Why does 不甲斐{ふがい}ない mean "worthless" while 甲斐{かい} means "worth"?

Question

JMdict:

• 不甲斐{ふがい}ない: disappointing; weak-minded; spiritless; cowardly; worthless; pusillanimous; feckless; faint-hearted; shiftless; tame; timid
• 甲斐{かい}: effect; result; worth; use; avail

The word 不甲斐ない has both 不 and ない around 甲斐, and to my understanding the prefix 不- is used to negate words, just like ない. By this logic, the meaning of the word should be "not-worthless" instead of anything negative.

Of course language doesn't work that simply and there must be even bigger "illogicalities" out there that I've just gotten used to, but maybe there is a reason for this one.

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Edit: there is also the word [甲斐無い]{かいない} (worthless; pointless; useless​) as pointed out by @naruto in comments. Seems like this one works as I would expect.

Answer 1

不甲斐ない was originally 腑甲斐ない. 腑 is an uncommon kanji meaning "gut." According to this article, 腑甲斐ない was much more commonly used by novelists in the Meiji and Taisho periods. According to this chiebukuro question, the first edition of 広辞苑, one of the most authoritative Japanese dictionaries, had only 腑甲斐ない as the kanji for ふがいない.

For some reason 不甲斐ない came into use and somehow overtook 腑甲斐ない during the Showa period. Many sites believe this was basically a misuse. Every so often controversial usages of words may become acceptable gradually over time...

BTW there are similar word pairs where ない doesn't appear to change the meaning, for example せわしい/せわしない, いたいけな/いたいけない, 危険極まる/危険極まりない. See the following article for details. I initially thought 不甲斐ない was also an example of this, but the case of 不甲斐ない seems to be another story.

• 国立国語研究所 ことばQ&A 「せわしない」はどうして「ない」がついても「せわしい」と同じ意味になるのでしょうか。