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TRIVIUM > QUADRIVIUM > PHILOSOPHY
Trivium: The Word.
Grammar (Primary School – repetition), Logic (Middle School – understanding ), Rhetoric (high school – argument)
Quadrivium: The Number.
Arithmetic(The Number), Geometry(The Number in Space), Music(in Time) and Astronomy(Motion(Space and Time))
Philosophy: The Idea
IMO Propertarianism completes Philosophy with Grammars (Metaphysics), Acquisitionism (Psychology), Compatibilism (Sociology), Propertarianism(Ethics), Natural Law (Politics), adds Group Strategy, and articulates Aesthetics.
Between the logic of the grammars, the logic of numbers, and the logic of cooperation (P), we have completed the systems of calculation available to the human mind.
THE EDUCATION IN THE SKILLS OF THINKING
Together, the trivium and the quadrivium comprised the seven liberal arts (based on thinking skills), as distinguished from the practical arts (such as medicine and architecture).
Educationally, the trivium and the quadrivium imparted to the student the seven liberal arts (essential thinking skills) of classical antiquity.
Grammar teaches the mechanics of language to the student. This is the step where the student “comes to terms,” defining the objects and information perceived by the five senses. Hence, the Law of Identity: a tree is a tree, and not a cat.
Logic (also dialectic) is the “mechanics” of thought and of analysis, the process of identifying fallacious arguments and statements and so systematically removing contradictions, thereby producing factual knowledge that can be trusted.
Rhetoric is the application of language in order to instruct and to persuade the listener and the reader. It is the knowledge (grammar) now understood (logic) and being transmitted outwards as wisdom (rhetoric).
The quadrivium (plural: quadrivia ) is the four subjects, or arts (namely arithmetic, geometry, music and astronomy), taught after teaching the trivium.
The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium, consisting of grammar, logic, and rhetoric.
The quadrivium was the upper division of the medieval education in the liberal arts, which comprised arithmetic (number), geometry (number in space), music (number in time), and astronomy (number in space and time).
In turn, the quadrivium was considered the foundation for the study of philosophy (sometimes called the “liberal art par excellence”) and theology.