Classification of true and false — how Plato applies it to Cognitions.
The highest of these Cognitions is set apart as Dialectic or Ontology: the Object of which is, Ens or Entia, eternal, ever the same and unchangeable, ever unmixed with each other: while the corresponding Subject is, Reason, Intelligence, Wisdom, by which it is apprehended and felt. In this Science alone reside perfect Truth and Purity. Where the Objects are shifting, variable, mixed or confounded together, there Reason cannot apply herself; no pure or exact truth can be attained.[147] These unchangeable Entities are what in other dialogues Plato terms Ideas or Forms — a term scarcely used in the Philêbus.
[147] Plato, Philêbus, p. 59 C. ὡς ἢ περὶ ἐκεῖνα ἔσθ’ ἡμῖν τό τε βέβαιον καὶ τὸ καθαρὸν καὶ τὸ ἀληθὲς καὶ ὃ δὴ λέγομεν εἰλικρινές, περὶ τὰ ἀεὶ κατὰ τὰ αὐτὰ ὡσαύτως ἀμικτότατα ἔχοντα — ἢ δευτέρως ἐκείνων ὅ τι μάλιστά ἐστι ξυγγενές· τὰ δ’ ἄλλα πάντα δεύτερά τε καὶ ὕστερα λεκτέον. 62 A: φρονῶν ἄνθρωπος αὑτῆς περὶ δικαιοσύνης, ὅ, τι ἔστι, καὶ λόγον ἔχων ἑπόμενον τῷ νοεῖν … κύκλου μὲν καὶ σφαίρας αὐτῆς τῆς θείας τὸν λόγον ἔχων.
Though pure truth belongs exclusively to Dialectic and to the Objects thereof, there are other Sciences which, having more or less of affinity to Dialectic, may thus be classified according to the degree of such affinity. Mathematics approach most nearly to Dialectic. Under Mathematics are included the Sciences or Arts of numbering, measuring, weighing — Arithmetic, Metrêtic, Static — which are applied to various subordinate arts, and impart to these latter all the scientific guidance and certainty which is found in them. Without Arithmetic, the subordinate arts would be little better than vague guesswork or knack. But Plato distinguishes two varieties of Arithmetic and Metrêtic: one purely theoretical, prosecuted by philosophers, and adapted to satisfy the love of abstract truth — the other applied to some department of practice, and employed by the artist as a guide to the execution of his work. Theoretical Arithmetic is characterised by this feature, that it assumes each unit to be equal, like, and interchangeable with every other unit: while practical Arithmetic adds together concrete realities, whether like and equal to each other or not.[148]
[148] Plato, Philêbus, p. 56 E.
It is thus that the theoretical geometer and arithmetician, though not coming up to the full and pure truth of Dialectic, is nevertheless nearer to it than the carpenter or the ship-builder, who apply the measure to material objects. But the carpenter, ship-builder, architect, &c., do really apply measure, line, rule, &c.: they are therefore nearer to truth than other artists, who apply no measure at all. To this last category belong the musical composer, the physician, the husbandman, the pilot, the military commander, neither of whom can apply to their processes either numeration or measurement: all of them are forced to be contented with vague estimate, conjecture, a practised eye and ear.[149]
[149] Plato, Philêbus, p. 56 A-B.
Valuable principles of this classification — difference with other dialogues.
The foregoing classification of Sciences and Arts is among the most interesting points in the Philêbus. It coincides to a great degree with that which we read in the sixth and seventh books of the Republic, though it is also partially different: it differs too in some respects from doctrines advanced in other dialogues. Thus we find here (in the Philêbus) that the science or art of the physician, the pilot, the general, &c., is treated as destitute of measure and as an aggregate of unscientific guesses: whereas in the Gorgias[150] and elsewhere, these are extolled as genuine arts, and are employed to discredit Rhetoric by contrast. Again, all these arts are here placed lower in the scientific scale than the occupations of the carpenter or the ship-builder, who possess and use some material measures. But these latter, in the Republic,[151] are dismissed with the disparaging epithet of snobbish (βάναυσοι) and deemed unworthy of consideration.
[150] Plato, Gorgias, pp. 501 A, 518 A. Compare Republic, i. pp. 341-342.