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So far I don't see any logic to it. It seems like it's just something you have to memorize, or is there a trick that I'm missing.

Update

To clarify, I'm not so much questioning the existence of the counter words, simply wondering how you determine which ones to use and when. Having followed the advice of reading the wikipedia article I see that they are in fact words with their own meaning and not just simple suffixes. It was much more confusing to think of them as suffixes because it was baffling to imagine why a concise language like japanese would need so many different counting suffixes.

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The Wikipedia article categorizes them quite well. You might want to ask a more specific question. –  Jesse Good May 21 '12 at 6:52
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Agree, this question is a little vague. What do you want to know the logic of? Why certain words use certain counters? The kanji (if any) of the counters? Why the counter for 3 usually has 濁音? –  istrasci May 21 '12 at 15:06
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>a concise language like japanese-- ??え、そうなん? –  Chocolate May 22 '12 at 13:48
    
Does it really seem that strange for a language to have things you just have to memorize? –  Ataraxia Sep 15 '12 at 17:31
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The believe that one language is more concise than another is an absolute myth. Every language is equally expressive, the fact that some indigenous language doesn't have words for "millisecond" or "cell-phone" is a cultural particular, not a deficit of language as matter of some sort of innate difference in linguistic structure. If you don't believe me, just think about it and try to formulate it more technically or at least make a verifiable claim. I think you'll find it a vacuous assertion. –  taylor Sep 21 '12 at 2:13
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4 Answers

Are you familiar with hito, futa, mi, yo, itsu, mu, nana, ya, kokono? They appear in the counter words for objects (eg hitotsu, futatsu), and in some counter words for people (hitori, futari, ..., yonin), and in some of the days of the month (the second day of the month being futsuka).

Edit: My understanding is that ichi, ni, san, shi, ... are Chinese words for the numbers, and that hito, futa, mi, yo, itsu, are the Japanese words for the numbers. Sometimes the Japanese use Chinese words for numbers in the counters, and sometimes they use the Japanese words. They tend to use the Japanese words more often when it comes to numbers containing 4 or 7, because of superstition. I think (but have no evidence for this) that hito and futa in hitori and futari because, well, one person and two people are special, and they don't want to replace their Japanese words for it with Chinese words.

And then there's the more or less constant part at the end of a counter. Sometimes it's constant, such as "ji" in hours of the day, and sometimes it varies slightly because of pronunciation, such as "fun" and "pun" in the counter words for minutes.

Once I realized that there was a number part and a more or less constant part in counter words, I found them easier to memorize, and a bit more logical.

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I was only familiar with yo and nana. –  Christian Schlensker May 21 '12 at 17:46
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I believe the question you're trying to ask is "why are there counter words in Japanese?" (or perhaps "why do I have to learn all these counter words?"). It does seem kind of strange coming from English, where you can just say a number, to where you have to start using a number plus different words depending on the size/shape/other characteristic of an object in order to count them. I, too, once thought as you do.

Is there a logic as to why there are counter words in Japanese? I would say no more or less so than any other part of any language. It's just a rule, like everything else. I will say this though: It's actually not as confusing as it first seems to be. Once you get used to how counter words are used, and you learn the basic ones, it just makes sense to use them in Japanese. You'll learn more as you go, and just generally get a feel for it. At least in my experience. You'll get to the point where if you're trying to say "two" when referring to a couple sheets of paper, and you say "ni", it sounds empty and wrong. It's "ni-mai".

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Can someone explain why this was down-voted? I'll gladly clarify anything that was wrong or misleading. –  silvermaple May 26 '12 at 15:18
    
Why does it seem "strange coming from English"? English has counters (aka. classifiers/measure words) too, they just aren't used with all nouns (countable vs. uncountable nouns). For example, you can't say "three musics", it would be "three pieces of music". If anything, it makes more sense in Japanese to not have that distinction. –  一二三 Dec 11 '12 at 13:28
    
@一二三: Of course you have to clarify in English if you're saying the thing you're counting...I'm not sure how to explain that properly, but take for example if I asked you "How many pieces of music are you playing at tonight's concert?" and you said "Four", that would be a completely acceptable exchange. That's not so in Japanese. I think we don't say "three musics" because that could be "three types of music" and "three pieces of music", and both Japanese and English have to distinguish there too...But if it's already stated in English, it is understood, and doesn't have to be repeated. –  silvermaple Dec 11 '12 at 18:40
    
But not all nouns in English require this classifier, only those that are mass nouns/uncountable nouns do. My point is that in Japanese, all nouns are effectively uncountable and require a counter. –  一二三 Dec 12 '12 at 0:05
    
@一二三: Yes, that's my point, so I guess I don't understand your confusion :( –  silvermaple Dec 12 '12 at 1:25
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My understanding was that originally Japanese only had the -tu and -ri endings for things and people respectively. Thus, pitotu, putatu, mitu (modern hitotsu, futatsu, mitsu) and pitori putari etc. These are attested in very old works when on'yomi had not yet become an integral part of the Japanese language and were used much like garaigo is used now.

Chinese has a very messy and complicated counter system. For example, when talking about animals 匹 is used for horses, donkeys, and mules (or similarly shaped animals, like llemas), 头 for oxen, sheep, and pigs, 条 for dogs and snakes only, and 只 for all other animals.

In the case of the animal counters Japanese seems to have only borrowed 匹. 匹 is pronounced /pi/ in Modern Chinese and /pik/ in Middle Chinese. Old Japanese borrowed it as /pikï/ which turned into /piki/ and then conditionally into /fiki/ and finally /hiki/ due to sound changes.

As for other counters, Japanese sporadically borrowed Chinese counters (using on'yomi readings) and changed their meanings to make them more logical. For example the counter 枚 (/mei/ in Chinese) in Chinese randomly refers to things like cookies, pens, bombs, CDs, and other things that cannot be reliably placed in a well-defined category. 本 (/ben/, MC /pon/) is a counter for pamphlets and books but not sheets of paper. Japanese redefined the first as referring to flat things and the latter to long thin things.

Basically, from what I know Japanese counters used with on'yomi numbers (ichi ni san etc) are generally counters borrowed from Chinese but repurposed to often quite distant meanings.

Edit: Old Japanese did not use counters the same way and the -tu and -ri were rather a shorthand for the noun. "pitotu" would mean literally "one thing" without having a noun after it, just as "hitori" means "one person" still in modern Japanese. OJ would have 一年(ひととせ) rather than the direct modern translation 一つの年(ひとつのとし)

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These answers have a lot of circumlocution around your actual question, which seemed to simply want a yes/no:

No, while counting itself has rules with decent regularity, there is not a formalized system for which counters to use. The only "logic" is each independent rule used to pick the right counter, and they often have contradictions: 本 for pencils and trains ("long thin objects"), but 匹 for snakes and 冊 for books.

You'll have to memorize and practice them, just like English learners with the difference between a "murder of crows" and "fleet of submarines." (Yes, that's not exactly the same thing, but it is a set of "counting words" with no logical system uniting them)

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