DIANOIA is ‘discursive thinking’. In Platon (Plato) the term <dianoia> indicates a specific kind of thinking for mathematical and technical subjects. It is the capacity for discursive thinking, which is different from immediate apprehension (<noesis> or <nous>). In fact, in philosophy, <nous> is ‘understanding’ or ‘reason’ meaning the entity that reasons, not the activity of reasoning. It is something similar to perception but it works within the mind (“the mind’s eye”). The basic meaning of <nous> is something like ‘awareness’. In colloquial English, <nous> also denotes ‘good sense’, which is close to an everyday meaning it has in Ancient Greece.
In Platon’s Republic, Sokrates (Socrates) 507a7-509b9 compares the ‘good’ to the ‘sun’. Then he tells Glaucon to envisage a line (AE) and to divide it into two unequal sections (AC and CE, with the former being longer). AC is the intelligible realm and CE is the visible one. Again these two sections need a further division, in the same proportion as AC to CE. Therefore AC is split into AB and BC. And CE into CD and DE. Sokrates assign four ‘states of mind’ to the four subsections. So intellect (<noēsis>) goes in combination with AB. Then thought (<dianoia>) goes with BC. Also belief (<pistis>) goes with CD. Moreover, imagination (<eikasia>) goes with DE. Intellect is on the highest level of clearness (<saphēneia>). Then come, in order, thought, belief, and imagination. Sokrates ascribes ‘intellect’ to dialecticians and ‘thought’ to mathematicians. He says that the dialectician moves from hypotheses back to their ultimate ‘principle’ (<archē>) while the mathematician takes hypotheses for granted and deduces conclusions from them.