得る vs ～られる potential form

Question

Recently I learned of a new way to express potential form. Here's a few example sentences:

• 今回は予測し得ないことが起きたけど、皆、落ち着いていた。
• 自分の意見を自由に言えないなんて、普通の国ではあり得ない。

The second example I put for contrast, because it illustrates one obvious difference which is that I don't think potential forms of ある and いる exist.

In the first example, however, it's not so clear. Instinctually, from looking at these and a few other examples, I think perhaps there is a sense of impossibility here that is not present in simple できる or ～られる form, but I have trouble articulating it, and it may be a red herring anyway.

For example, change the first sentence to this:

• 今回は予測できないことが起きたけど、皆、落ち着いていた。

Does it have a different nuance now?

Can someone elaborate on the differences between these two constructs?

Answer 1

First, I think that 連用形+得る is more formal than the classical potential forms. Then, I feel a slight nuance: the 得ない form dissociates the speaker from the impossibility. Overstating, it's like When you say できない, it means you cannot do it; when you say し得ない, it means that it cannot be done.

Second, potential form of いる exists: I'm pretty sure I already heard:
"ここにいられません。すぐ出てください！" (You can't be here, go away right now!)

For ある, there is あられる, but it's some 敬語, and no more a potential indeed.

Answer 2

• 今回は予測し得ないことが起きたけど、皆、落ち着いていた。
• 今回は予測できないことが起きたけど、皆、落ち着いていた。

When you compare the two, the first one is just stronger than the later. In the first one, there is an emphasis on the impossibility. It kind of stands out. So you have 50% emphasis on the impossibility part, and another 50% on the 落ち着いていた part.
In the latter, perhaps the speaker has already talked about the impossibility and is not intending to place focus here. The emphasis is much more on the 落ち着いていた part now.

得ない would translate to something like "totally impossible", while できない would translate to "cannot" or something.

Answer 3

Japanese here. The two "得ない" are same to me at least. The first example talks about "some thing that couldn't possibly be anticipated happened", and the second example talks about that "there is no way that this happens in a normal country".
They both simply express impossibility. Only the proceeding verb (predict/exist) is different.