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My first thought is that いかない in this phrase conveys the meaning of 行かない, that is, not progressing to something. But this is mere guesswork.

What is the history of いかない in ~わけにはいかない? Does it have roots in the verb 行く or is this way off base?

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I think this is more of a question of "How did いかない come to acquire meanings of impossible/prohibited/bad?" Because 〜わけにはいかない is like "It can't (not) be possible for that situation". –  istrasci Aug 26 '11 at 14:45
    
Not only that, the archaic いかぬ also has the meaning of ダメ, although いかない version is always used with わけには. –  syockit Aug 26 '11 at 17:17
    
I thought that was the question. I'm interested in where it came from and why it means what it does. I was merely guessing in the original question due to the same pronunciation. –  phirru Aug 26 '11 at 17:29
    
Great question! I always thought it was interesting that 「わけにはいかない」 uses the "regular" 「行く」 while 「なくてはいけない」 uses the potential form. To make matters worse, expressions like 「うまくいく to go well」 use the "regular" form strictly, so 「うまくいけた」would be incorrect, for instance. It seems like there are three イクs: the regular, volitional "I go" イク, the non volitional "it goes" イク, and the bastard child イケル, wherever that fits in. –  jefflovejapan Sep 7 '11 at 12:23
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3 Answers

EDICT shows the full thing as 「訳には行かない」, so I would venture to guess that the derivation from 「行く」's additional meanings of "to proceed" or "to take place" is correct.

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Personally, I understand that いかない just as 行かない and would take like "(It) won't go that way" for ~わけにはいかない.

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From what I gathered from reading Steven Pinker's The Stuff of Thought, humans evolved in a world with tangible physical objects and obvious physical actions, so almost all of our thinking is based in that reality.

As a result, most of what appears to be highly abstract thinking is actually built on our attempts to attach metaphors of tangible things and actions to intangible concepts.

Which is an academic way of getting around to the fact that I think you'll find the concept of "go", or 行く【い・く】, to most likely come to take on a meaning of "possibility" in a lot, if not all, languages.

In a tangible world, a ball can not go to another place if there is a wall between here and there. And so it follows that the abstract ball can not achieve its destination if a conceptual barrier prevents it. Resulting in an attachment of an idea can not become possible because it can not "go" there.

I believe what you are looking for, then is an origin of how 行く came to take on the meaning of "possible" in a Japanese context, but I think the reality is that it is more of a broader issue, and so you are unlikely to find an etymological explanation that is exclusive to Japanese.

The one thing I think can be said that is strictly defined in the realm of Japanese is that it is more common to see 行く written in kana, いく, when used in the more metaphorical sense, as in the phrase 訳にはいかない. Not a hard and fast rule by any means, but I believe that to be the case, because the kanji is tied too much to the literal "go".

Also, just as sort of "bonus reading", see this page for a bit of discussion in Japanese about how exactly 訳にはいかない is used. I hadn't really thought of it in opposition to したい, as one answer puts it.

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