Short answers, pulled from the story.
Positive law refers to human-made laws that oblige or specify an action within a society. It stands in sharp contrast to natural law, which comprises inherent rights conferred by God, nature, or reason rather than legislation.
Thomas Aquinas conflated man-made law with positive law while Thomas Mackenzie divided law into four parts including divine positive law. Hans Kelsen worked on legal positivism theories until his death in 1973 and H. L. A. Hart emerged as another foremost proponent of legal positivism in the twentieth century alongside Kelsen.
François Gény introduced the notion of free scientific research in positive law during his career spanning 1861 to 1959. His work contributed to the normative theory of law put forth by the Brno school which gave pre-eminence to positive law because of its rational nature.
Governments enact specific laws that oblige or specify actions for citizens and organizations under their jurisdiction. Courts interpret these statutes to resolve civil disputes while maintaining order and safety across communities through statutory law and binding case law.
Positive law functions as law actually and specifically enacted by proper authority for the government of an organized jural society. It is necessary because it protects individual rights, resolves civil disputes, and maintains order and safety within a community.