λογιστικὴ καὶ μετρητικὴ ἡ κατὰ τεκτονικὴν καὶ κατ’ ἐμπορικὴν τῆς κατὰ φιλοσοφίαν γεωμετρίας τε καὶ λογισμῶν καταμελετωμένων — πότερον ὡς μία ἑκατέρα λεκτέον, ἢ δύο τιθῶμεν;
Compare Aristotel. Ethic. Nikom. i. 7, p. 1098, a. 30.
[68] Plato, Philêbus, p. 56 D-E. οἱ μὲν γάρ που μονάδας ἀνίσους καταριθμοῦνται τῶν περὶ ἀριθμόν, οἷον στρατόπεδα δύο καὶ βοῦς δύο καὶ δύο τὰ σμικρότατα ἢ καὶ τὰ πάντων μέγιστα· οἱ δ’ οὐκ ἄν ποτε αὐτοῖς συνακολουθήσειαν, εἰ μὴ μονάδα μονάδος ἑκάστης τῶν μυρίων μηδεμίαν ἄλλην ἄλλης διαφέρουσάν τις θήσει.
[69] Plato, Philêbus, p. 57 D.
Dialectic is the truest and purest of all Cognitions. Analogy between Cognition and Pleasure: in each, there are gradations of truth and purity.
We thus make out (continues Sokrates) that there is a difference between one variety and another variety of science or knowledge, analogous to that which we have traced between the varieties of pleasure. One pleasure is true and pure; another is not so, or is inseparably connected with pain and non-pleasurable elements — there being in each case a difference in degree. So too one variety of science, cognition, or art, is more true and pure than another: that is, it is less intermingled with fluctuating particulars and indefinite accompaniments. A science, bearing one and the same name, is different according as it is handled by the practical man or by the philosopher. Only as handled by the philosopher, does science attain purity: dealing with eternal and invariable essences. Among all sciences, Dialectic is the truest and purest, because it takes comprehensive cognizance of the eternal and invariable — Ens semper Idem — presiding over those subordinate sciences which bear upon the like matter in partial and separate departments.[70]
[70] Plato, Philêbus, pp. 57-58.
Difference with Gorgias, who claims superiority for Rhetoric. Sokrates admits that Rhetoric is superior in usefulness and celebrity: but he claims superiority for Dialectic, as satisfying the lover of truth.
Your opinion (remarks Protarchus) does not agree with that of Gorgias. He affirms, that the power of persuasion (Rhetoric) is the greatest and best of all arts: inasmuch as it enables us to carry all our points, not by force, but with the free will and consent of others. I should be glad to avoid contradicting either him or you.
There is no real contradiction between us (replies Sokrates). You may concede to Gorgias that his art or cognition is the greatest and best of all — the most in repute, as well as the most useful to mankind. I do not claim any superiority of that kind, on behalf of my cognition.[71] I claim for it superiority in truth and purity. I remarked before, that a small patch of unmixed white colour was superior in truth and purity to a large mass of white tarnished with other colours — a gentle and unmixed pleasure, in like manner, to one that is more intense but alloyed with pains. It is this superiority that I assert for Dialectic and the other sister cognitions. They are of little positive advantage to mankind: yet they, and only they, will satisfy both the demands of intelligence, and the impulse within us, in so far as we have an impulse to love and strain after truth.[72]