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In the song イドラサーカス sung by 鏡音{かがみね}リン, there is the line,
「青{あお}い空{そら}が汚{よご}れて見{み}えますか？」I translated it using て as the present
continuous. "Can you see the blue sky becoming dirty?" Is my translation right
and, if so, why would you say 見{み}えます? Wouldn't you conjugate 見{み}ます using ます
form?
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conjugations て-form potential-form
Why would you use 見えます instead of 見ます?
You're confusing [見る](https://jisho.org/search/%E8%A6%8B%E3%82%8B) (to see)
with [見える](https://jisho.org/search/%E8%A6%8B%E3%81%88%E3%82%8B) (able to see
/ to be seen). Similarly there is 聞く (to hear) and 聞こえる (to be able to hear /
to be heard).

I have a hard time describing the differences, but luckily there [is another
answer here](https://japanese.stackexchange.com/questions/5287/what-is-the-
difference-
between-%E8%A6%8B%E3%81%88%E3%82%8B-%E3%81%BF%E3%81%88%E3%82%8B-%E8%81%9E%E3%81%93%E3%81%88%E3%82%8B-%E3%81%8D%E3%81%93%E3%81%88%E3%82%8B-and-%E8%A6%8B%E3%82%89%E3%82%8C%E3%82%8B-%E3%81%BF%E3%82%89%E3%82%8C%E3%82%8B-%E8%81%9E%E3%81%91%E3%82%8B-%E3%81%8D%E3%81%91%E3%82%8B).
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The verb you are seeing is
[見える](https://jisho.org/word/%E8%A6%8B%E3%81%88%E3%82%8B), which means either
"to be visible" or "to seem/appear/look". `te-form + 見える` usually means the
latter, "to appear to (have) ～" or "to appear as if ～".

>   * 彼が若返って見える。  
>  He looks as if he has gotten younger.
>   * まるで時間が止まって見える。  
>  It appears as if the time stopped.
>   * 青い空が汚れて見えますか？  
>  Does the blue sky appear to be dirty (to you)?
>
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