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What is dianoia?

What is dianoia? Here are some definitions.

Noun
  1. (philosophy) discursive thought on mathematical or scientific subjects
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Examples
In Plato's divided line, the equivalence of mathematics and dianoia shows that mathematics plays an important preliminary role in education.
The physician Aretaios describes the consequences of epilepsy in damaging the patient's dianoia and causing his mOrainein.
Since both noesis and dianoia correspond to invariable objects, the line's account of rationality is not a counterpart to Aristotle's practical rationality.

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