Grammar justification for 連用形 ＋ 係助詞「は」＋（ない・ある）


So recently I came across these two answers to two very interesting questions,
and related: [one](https://japanese.stackexchange.com/a/12641/2977) and
[two](https://japanese.stackexchange.com/a/19700/2977).

Both mention the following form:

> (連用形{れんようけい} of something) + (optional 係助詞{かかりじょし}) + (ない or ある)

I do understand the difference in nuance (between 悪くない vs 悪くはない, for example),
but I don't understand why it is acceptable grammatically.

Correct me if I'm wrong but は here emphasizes and contrasts 悪く, but what is
悪く, really? It translates into 'badly', which is an adverb that is usually
supposed to modify a verb or connect to another adjective. With that logic in
mind, the overall (literal) translation would be 'There is no badly', which is
just weird.

I feel like I'm missing something about conjugations they don't usually teach
you in textbook Japanese, which is why I'm after the historical reasoning
behind it.




As the other answers say, 悪く is a **連用形** ("continuative form") of 悪い. This
form can work as an adverb on its own, but here it's merely a form that
precedes ない. As a rule, whenever you want to use ない with an i-adjective, you
must use this 連用形 form. 悪くない just means "not bad".

For convenience, in some beginner materials, 悪くない is often described simply as
"negative-form / nai-form of i-adjectives," and 悪く as "adverb form", as if
they were totally different. You may be already familiar with these terms.
However, 悪くない is actually two words (i.e., the 連用形 of an adjective followed by
an auxiliary ない). That's why the contrast marker は can be inserted between 悪く
and ない. As you learn Japanese grammar (especially using monolingual
resources), you'll see the term 連用形 more and more often.

Unfortunately, one verb/adjective can have up to two 連用形. The 連用形 of 悪い are
`悪かっ` and `悪く` (see [this
chart](https://www.kokugobunpou.com/%E7%94%A8%E8%A8%80/%E5%BD%A2%E5%AE%B9%E8%A9%9E-2-%E6%B4%BB%E7%94%A8/)),
and the 連用形 of 書く are `書き` and `書い`. This is not a big problem for native
Japanese speakers, but can be a huge problem for learners. I think this is one
of the reasons the word 連用形 is not popular for beginners. See also: [Does "te-
form" of a verb always include て/で?
Why?](https://japanese.stackexchange.com/q/36310/5010).

