Lesson 34: Not wanting with まい and permission with いい, ますか/ませんか
"Negative volition" means basically "determined not to X". There are several ways to express this in japanese. Most of them are phrased literally and you can figure them out with a dictionary, but まい deserves direct explanation.
まい is kind of a modern writing thing. Being modern means it shows in speech.
まい normally acts like some kind of auxiliary noun. However, for one-form verbs, it can also act as an auxiliary verb, attaching to the inherent base.
行くまい
食べるまい
食べまい
来るまい
するまい
For する and くる, you sometimes see すまい and こまい. しまい also happens.
まいとする expresses "try not to do X".
食べまいとする Trying not to eat
Negative volition can also invite ideas, just like positive volition (compare だろう, でしょう, etc). This is one of the more common uses of まい in speech.
そんなわけでもあるまい Such a thing is out of the question.
いい just means "good" or "fine" and isn't a grammatical term in itself, but it's used directly in patterns about permission.
食べていい？
いいよ
When people use よかった they're normally expressing gladness, not goodness. よかった shouldn't be used for permission.
When negation is involved, "permission" statements with いい often walk the line between permission and request, just like excessively polite english. The くて form of い-adjectives can be used here, but acts like an entity, not as a linker, like how it's an entity in なくては.
食べないでいいよ (fine not to eat)
食べなくていいよ (fine if you don't eat)
Sometimes, ますか and ませんか are a way of inviting permission politely, rather than asking a negative question. Think of this the same way as how ていい is used for permission even though it doesn't say "permission" anywhere.
食べますか Won't you eat?
舐めてませんか？ ねえ？ Won't you try it? How about it?
お仕事お休みできませんか……？ Is it impossible to take the day off...?