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Prudence then stands opposite to Intelligence; for Intelligence1 apprehends definitions, which cannot be proved by reasoning, while Prudence deals with the ultimate particular thing, which cannot be apprehended by Scientific Knowledge, but only by perception: not the perception of the special senses,2 but the sort of intuition whereby we perceive that the ultimate figure in mathematics is a triangle3; for there, too, there will be a stop.4 But the term perception applies in a fuller sense to mathematical intuition than to Prudence; the practical intuition of the latter belongs to a different species.56

1 See notes on 6.2 and 11.4. Definitions are the first principles of science.

2 Literally ‘of the objects peculiar to the special senses.’ Shape was one of the ‘common sensibles,’ perceived through the medium of more than one of the special senses, by the ‘common sense.’

3 A triangle is the last form into which a rectilinear figure can be divided: two straight lines cannot enclose a space. Or the words may possibly mean ‘whereby we perceive that a particular mathematical figure is [for example] a triangle.’ But this would rather be expressed by τοδὶ τὸ ἔσχατον, or τοδί alone.

4 That is, we reach the limit of analysis just as much when we descend to particulars as when we ascend to first principles or definitions (Burnet). Or the words may mean ‘in mathematics as in problems of conduct there is a point where analysis must stop.’

5 The intuition of particular facts which is a part of Prudence also belongs to the genus perception, but it is intellectual, not sensuous. The Greek may however conceivably mean, ‘But the intuition of the ultimate particular in problems of conduct approximates more to sensation than to prudence, though it is a different species from the perception of the separate senses.’

6 In the mss. the chapter begins with the sentence ‘But deliberation,’ etc., here transferred to the middle of 9.2.

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