Final answer:
Act utilitarianism might endorse Batman killing the Joker to save lives, but it faces criticism for justifying actions contrary to moral standards and could lead to societal distrust.
Step-by-step explanation:
The ethical philosophy that might endorse Batman killing the Joker to save many lives is act utilitarianism, which suggests that an action is moral if it maximizes happiness for the greatest number of people. In the scenario where Batman considers killing the Joker, act utilitarianism would assess this action based on whether it results in more overall happiness or less suffering in the world, by preventing future crimes that the Joker might otherwise commit.
However, this view is not without its criticisms. Some argue that act utilitarianism can justify actions that contravene moral standards, like vigilantism, which could lead to a breakdown in societal trust and security. Moral pluralism, as proposed by Sir William David Ross, critiques utilitarianism's simplification of morality and suggests considering multiple moral obligations in decision-making. This could apply to Batman's dilemma, as he may have to balance the duty not to kill against the duty to save lives.
Ultimately, the debate on whether it is justified for Batman to take such an action remains contentious and is subject to different interpretations of moral philosophy.