Verb + うる form. What is this?

Question

Can't really understand this form:
I've seen already this form with 考える and translated it like this:

考えうることだ - conceivable (possible)

However how do you translate with other verbs? is this some kind of potential?

1.人生の目的は何かという問題に対してみんなが納得しうる答えを出すのは難しい。

Answer 1

Yes, ～うる (or ～える) can be thought of as a potential form. It's an auxiliary that expresses "can", and it attaches to the continuative form (連用形) of a verb. That's the same form of the verb you use before the polite auxiliary ～ます, so we get forms like these:

　　ある　　　→　　ありうる  
　　考える　　→　　考えうる  
　　する　　　→　　しうる  

In kanji, this verb is written 得る, but in this auxiliary usage it's often written in kana.

As an independent verb 得{う}る is now uncommon—得{う} became 得{え}る in modern Japanese. But as an auxiliary expressing potentiality, both ～うる and ～える are common, though ～うる may sound a little older/more literary than ～える.

Most conjugated forms besides ～うる itself begin with ～え, not ～う. So although you'll see both ありえる and ありうる commonly enough, you'll only see ありえない and ありえて, never *ありうない or *ありうて.

Answer 2

It's a variant reading of 得る【える】, and is used to indicate possibility. The most common place I've seen this construction is in ありうる (or more frequently, the frustrated exclamation ありえない！, which is along the lines of "It can't be!").

If it has any additional nuances beyond simple possibility, I'm afraid I'll have to leave that to a native speaker to clarify.