**The Republic** is a long dialogue written by Plato, which covers a wide range of philosophical topics. The question of the best political organization of the *polis*, or city state, is the central theme of the book. In describing the role of mathematical training in the formation of the city-state’s future leaders, or Guardians, Plato gives expression to his views on mathematics through the words he gives to Socrates. In particular, Plato divides mathematics into five branches: arithmetic, plane geometry, solid geometry (see also Platonic solids), astronomy, and harmonics. This syllabus was taken up in medieval university as the quadrivium.

Here the study of astronomy and of harmonics is claimed to be related (by what later came to be called the *The Music of the Spheres*):

As the eyes, said I, seem formed for studying astronomy, so do the ears seem formed for harmonious motions: and these seem to be twin sciences to one another, as also the Pythagoreans say. (Republic VII.XII)

The Guardians are to study mathematics for many years to ‘awaken the eye of the soul’, the faculty by which they can appreciate also the Forms, especially those of Goodness and Beauty. On this theme, the dialog is also famous for the allegory of ‘The Cave’, where the best education is likened to releasing a prisoner condemned to see only shadows projected on a wall and eventually to emerge from the cave into the light (see at *doctrine of ideas*).

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*Republic (Plato)*

Last revised on February 5, 2016 at 13:01:27. See the history of this page for a list of all contributions to it.