The potential form of ある isn't "あれる"! It's actually ありえる/ありうる, depending on which one you want to use. When negating the potential form of ある, note that only ありえる is used: it becomes ありえない. "ありうらない" is wrong.
There is another potential form for group 2 verbs, which is used only in colloquial speech. It takes the form 'verb stem' + れる. あける --> あけれる, 食べる --> 食べれる, 見る --> 見れる etc.
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Can A; be possible to A; (possibility of the subject to do A)
Can A; be able to A (ability of the subject)
Can A; be possible to A; (possibility of the subject to do A)
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そのボタンを押したらロボットを動かせるよ。
If you push this button, you canmake the robot move.
I had a long talk about what you're trying to say, and it seems to be rather hard to say 'unnatural' in regards to human ideas - we did not make a lot of ground on that front.
With the potential, though, we decided that it would be best to use 'ことがある', which loosely means 'there are times/instances of ...' http://www.renshuu.org/index.php?page=grammar/individual&id=33
You could say something like 時に人間の思想が間違うことがある。 There are times where human ideas are mistaken.
Check out that grammar page - hopefully that'll help some.
However, I'm not quitely talking about right or mistaken ideas. It sounds quite abstract but I'm writing about nature (自然) in a kinda philosphical way and I was trying to express that reality is all natural, but our ideas might not flow according to nature's way, of course that might be somehow equivalent to the concepts of truth and falsehood, but it was another way to say it, "unnatural".
In case "不自然な思想" is a valid concept, something like this would be right?...
The reason I didn't rewrite it with the 不自然 bit is that we (my Japanese friend and I) could not figure out a good way to translate the English into Japanese. Especially since it's abstract, as you put it, it's hard to make a direct translation.
Because of that, I used the 'mistaken' example not as a replacement, but as a way to explain that grammar point.
As for ことがある and です, you don't need to actually put in です. I think the best way (will double check) would be ...不自然ということがあります.
That takes the statement preceding it and turns it into a noun. Again, I think this works, but I'm not positive. I can say with certainty that you a)do not put です in from of こと, and b)you would not use あれる (I don't think I've ever heard someone say あれる in any context).
You might want to cross-post this in the site's forums (link at the top) - I haven't quite figured out how to get more eyes on these discussion pages, but more people will see a question in the forum.
Yea - it's not necessarily what has changed (exactly), but is used to draw focus to the change - it's from where the word starts to change until the end of the word.
oh ok, i guess i just don't understand then ... I was thinking that the そ in 急ぐ wasn't part of the verb ending and therefore wouldn't be a part of the change ...
on Can A; be able to A (ability of the subject) example no 8 (しんじる).can you tell me why しんじる became しんじられる. not follow the pattern (るーれる and its negatif form should it be しんじれらない) ?
ringo - that's because しんじる is a る verb (or an いちだん verb), like 食べる or あける (the latter being used in the construction box above). The るーれる pattern you're seeing (exemplified by とる in the box) is for う verbs (or ごだん verbs) that happen to end in る.
My Japanese friend once stated, that the potential form of 一段 verbs is just ~れる (e.g. 食べれる). And even my text book (namely JFBP) agrees, that ~れる is sometimes used in colloquial speech.
Although I have to admit, that is looks and sounds somewhat strange, for someone like me, who deals with linguistic terms like 未然形, 連用形 etc., it would make perfectly sense to simply add ~る to the 仮定形 of verbs. And it would be soo much easier. :-[
Anyway, I don't know how you think about it, but maybe it's worth a side note?
I could have sworn we had already added that in the past.
If you would like to add it as a usage note (and I will be happy to check it when you are done), you'll get credit for it, and it'll save me some time :)
looking at the example sentence 「その女の子は突然猫に変身為ました!信じられない!」, the first exclamation point is the only thing highlighted - shouldn't the 信じられない be highlighted instead?