Plato on Philosopher Rulers, Education, and True Knowledge
Philosopher Rulers and Citizen Happiness
Philosopher-rulers will not condemn themselves to unhappiness but will ensure their own happiness and that of the citizens. The philosophers will persuade others, seeing they have contracted a debt for their education.
Curriculum for Soul Conversion
Studies must ensure the soul’s conversion from the realm of becoming to the realm of being. We rule out music, gymnastics, and other arts dealing with sensible things. We must implement by law the study of:
- The nature of numbers (arithmetic)
- Surfaces (geometry)
- Bodies at rest (stereometry)
- Bodies in motion (astronomy)
- Harmony
Mathematics as Prelude to Dialectics
The study of mathematics (numbers, geometry, stereometry, astronomy, and harmony) is the necessary prelude to the study of dialectics.
Interpreting the Allegory of the Cave
Dialectics and Understanding Reality
Dialectic, the philosophical art or science, allows reason, without relying on sensory images, to grasp the Forms (Ideas) and ascend to the knowledge of the Idea of the Good. This corresponds to the prisoner in the allegory of the cave reaching the external reality, progressively viewing enlightened beings until directly gazing at the sun itself, which illuminates all.
Mathematics and Liberation from the Cave
The study of mathematics (arithmetic, geometry, stereometry, astronomy, harmony), as propaedeutic arts, prepares the soul for true knowledge, which only dialectics can provide. This corresponds to the prisoner’s release, contemplating objects in the cave by the firelight, and the ascent to the world outside, viewing shadows or reflections before seeing true objects.
(This text implies three types of knowledge: sensitive/pre-scientific, scientific, and philosophical/dialectical. This tripartite division, potentially justifying the three citizen classes in the ideal Republic, differs from the four levels—eikasía, pistis, dianoia, and noesis—presented in the simile of the line in Book VI and later in Book VII.)
Mathematics vs. Dialectics
Only the dialectical method allows us to know the real truth. In contrast, the mathematical arts focus on the sensible, yielding only opinion (doxa). While they elevate the soul towards the intelligible, they ‘dream’ of true reality because they use sensible images and start from hypotheses (axioms) they cannot demonstrate. Therefore, we cannot expect deductions from them to provide true knowledge.
(Note: Arithmetic might initially use sensible aids but can operate without them later. A critique could be that geometry uses ‘imaginary phantasms,’ and even philosophy might use imagined sensible images to check results. Plato’s distinction between science and philosophy may not be as rigid as presented.)
The Dialectical Method’s Superiority
The dialectical method does not treat its starting assumptions (hypotheses) as self-evident axioms. Instead, it uses them as stepping stones to reach an unhypothetical first principle—the Idea of the Good—upon which everything else is built. The auxiliary studies mentioned (mathematics) raise the soul from the ‘mud’ of the sensible world, providing intelligible insight (dianoia) superior to mere opinion (doxa), but still less than true knowledge (noesis).
(The knowledge from mathematics is often termed discursive thought or dianoia. Noesis describes the knowledge provided by philosophy or dialectic.)
Knowledge Levels: Line and Cave Analogy
Recalling the simile of the line and its correspondence with the allegory of the cave:
Sensible World (Becoming)
Realm: Change, Pseudo-reality
Levels:
- Eikasía (Illusion/Imagination) – Corresponds to shadows in the cave
- Pistis (Belief) – Corresponds to objects in the cave
Overall Cognitive State: Doxa (Opinion)
Intelligible World (Being)
Realm: Immutability, Authentic Reality
Levels:
- Dianoia (Thought/Understanding) – Corresponds to mathematical objects, reflections outside the cave
- Noesis (Intellection/Reason) – Corresponds to Forms/Ideas, objects outside the cave, the Sun (Idea of the Good)
Overall Cognitive State: Episteme (Knowledge)