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The definitions on this list are mostly helpful, but the term "Understanding" is incorrect and misleading. The highest grade of cognitive activity in Plato's fourfold epistemological scheme is, in Greek, "noesis." In English this should be called Intellection, Higher Reason, or simply Noesis. To call it Understanding badly confuses things because of the myriad unrelated meanings and senses of "understanding" in English.
Similarly, what the list above calls "Reason" would be better termed ratiocination, calculation, reasoning, or lower reason. To simply call this faculty Reason confounds two distinct faculties: ratiocination (dianoia) and Higher Reason (nous or Nous). Ratiocination is somewhat like the ability that animals have to think and plan. It is the Higher Reason that is associated with mans immortal soul, and on which basis, according to Plato, man may attain "likeness to God insofar as possible."
Spouses in the republic are not drawn by lot, as is asserted in the summary for Book V. Rather, they are chosen so that 'bronze-souled' individuals will be paired off with other bronze-souled individuals, and gold-souled with other gold-souled. The idea of the lottery is a lie fabricated by the framers of the city to placate citizens.