They exist outside and independant of human interpretation. If they are real and nonsubjective, then they must reside inside of some meta-intelligence. These conceptual objects reside in God's mind, and indeed expose God's nature and thus the nature of our reality. Of course not, its a scientific reality that bugs like fruit, and if you wait too long they'll have it. Indeed, this should not surprise us.
Humans are a new type of animal.
We survive by our Reason, not our strength, speed, teeth, camaflouge. In summary, the concept of justice has allowed man to survive and flourish, and the concept is universal. These two facts make it a Objective Concept. Since it is readily apparent that justice is often missed by humans, even with the best intentions and information available, we must say that the remainder, balancing of the scales, righting the wrongs, is done in the after life, by a loving and just God. A robot may not injure a human being, or, through inaction, allow a human being to come to harm.