得る【える / うる】

得る goes after a verb's ます-stem and means "can", in the sense "it is possible that this happens". It is formal and mostly written. In conversation you meet it in ありうるあり得る and ありえないあり得ない, and otherwise use the potential form.

える or うる

The dictionary form reads either える or うる. うる is the older reading and sounds more formal; ありえる and ありうる are both everyday. Every other form is built on え: 得ない is えない, 得た is えた, 得ます is えます.

• × ありうない → ありえない

得る or the potential form

得る talks about what is possible in principle: an event, a plan, a result. What a person can do in everyday terms – swim, read kanji, speak Japanese – takes the potential form.

• × 私は日本語を話し得る → 私は日本語が話せる