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Inspired by a recent question about the proper way to write 生きがい, I wanted to ask a long-standing question.

According to Kotobank, 甲斐 has the following definitions (my poor translations follow):

かい

  1. An old Japanese state, lying within modern Yamanashi.
  2. A city in western Yamanashi.

がい

  1. When attached to the ren'youkei, expresses the effect, value or worth of the action.
  2. When attached to a noun, expresses that something commands a quality appropriate to that thing.
  3. When attached to a phrase that expresses a negation, expresses the extent to which it is fortunate that it is not so.
  4. When attached to a phrase that expresses a wish or desire, expresses the desire to do it as much as one pleases.

I do see the semantic relationship between the four senses of がい — all relate to a sense of worthiness or appropriateness — but why were these kanji, which relate to a place name of all things, applied to this concept?

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    They may well not -- as in 寿司, ateji are often completely arbitrary. However there are often reasons for the choice. In 寿司, for instance, the characters have vaguely positive connotations. I tentatively rule out the possibility that 甲斐 is used purely for its phonetic value, as there are many words in basic vocabulary with that reading. So why those characters? – jogloran Nov 15 '14 at 8:13
  • Actually, I may be completely wrong in this case. If this page has any validity: oshiete.goo.ne.jp/qa/576294.html – virmaior Nov 15 '14 at 8:19
  • Right, I see. It's possible that the suffix came first and the placename came after. However with the initial 連濁 in the suffix, I would suggest either the two words are unrelated, or the placename came first and then somehow became a suffix. – jogloran Nov 15 '14 at 8:21
  • @virmaior: Fascinating, I thought it might have been something to do with 貝. If the page is correct, then 甲斐 is completely arbitrary but the suffix is connected with the verb 交う (the exchange of goods, implying value or worth). – jogloran Nov 15 '14 at 8:25
  • @virmaior -- I was following along that oshiete poster's logic right until the end: "もっとももともとの日本語の意味は、『「か」・・・仮の、「ひ」・・・中心』です。" Shogakukan's 国語大辞典 also lists the かひ>かふ derivation. If this kahi is from a verb, then the poster's comment about monosyllabic ka + hi as a noun compound is way off the mark -- the hi is simply the 連用形【れんようけい】 (and nominal) ending of the verb kafu. And, FWIW, the only thing I can find about the kanji has to do with the placename, and even then, I've not yet found any derivation or reasoning for this spelling. – Eiríkr Útlendi Nov 15 '14 at 22:37
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In the first place, -がい is the rendaku form of an independent noun かい, which is defined under デジタル大辞泉 section of the Kotobank page you cited (I don't understand why 大辞林 第三版 section is missing this definition for かい).

This かい (from archaic かひ) is, according to 小学館's 日本語源大辞典 which I own, a nominalization of archaic verb かふ "to substitute, compensate" (corresponds to modern [代]{か}える). This usage is found as early as in [万葉集]{まんようしゅう}, the oldest poem anthology from the 8th century.

On the other hand, the geographical かい is, the same dictionary says, supposedly derived from archaic かひ "a canyon, gorge". This word is found in 万葉集 too.

So, etymologically speaking, these two words have nothing to do with each other at all. This is a plain ateji case, though I don't know which definition first used the kanji 甲斐.

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