Because every case of preventing one person from harming another is a case of harm prevention, but not vice versa, HP1 is narrower than HP2. Indeed, HP1 is a proper part of HP2. Whereas HP1 justifies intervention only when the target herself would be the cause of harm to others, HP2 would justify intervention to prevent harm to others, whether that harm would be caused by the target or in some other way. Clearly, HP2 will justify more intervention than HP1. As we have seen, it is hard to justify