which item.
For checking which counter to use, one can consult
[数え方の辞典](https://www.shogakukan.co.jp/books/09505201), which gives explanatory
notes to each counter, e.g.

> **かみ** 【紙】
>
> **枚【まい】、葉【よう】、本、ロール、巻き【まき】、片【ひら】、束【たば】**
>
>
> 「葉【よう】」は葉【は】のように手に取ることができる程度の大きさで、折りたたまれていない紙を数える語です。FAX紙のようなひと巻きの紙は「本」「ロール」「巻き」で数えます。「片」はメモ用紙や紙切れ、紙吹雪などを数える語です。束ねたものは「束」で数えます。
>
> **帖【じょう】、締め【しめ】、連【れん】、丸【まる】**
>
>
> 小売単位は「帖」を用います。半紙20枚、美濃紙【みのがみ】は48枚で「1帖」です。和紙2000枚を「ひと締め」、洋紙1000枚を「1連」といいます。「丸」は、和紙の取引単位です。

Just like we have to use a counter for paper in English. Roughly corresponding
to the above, we have

> a **sheet** of paper, a **scrap** of paper, a **piece** of paper, a **roll**
> of paper
>
> a **ream** of paper, one
> [**quire**](https://en.wikipedia.org/wiki/Units_of_paper_quantity) of paper,
> one **bale** of paper, etc.
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