The emergence of rational thought ----------------------------------
In Book VI of Plato's La République (The Republic), Socrates says to his pupil Glaucon: "You are aware, I suppose, that those who study geometry, arithmetic, and other such sciences assume the odd and the even, figures, three kinds of angles, and other analogous things according to the subject of their inquiry. They treat them as known, and, having adopted them as hypotheses, consider themselves under no obligation to account for them either to themselves or to others, since they are evident to everyone. Finally, starting from these hypotheses and proceeding through every step, they arrive by logical inference at the proof they had set out to find. "
The advent of rationality in a civilization that prized reasoned discourse—carefully regulated and intended to persuade through shared rules—went hand in hand with democracy, mathematical science, and philosophy…
Although geometers use figures, Socrates draws a distinction: "they seek to see the absolute figures, objects that no one can perceive except through thought."