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On http://www.guidetojapanese.org/learn/grammar/should#part5, the author doesn't explain the etymology of べからず. Can anyone explain?

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Conjugation of べき

べき, or rather べし (kanji 可し), is an auxiliary adjective* just like for example 熱い.

However, it retains the classical conjugation of adjectives. 熱い had once been 熱【あつ】き, and there existed an additional form 熱【あつ】し. 熱き is used for modifying nouns (熱き炎), 熱し for ending sentences (炎は熱し).

In the classical conjugation, there existed an あり-form for each adjective: The verb ある (to be) joined with the adjective (in its 連用形-base/masu-form)**.

  • 熱き → 熱く+ある → 熱かる***
  • べき → べく+ある → べかる

Literally it meant to be [adjective], and it could now be modified further like any other verb, and be joined with some helper verbs etc. that required a verb.

Other than the adjective ない for negation, in classical Japanese you could negate verbs by adding the helper verb ず/ぬ. Some traces of this remain in modern Japanese in あらぬ疑い or in the shortened form せん (negation of する).

Like with ない, ず/ぬ is added to the 未然形-base:

  • 行く→行かない→行かず
  • ある→あらない→あらず

Thus:

  • 熱かる→熱からず
  • べかる→べからず

Finally, ず is both the 終止形 (for ending sentences) and 連用形 (for joining words/actions), while ぬ is the 連体形 (for modifying nouns).

Note that you can add ある again to form べからざる. This is often used to modify nouns (instead of べからぬ).

Examples:

  • 無用の者立ち入るべからず
  • 働かざる者食うべからず
  • 許すべからざる行為
  • この庭のいたづらに広きこと、あさましく、あるべからぬ事なり。 (from 徒然草, 第224段, modern: この家の庭はいたずらに広くて、みっともないものである。)

Further reading:


Notes

* As far as its conjugation is concerned, べし mostly behaves like any other i-adjective. However, note that its usage is rather odd, especially what remains in modern Japanese: you would expect adjectives to join to the 連用形 (such as 分かりやすい) - or perhaps to the 未然形 like ない. But in reality we have got forms such as 来るべき時.

** Sources for this etymology:

〔形容詞、または形容詞型に活用する助動詞「べし」「まじ」「ごとし」などの連用形語尾「く」に、動詞「あり」が付いた「くあり」のつづまったもの〕

  • A history of the Japanese language, by Bjarke Frellesvig (Cambridge University Press, 2010), p. 233, chapter 8.2.1 Secondary conjugations: ar- extended forms

In OJ the existential verb ar- was used with the infinitive of the adjectival copula (-ku), the regular copula (ni, to) and the negative auxiliary (-zu) to form analytic forms, and these combinations sometimes fused phonologically: ADJ-ku ar => ADJ-kar, [...] In EMJ [Early Middle Japanese] the fused forms gave rise to secondary conjugations, all of which belong to the r-irr conjugation and have the basic paradigm in Table 8.7. [eg. for adjectives: -kar, kara, kaQ-, kari, kari, karu, kare, kare]

*** This plain form is rarely used, because as mentioned, it is used mainly for more complex conjugations. See this question, the function of あり in i-adjectives. Occasionally, the plain form gets used: 「はしたなめ、煩はせ給ふ時もおほかり」(from 源氏物語, modern: (桐壺の更衣を)きまり悪い目にあわせ、苦しめ困らせなさるときも多い。)

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