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The Trivium, or artes sermocinales, are the language studies of the seven Liberal Arts of the universities of medieval Europe. The other four arts were the mathematical: the Quadrivium, or artes reales, or physicae. All seven "liberal" would be contrasted from the artes illiberales, or "mechanical arts", those studies which were deemed useful to making war or money, but not necessary components in the education of gentlemen, doctors, lawyers and priests.
The "three roads" of the Trivium were denominated "grammar, rhetoric and logic", but the meanings of all these words have shifted since the Middle Ages:
"Grammar" is an anglicized Greek word: "gramma", which meant "letters". "Letters" in the archaic sense of "literature" is what was meant by "grammar". While the study of classic literature will serve to school one in the accepted and proper usage of the language, this was not the only benefit the student was expected to enjoy. Grammar was certainly not confined to the study of a collection of "grammar" rules or the avoidance of common errors. In the Middle Ages, books were rare and it was a simple matter to direct the student to read everything. The Bible, of course, would have been the primary text. Today we must be more selective. Inevitably, what gets selected as a "canon" of classic literature will be a matter of dispute. However, certain examples of English literature suggest themselves: Shakespeare, perhaps, or for a more modern vernacular, T.S. Eliot.
"Rhetoric" has, since Plato castigated the Sophists of his day, always suffered from a tawdry reputation. It was, however, as Webbie puts it, citing Locke: "the art of speaking with propriety, elegance, and force". As such, for the gentleman for whom a "liberal" education was intended, Rhetoric is the only truly useful "art" among them. This is why the Greek aristocracy sent their sons to the Sophists, and why the Romans picked up the art of rhetoric with considerably greater enthusiasm than they demonstrated for, e.g., astronomy. In the Middle Ages, in addition to the use of rhetoric in courtly argument, it was the basis for the priestly skill of giving sermons or homilies. Thus, when three primary graduate schools were Law, Medicine and Theology, at least two of those required a sound preparation in Rhetoric. Today, scholars see no need for speaking appropriately, concisely or well. Pick up any scientific paper, or article from a legal or medical journal, or worse, go to a conference and hear them speak: it becomes self-evident. To a very limited extent, eloquence survives as a black art practiced by some specialists in the legal profession, and those lawyers who would make a career in politics, but the true modern home of Rhetoric is in the business school: in advertising, marketing and public relations.
"Logic" included some matters we might call Logic today: analytics (as presented in Aristotles' Prior Analytics or Posterior Analytics). Mostly, however, it was a more Platonic study: dialectic, albeit in a somewhat rigid and devolved debating format that one sees in medieval works of theology, such as the Summa Theologica of Thomas Aquinas. Nineteenth Century political philosophers, such as Marx and Hegel still used the term "Logic" in this medieval sense. It certainly did not mean a formal algebra of language, as one might encounter in a university setting today.
Sources:
Decades of propaganda from my alma mater, St. John's College.
Otto Willmann, "The Seven Liberal Arts", The Catholic Encyclopedia (1907), http://www.newadvent.org/cathen/01760a.htm.
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