Education in the trivium, from the ancient world to the present day, asks the student to proceed to master letters, i.e. to become literate, by degrees: first by mastering grammar, then by applying one’s mind to the study of logic, then by combining these studies into the art of rhetoric. These “ways” of free-thinking into intellectual liberty progress from language itself to thought itself, and then (and only then) to argument, since argument combines structures of language with structures of thought in an unassuming, unaffected, and hence compelling manner.
Intersecting with the student’s immersion in the arts of the trivium should be the crossroads of the sciences. Viewed through the lens of liberal education, however, not just any sciences can take the place of the quadrivium, the mastery of which requires, once again by degrees, the study of number per se (arithmetic), number spatially conceived (geometry), number temporally grasped (music, with an emphasis on interval, balance, proportion, and harmony), and all of the above combined into a single, unified whole, traditionally represented in the subject of astronomy, in which number is instantiated in itself as well as in time and in space (thereby combining the “virtues” of arithmetic, music, and geometry, respectively).
—11/2015
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