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I think he does believe vengeance is wrong. Check out Dantes' mentor Abe says,
Abbe Faria: Here is your final lesson - do not commit the crime for which you now serve the sentence. God said, Vengeance is mine.
Edmond Dantes: I don't believe in God.
Abbe Faria: It doesn't matter. He believes in you. ” (Chapter 6)