Gramm loquitur, Dia verba docet, Rhet verba colorat, Mus canit, Ar numerat, Geo ponderat, Ast colit astra.
Grammar speaks, Dialectics teaches, Rhetoric colors words, Music sings, Arithmetic counts, Geometry weighs, Astronomy takes care of the stars.
Scholastic: Ferdinand Buisson's Dictionary of Pedagogy
Plato (Πλάτων / Plato (plattɔːnot)) offers us a method of discovery and study of the sensitive world made up of seven disciplines. Mastering these seven disciplines allows each human being to distinguish reality from fiction. This method aims to teach us How? 'Or' What think rather than teach us what think.
These disciplines or liberal arts divide Trivium and Quadrivium.
The Trivium or "three ways" or "three ways or subjects of studies" in Latin, concerns the "power of the language" (expression, reasoning, persuasion and seduction). It is divided into grammar, dialectic, rhetoric.
The Quadrivium, or “four ways” or “four ways beyond the trivium”, refers to the “power of numbers”. It consists of arithmetic, music, geometry, astronomy.
A preserved fragment of the Pythagorean Archytas (around 360 BC) testifies to the existence of this idea in the teaching of Pythagoras. Fragment 1 of Archytas:
Mathematicians, in my opinion, know how to properly discern and understand (and this is hardly surprising) the nature of everything (…). Also, touching the speed of the stars, their rising and setting, they gave us a clear knowledge, as much as in plane geometry, arithmetic and spherical, without forgetting music either. Because these sciences seem to be sisters, since they take care of the first two forms of being, which are themselves sisters.
Porphyry, Commentary on the Harmonics of Claude Ptolemy
Plato evokes in La République a rapprochement between these sciences: science of numbers, plane geometry, geometry of solids, science of movers.
He speaks of astronomy and the harmonic as "sister sciences", explaining that astronomy is made for the eyes as the harmonic is made for hearing.
It relates the harmony of the spheres to the celestial orbits (the harmony of the spheres or Music of the Spheres is a theory of Pythagorean origin, based on the idea that the universe is governed by harmonious numerical relationships, and that the distances between the planets in the geocentric representation of the universe – Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, fixed sphere – are distributed according to musical proportions, the distances between planets corresponding to musical intervals).
This harmony of spheres is not only present in Plato. It is also found in the Tripityaka:
The monk, (…) with this clear, celestial ear surpassing the ear of men, hears both human and celestial sounds, whether distant or close.
Tripityaka, Sutta-pitaka, I: Dîgha-nikâya, 2: Sâmañña-phala-sutta, 87
In the Gorgias, Plato speaks of the "wise men" who, seeing the link between earth and heaven, the gods and men, gave the All the name of kosmos (order, arrangement) …
By mastering these seven liberal arts, each man becomes able to distinguish reality from fiction.
Liberal arts originate from Porphyry in "On the Return of the Soul" (c. 270).
Saint Augustine in “On Order” shows how reason generates grammar, then dialectic, rhetoric. To access God then comes geometry, astronomy and arithmetic.
Martianus Capella, in the “Wedding of Philology and Mercury” (around 410-439), presents them in the form of an allegorical. Mercury offers seven gifts to Philology: grammar, dialectic, rhetoric, geometry, arithmetic, astronomy, harmony.
Boethius († 524) defined the content of the quadrivium, he invented the word in The arithmetic institution (around 505-507). The "quadruple path" brings together scientific disciplines: arithmetic, music, astronomy and geometry.
Cassiodorus, in “Divine and Human Institutions” (around 560-580), develops the trivium which brings together literary disciplines: grammar, dialectic, rhetoric.
The figure below shows the Trivium and the Quadrivium in a Pythagorean triangle.
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1. Methodically gather raw and factual data through our 5 senses, in a coherent body of knowledge. The Greek word grammatikē means "art of letters", gramma means "letter of the alphabet" or "thing written". The first art of Trivium allows us to write reality.
2. Acquire an understanding of this coherent whole by systematically eliminating all the contradictions revealed within it. The Greek word dialektikē means "art of debate". The second art of Trivium is about inner debate, reflection which helps to reach understanding and refute logical errors. The sole arbiter of this debate is formal logic.
3. Express and use this knowledge in a pragmatic and useful way in reality. The third art of Trivium, Classical Rhetoric concerns the expression and use of knowledge, that is, doing it.
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