We learned in a previous lesson that the volitional form is used when one is set out to do something. In this section, we're going to cover some other ways in which the volitional form is used, most notably, the negative volitional form.
You may have seen the negative volitional form in a verb conjugation table and wondered, "What the heck is that used for?" Well the answer is not much, or to put it more accurately, there are various ways it can be used but almost all of them are extremely stiff, formal, and seldom used. In fact, it's so rare that I only found one explanation in English on the web or anywhere else. (I also found this one in Japanese.)
The negative volitional is used to express negative intention. This means that there is a will for something to not happen or that someone is set out to not do something. As a result, because one is trying not to do something, it's probably not going to happen. Essentially, it is a very stiff and formal version of 「でしょう」 and 「だろう」. While this form is practically never used in daily conversations, you might still hear it in movies, etc.
Verbs are conjugated to the negative volitional by simply attaching 「まい」 to the verb. Another alternative is to attach 「まい」 to the stem. The conjugation for the negative volitional is quite different from those we are used to because it is always the last conjugation to apply even for the masu-form. There is no way to conjugate 「まい」 to the masu-form, you simply attach 「まい」 to the masu-form conjugation.
We already learned that you could use the volitional form to say "let's" and to express an attempt do something. But that doesn't mean you can use the negative volitional to say "let's not" or "try not to". The tone of this grammar is one of very strong determination to not do something, as you can see in the following examples.
In order to express "let's not", you can use the verb, 「やめる」 with the regular volitional. In order to express an effort to not do something, you can use 「ようにする」 with the negative verb.
We will now learn a grammar that's actually practical for everyday use using the negative volitional grammar. Basically, we can use both volitional and negative volitional forms to say it doesn't matter whether something is going to happen or not. This is done by attaching 「が」 to both the volitional and the negative volitional form of the verb that doesn't matter.
We already found out that the negative volitional can be used as kind of a formal version of 「でしょう」 and 「だろう」. You may wonder, how would you do the same thing for the volitional? The answer is to conjugate the verb 「ある」 from the formal state of being 「である」 to the volitional to produce 「であろう」. Remember 「でしょう」 can already be used as a polite form, so this form is even a step above that in formality. We'll see what kind of language uses this form in the examples.
We learned in the lesson about formal grammar that 「ではない」 was the negative of 「である」. So how would we say something like 「であろう」 but for the negative? The answer is to use yet another type of volitional for negatives and i-adjectives used only in formal and literary contexts. You can think of this grammar as a very old-fashioned version for i-adjectives and negative 「い」 endings.
The conjugation rule is simple: remove the last 「い」 and attach 「かろう」. You can use it for negatives and i-adjectives just like the 「かった」 past conjugation form.