[64] Plato, Philêbus, p. 54 D. ἡδονὴ εἴπερ γένεσίς ἐστιν, εἰς ἄλλην ἢ τὴν τοῦ ἀγαθοῦ μοῖραν αὐτὴν τιθέντες ὀρθῶς θήσομεν.
Other reasons why pleasure is not the Good.
Indeed we cannot reasonably admit that there is no Good in bodies and in the universe generally, nor anywhere except in the mind:— nor that, within the mind, pleasure alone is good, while courage, temperance, &c., are not good:— nor that a man is good only while he is enjoying pleasure, and bad while suffering pain, whatever may be his character and merits.[65]
[65] Plato, Philêbus, p. 55 B.
Distinction and classification of the varieties of Knowledge or Intelligence. Some are more true and exact than others, according as they admit more or less of measuring and computation.
Having thus (continues Sokrates) gone through the analysis of pleasures, distinguishing such as are true and pure, from such as are false and troubled — we must apply the like distinctive analysis to the various modes of knowledge and intelligence. Which varieties of knowledge, science, or art, are the purest from heterogeneous elements, and bear most closely upon truth? Some sciences and arts (we know) are intended for special professional practice: others are taught as subjects for improving the intellect of youth. As specimens of the former variety, we may notice music, medicine, husbandry, navigation, generalship, joinery, ship-building, &c. Now in all these, the guiding and directing elements are computation, mensuration, and statics — the sciences or arts of computing, measuring, weighing. Take away these three — and little would be left worth having, in any of the sciences or arts before named. There would be no exact assignable rules, no definite proportions: everything would be left to vague conjecture, depending upon each artisan’s knack and practice which some erroneously call Art. In proportion as each of these professional occupations has in it more or less of computation and mensuration, in the same proportion is it exact and true. There is little of computation or mensuration in music, medicine, husbandry, &c.: there is more of them in joinery and ship-building, which employ the line, plummet, and other instruments: accordingly these latter are more true and exact, less dependent upon knack and conjecture, than the three former.[66] They approach nearer to the purity of science, and include less of the non-scientific, variable, conjectural, elements.
[66] Plato, Philêbus, pp. 55-56.
Arithmetic and Geometry are twofold: As studied by the philosopher and teacher: As applied by the artisan.
But a farther distinction must here be taken (Sokrates goes on). Even in such practical arts as ship-building, which include most of computation and mensuration — these two latter do not appear pure, but diversified and embodied in a multitude of variable particulars. Arithmetic and geometry, as applied by the ship-builder and other practical men, are very different from arithmetic and geometry as studied and taught by the philosopher.[67] Though called by the same name, they are very different; and the latter alone are pure and true. The philosopher assumes in his arithmetic the exact equality of all units, and in his geometry the exact ratios of lines and spaces: the practical man adds together units very unlike each other — two armies, two bulls, things little or great as the case may be: his measurement too, always falls short of accuracy.[68] There are in short two arithmetics and two geometries[69] — very different from each other, though bearing a common name.
[67] Plato, Philêbus, p. 56 D-E. Ἀριθμητικὴν πρῶτον ἆρ’ οὐκ ἄλλην μέν τινα τὴν τῶν πολλῶν φατέον, ἄλλην δ’ αὖ τὴν τῶν φιλοσοφούντων; . . .