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I understand the grammatical usage of these words, but I don't understand why they (roughly) mean "cannot" and "can".

For example, if we write them with kanji, we get 兼ねる and 兼ねない. According to jisho.org, that kanji has the following meanings: "concurrently, and, beforehand, in advance". None of these meanings directly corresponds to the meaning of "cannot" and "can", so why would that kanji be used?

Here's the research so far:

I'm trying to find an intuitive way to understand how this usage came to be, to better "feel" the intention of the word. Any help appreciated!

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First of all, the auxiliary-かねる, or かぬ in archaic Japanese, meaning "cannot", is almost never written with the kanji 兼 today. I personally have never seen something like 言い兼ねる, and I have believed the verb 兼ねる and the auxiliary-かねる are two different words.

Second, the history of auxiliary-かぬ is very old, and even 万葉集 has examples of it.

世間乎 宇之等夜佐之等 於母倍杼母 飛立可祢都 鳥尓之安良祢婆
(飛立可祢都 = とびたちかねつ = 飛び立てない)

This means it's almost impossible to trace the correct etymology of auxiliary-かねる. Still, there seems to be a few speculations:

  • Auxiliary-かねる may be etymologically related to 悲し(い) because they share the nuance of "that's beyond my control."
  • Auxiliary-かねる may be etymologically related to 予ぬ【かぬ】 because they share the nuance of "something bad is anticipated."
  • Auxiliary-かねる may be etymologically related to 兼ぬ because they share the meaning of "two situations happening simultaneously (i.e., ideal vs reality)". (This is 時代別国語大辞典's speculation, from here)

I have no idea how true these are, but I can at least say these are far from intuitive :)

Anyway, I think it's best to treat the auxiliary-かねる as something unrelated to 兼ねる meaning "to have more than one role."

Reference:

(EDIT: Added one more speculation regarding the etymology of auxiliary-かぬ, although I personally think it's the least convincing. Most 古語辞典 regard the two かぬ as two distinct words.)

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    Both versions of kaneru have the same kanu form in OJP. I note too that 兼ねる has senses of 遠慮する・気兼ねする, and the base sense of 二つ以上を合わせる、もつ could even apply in terms of "trying to do one thing, winding up with a different result". Also, Daijirin lists both the standalone and the auxiliary verb senses under the one 兼ねる heading, as visible as sense ⑥ (that's a 6) here. – Eiríkr Útlendi Aug 31 '18 at 18:05
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    @EiríkrÚtlendi And most 古語辞典 treat them as different words, which I feel is more reasonable. As a matter of fact, at least modern Japanese people almost never write the auxiliary-かねる using 兼 because this kanji appears clearly unsuitable. – naruto Aug 31 '18 at 19:14
  • Re: modern use, certainly. In fact, it seems to me that most auxiliaries are written in kana, even when kanji spellings are commonplace for the same verb in a non-auxiliary context (such as つく, etc.). I should have been more explicit -- I was replying to your comment that the two are unrelated. I think there's circumstantial evidence suggesting that these started as the same term and diverged in meaning and function, even while the forms are basically identical (for phonetics and conjugation). For modern JA, I agree that it's probably best to treat them as wholly separate. – Eiríkr Útlendi Aug 31 '18 at 19:28
  • I'm thinking of the opposite; there is very little evidence that these two かぬ are etymologically related. かぬ meaning "cannot" showed limited conjugation patterns (it was not used in 終止形), and it's categorized as a suffix in some 古語辞典. But, later in the history, they somehow "merged" at least in the dictionary (perhaps a kind of back-formation), and the kanji 兼 was "accidentally" assigned to かねる meaning "cannot". If かねる meaning "cannot" were really a verb directly related to 兼ねる, it should be more like a compound-verb element like 飛び付く or 仕込む, and it could be written in kanji. – naruto Aug 31 '18 at 20:35

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