Short answers, pulled from the story.
Positive law, known in Latin as ius positum, consists of human-made laws that oblige or specify an action, enacted by a recognized authority such as a legislature or court. Natural law, by contrast, comprises inherent rights conferred not by legislation but by "God, nature, or reason". Where natural law is discovered through reason or revelation, positive law is deliberately created and posited by an authoritative source.
Thomas Aquinas recognized both divine positive law and human positive law, placing no requirement on the person who posits law that would exclude either humans or the divine. In the Summa contra Gentiles he wrote of divine positive law: "Si autem lex sit divinitus posita, auctoritate divina dispensatio fieri potest" - if the law be divinely given, dispensation can be granted by divine authority. He also conflated man-made law (lex humana) with positive law (lex posita), treating them as effectively equivalent.
Hobbes and Austin both held that sovereignty must be singular and undivided, which led them to deny the existence of divine positive law. They argued that a temporal sovereign cannot truly be sovereign if humans are also subject to divine positive law. Their solution was to invest all positive law in the temporal authority, which they saw as responsible for translating divine natural law into enacted human positive law.
Thomas Mackenzie divided law into four parts: divine positive law, natural law, the positive law of independent states, and the law of nations. Divine positive law concerns the duties of religion and derives from revelation, while divine natural law is recognized by reason alone without revelation. The positive law of independent states is posited by the supreme power in the state, and the law of nations regulates independent states in their dealings with each other.
Hans Kelsen and H. L. A. Hart were among the foremost proponents of legal positivism in the twentieth century. Kelsen's career spanned his European years prior to 1940 and his American years until his death in 1973. Hart was a British philosopher who, alongside Kelsen, gave legal positivism its most rigorous modern form.
The name positive law derives etymologically from the Latin verb to posit, meaning to lay down or declare. The Latin term ius positum reflects the idea that such law is deliberately set in place by an authority, in contrast to natural law which exists independently of any human act. The distinction between lex humana (human-made law) and lex posita (posited law) captures a subtle difference: the first regards law from its origins, the second from its legitimacy.