of correct reasoning. The traditional text for teaching logic was Aristotle's Logic. In the modern renaissance of classical education, this logic stage (or dialectic stage) refers to the junior high or middle school aged student, who developmentally is beginning to question ideas and authority, and truly enjoys a debate or an argument. Training in logic, both formal and informal, enables students to critically examine arguments and to analyze their own. The goal of the logic stage is to train the student's mind not only to grasp information, but to find the analytical connections between seemingly different facts/ideas, to find out why something is true, or why something else is false. Rhetoric Rhetorical debate and composition are taught to somewhat older (often high-school-aged) students, who by this point in their education have the concepts and logic to criticize their own work and persuade others. According to Aristotle, "Rhetoric is the counterpart of dialectic", concerned with finding "all the available means of persuasion". Students learn to articulate answers to important questions in their own words, to try to persuade others with these facts, and to defend ideas against rebuttal. The student learns to reason correctly in the Logic stage so that they can now apply those skills to Rhetoric. Traditionally, students would read and emulate classical poets in learning how to present their arguments well. Secondary education – the quadrivium Secondary education, classically the quadrivium or "four ways", consists of arithmetic, geometry, music, and astronomy. Sometimes architecture is taught alongside these, often from the works of Vitruvius. History is taught to provide a context and show political and military development. The classic texts were from ancient authors such as Herodotus, Thucydides, Livy, Cicero, and Tacitus. Biographies were often assigned as well, with the classic example being Plutarch's Lives. Biographies help show how persons behave in their context, and the wide ranges of professions and options that exist. As more modern texts became available, these were often added to the curriculum. In modern terms, these fields might be called history, natural science, accounting and business, fine arts (at least two, one to amuse companions, and another to decorate one's domicile), military strategy and tactics, engineering, agronomy, and architecture. These are taught in a matrix of history, reviewing the natural development of each field for each phase of the trivium. That is, in a perfect classical education, the historical study is reviewed three times: