How does Greek philosophy of reason and inquiry as expressed in Greek dramas relate to the modern world today?
Many of the concepts of reason to which we now adhere were first developed by the ancient Greeks and expressed in their dramatic, philosophical, and gnomic literature.
One important characteristic of Greek drama is that decisions are often made by a process of rational deliberation or argument. For example, in Sophocles' Antigone, the protagonist and Creon debate the respective obligations of justice for the city and family in a process of logical deductive argument from principles.
Aeschylus' Eumenides gives a rational account of justice. Rather than accept a cycle of vengeance, we see the development of the court of the Areopagus, in which, rather than families taking vengeance on their enemies or vigilante justice, we see the evolution of a rational system of justice based on te rule of law and fair trials.