Natural law theory can be divided into traditional natural law and early modern natural law. Traditional natural law began in ancient Greek philosophy, passed through Plato, Aristotle and the Stoics, and was completed as a theoretical system by Aquinas, the leading Scholastic thinker, on the basis of theology and religious philosophy. Early modern natural law, by contrast, began with Pufendorf and dominated the philosophy of law until it was challenged by the historical school and legal positivism in the 19th century; in the modern era natural law was freed from the constraints of the Church and came to be explained from the standpoint of modern rationalism. Grotius explained the existence of natural law grounded in human reason, and as modern individualism, rationalism and utilitarianism rose, he separated the theological meaning from traditional natural law and advanced a new early modern natural law based on human reason. In traditional natural law, natural law was a social order for humans ordained by God that existed metaphysically, whereas in early modern natural law it exists by being recognized through human reason.

Legal positivism began in the modern era when Comte's positivist philosophy influenced jurisprudence. It rejects philosophical inquiry into supernatural things that human senses cannot grasp, such as the world of God, and studies only law that the human senses can perceive, that is, existing positive law. Socrates in antiquity is said to have said 'a bad law is still the law' and drunk the hemlock, which can be seen as a strong spirit of obeying the law. Legal positivism can be seen as resting on this attitude. But believing in it too blindly can give rise to a dictator like Hitler.

Natural law and legal positivism have a very important influence as the theoretical foundations of modern jurisprudence. Whether all application of law should follow legal positivism based on objectivity, or natural law based on morality and human conscience, remains a matter of debate. Legal positivism and natural law are major topics in international law. Many scholars have studied whether the two concepts can coexist, how to reconcile them if so, and which one is right if they cannot. The two theories remain contested despite research and conflict continuing since the 20th century because problems often arise in our society that cannot be solved by relying entirely on law.

As in the maxims 'law is the maximum of morality' and 'criminal law is the backbone of morality,' law sets out in written form the minimum morality, ethics and values that members of society must observe and gives them binding force. The problem is that morality, ethics and values take many forms, and individuals differ in which ones they consider important.

To add: Article 38(1) of the Statute of the International Court of Justice lists treaties, international custom and the general principles of law recognized by civilized nations as the bases for decisions, with judicial decisions and the teachings of scholars as subsidiary means. Peremptory norms (jus cogens) under Article 53 of the Vienna Convention on the Law of Treaties are often cited as a concept influenced by natural law thinking. The paper's 'law is the maximum of morality' should read Jellinek's 'law is the minimum of morality,' and early modern natural law is usually traced to Grotius's On the Law of War and Peace (1625). Socrates's 'a bad law is still the law' is known not to appear as such in Plato's writings. The GATT ruling is Supreme Court Decision 2008Du17936 of January 30, 2009.