Justice in this case is not equivalent to “正義”. If “justice” means “正義” — correct principle, then the discussion is over. “Justice” should be translated to “公平” where acceptable action is determined by people. Justice is not a universal nor God given principle that leaves no room for further discussion. He emphasizes the ambiguous aspects of “justice” and tries to construct a fair consensus among people to maximize common utility. So putting “正義” upfront seems to be odd.
It is probably easier to follow his lectures in English and more meaningful.