How does the character of Batman challenge the reader to think about superheroism (doing what is right according to the law) and vigilante (doing right even if outside the law) crime-fighting

It causes you to think about what he can do within the realm of the law as it resorts to nonphysical violence. However, the vigilante justice comes in the form of someone getting injured that he is close to etc. Rather than contact the authorities, Batman locates the individual and takes justice into his own hands wherein he sometimes inflicts physical pain.