This lesson will focus on more difficult potential phrases in Japanese. Pay close attention to even the most minute differences.
可能 is a 形容動詞 meaning "possible". Impossible is 不可能.
It's possible, but it's really difficult.
Solving a statistics problem in an instant is what's impossible!
That is all but impossible.
Word Note: 可 is in some words to mean "-able". Ex. 可燃ごみ ＝ combustible refuse.
To dispute propriety.
Although now quite old-fashioned, you may still come across this potential word. It's normally limited to 連体形+｛（こと）・に｝あたわず. The affirmative potential form of verbs became used in Japanese from Western influence when the first translations of Western works were attempted. So, starting from then, あたう became used as well.
Pronunciation Note: あたう is often written as あとう because it's pronounced as あとー.
8. 行くことあたわず。(Very old-fashioned)
I can't go.
9. 称賛おくあたわず。(Very old-fashioned)
I can't help but admire you.
I will try to the best of my abilities.
Usage Note: あたうる限り is a common misuse by natives.
The potential form of ある is あり得（え・う）る. However, ありうる should be used only as the 連体形. This is a remnant feature of the original verb 得（う） in Classical Japanese.
It is impossible that he is alive.
Lie! I can't believe it! That's impossible. Such a nice person killing someone...
A possible disaster
That kind of accident is possible in reason, but above all, it won't really happen.
Following from above, it is also a common practice in semi-classical format to use 得る after the 連用形 of a verb. It can be read as うる in the 連体形, but in very old-fashioned speech, you can also see it used at the end of a sentence. With a transitive verb, we see that even this option allows を to mark the direct object.
With a verb of non-volition, this shows possibility. When added to a verb of volition, it expresses rating or degree of ability to do something. Remember that non-volitional verbs don't have a 可能形.
It can take it like this.
Smiling is irresistible.
Loess flying in is possible in this time?
Word Note: 黄砂 is dust from the Yellow River region of China.
Tobacco can hurt your health.
He can't escape death.
It was because of me being there that they were able to stay being their bare guerrilla fighter
From 光の雨 by 立松和平.
Grammar Note: The ～たり in たり得る is a classical copular auxiliary verb.
22. ｛できうる △・なしうる｝限り
To the best of one's ability
Notation Note: The triangle indicates that this is acceptable to some but not all speakers. The meaning is doubled, which should make it ungrammatical. However, you still see it used.
Verb Note: なす is the transitive verb pair for なる and is used just like する. It is only used in the spoken language in expressions like 財をなす(to build a fortune), 色をなす (to change one's complexion when angry), 成し遂げる (to accomplish), etc.
In speaking of なす, なせる can't be used as the potential form. This is because it would be a look alike to the actual interpretation of "done". In Classical Japanese, there was an auxiliary equivalent to English's perfect tenses: り. This attached to the 已然形. So, you would get なせり. When used before a noun, it becomes なせる. This grammar point is only found in set phrases.
An act of God
I was finally able to get away from the watch of the enemy.
We will have no choice but to question.
As you can see, the verb 得る can also function as a potential verb, which makes sense if it can do so as a supplementary verb. Here, in these rare cases it is always after を and usually after a nominalized form of a verb. In the case of ～ざる, the 連体形 of the classical negative auxiliary ～ず, case particles after the 連体形 was sufficient in Classical Japanese to use a verb phrase as a noun. So, the same principles still apply.
History Note: The sound change that lead to independent potential verbs for 五段 verbs is uncertain. One idea is that it is a contraction of the 連用形 of 五段 verbs plus ～得る.
Ex. 書き得る → 書ける
A more plausible account, however, is that a subset of intransitive verbs that showed spontaneity (phenomena that occur naturally) promoted the generalization to all 五段 verbs.
切れる is the intransitive verb form of 切る. Its use as the potential form of 切る is only recent. It is most simply translated as "to be cut", but it has many other nuances. One nuance in particular aids in visualizing the jump from spontaneity to potential. For instance, in the sentence よく切れた球が戻ってきた, we envision a tennis-like ball making a good return with a good spin. The importance, though, is similar usages in these verbs of spontaneity is what makes this such a compelling theory.
Also, historically, the endings ～られる and ～れる, though different in appearance, have stood for and continue to be used for not only potential but also passivization, spontaneity, and light honorifics. It's believed, though, that the root usage is to show spontaneity. For a potential pattern to evolve from another line of spontaneity phrases shouldn't be a surprise in light of this.