Q:

Why would you use 見えます instead of 見ます?

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?

A:

The verb you are seeing is 見える, 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)?

