Socrates concludes by professing his disinterested love of the truth, and remarks on the singular manner in which he and his adversary had changed sides. Protagoras began by asserting, and Socrates by denying, the teachableness of virtue, and now the latter ends by affirming that virtue is knowledge, which is the most teachable of all things, while Protagoras has been striving to show that virtue is not knowledge, and this is almost equivalent to saying that virtue cannot be taught. He is not satisfied with the result, and would like to renew the enquiry with the help of Protagoras in a different order, asking (1) What virtue is, and (2) Whether virtue can be taught. Protagoras declines this offer, but commends Socrates' earnestness and his style of discussion.

The Protagoras is often supposed to be full of difficulties. These are partly imaginary and partly real. The imaginary ones are (1) Chronological,—which were pointed out in ancient times by Athenaeus, and are noticed by Schleiermacher and others, and relate to the impossibility of all the persons in the Dialogue meeting at any one time, whether in the year 425 B.C., or in any other. But Plato, like all writers of fiction, aims only at the probable, and shows in many Dialogues (e.g. the Symposium and Republic, and already in the Laches) an extreme disregard of the historical accuracy which is sometimes demanded of him. (2) The exact place of the Protagoras among the Dialogues, and the date of composition, have also been much disputed. But there are no criteria which afford any real grounds for determining the date of composition; and the affinities of the Dialogues, when they are not indicated by Plato himself, must always to a great extent remain uncertain. (3) There is another class of difficulties, which may be ascribed to preconceived notions of commentators, who imagine that Protagoras the Sophist ought always to be in the wrong, and his adversary Socrates in the right; or that in this or that passage—e.g. in the explanation of good as pleasure—Plato is inconsistent with himself; or that the Dialogue fails in unity, and has not a proper beginning, middle, and ending. They seem to forget that Plato is a dramatic writer who throws his thoughts into both sides of the argument, and certainly does not aim at any unity which is inconsistent with freedom, and with a natural or even wild manner of treating his subject; also that his mode of revealing the truth is by lights and shadows, and far-off and opposing points of view, and not by dogmatic statements or definite results.

The real difficulties arise out of the extreme subtlety of the work, which, as Socrates says of the poem of Simonides, is a most perfect piece of art. There are dramatic contrasts and interests, threads of philosophy broken and resumed, satirical reflections on mankind, veils thrown over truths which are lightly suggested, and all woven together in a single design, and moving towards one end.

In the introductory scene Plato raises the expectation that a 'great personage' is about to appear on the stage; perhaps with a further view of showing that he is destined to be overthrown by a greater still, who makes no pretensions. Before introducing Hippocrates to him, Socrates thinks proper to warn the youth against the dangers of 'influence,' of which the invidious nature is recognized by Protagoras himself. Hippocrates readily adopts the suggestion of Socrates that he shall learn of Protagoras only the accomplishments which befit an Athenian gentleman, and let alone his 'sophistry.' There is nothing however in the introduction which leads to the inference that Plato intended to blacken the character of the Sophists; he only makes a little merry at their expense.

The 'great personage' is somewhat ostentatious, but frank and honest. He is introduced on a stage which is worthy of him—at the house of the rich Callias, in which are congregated the noblest and wisest of the Athenians. He considers openness to be the best policy, and particularly mentions his own liberal mode of dealing with his pupils, as if in answer to the favourite accusation of the Sophists that they received pay. He is remarkable for the good temper which he exhibits throughout the discussion under the trying and often sophistical cross-examination of Socrates. Although once or twice ruffled, and reluctant to continue the discussion, he parts company on perfectly good terms, and appears to be, as he says of himself, the 'least jealous of mankind.'

Nor is there anything in the sentiments of Protagoras which impairs this pleasing impression of the grave and weighty old man. His real defect is that he is inferior to Socrates in dialectics. The opposition between him and Socrates is not the opposition of good and bad, true and false, but of the old art of rhetoric and the new science of interrogation and argument; also of the irony of Socrates and the self-assertion of the Sophists. There is quite as much truth on the side of Protagoras as of Socrates; but the truth of Protagoras is based on common sense and common maxims of morality, while that of Socrates is paradoxical or transcendental, and though full of meaning and insight, hardly intelligible to the rest of mankind. Here as elsewhere is the usual contrast between the Sophists representing average public opinion and Socrates seeking for increased clearness and unity of ideas. But to a great extent Protagoras has the best of the argument and represents the better mind of man.

For example: (1) one of the noblest statements to be found in antiquity about the preventive nature of punishment is put into his mouth; (2) he is clearly right also in maintaining that virtue can be taught (which Socrates himself, at the end of the Dialogue, is disposed to concede); and also (3) in his explanation of the phenomenon that good fathers have bad sons; (4) he is right also in observing that the virtues are not like the arts, gifts or attainments of special individuals, but the common property of all: this, which in all ages has been the strength and weakness of ethics and politics, is deeply seated in human nature; (5) there is a sort of half-truth in the notion that all civilized men are teachers of virtue; and more than a half-truth (6) in ascribing to man, who in his outward conditions is more helpless than the other animals, the power of self-improvement; (7) the religious allegory should be noticed, in which the arts are said to be given by Prometheus (who stole them), whereas justice and reverence and the political virtues could only be imparted by Zeus; (8) in the latter part of the Dialogue, when Socrates is arguing that 'pleasure is the only good,' Protagoras deems it more in accordance with his character to maintain that 'some pleasures only are good;' and admits that 'he, above all other men, is bound to say "that wisdom and knowledge are the highest of human things."'

There is no reason to suppose that in all this Plato is depicting an imaginary Protagoras; he seems to be showing us the teaching of the Sophists under the milder aspect under which he once regarded them. Nor is there any reason to doubt that Socrates is equally an historical character, paradoxical, ironical, tiresome, but seeking for the unity of virtue and knowledge as for a precious treasure; willing to rest this even on a calculation of pleasure, and irresistible here, as everywhere in Plato, in his intellectual superiority.

The aim of Socrates, and of the Dialogue, is to show the unity of virtue. In the determination of this question the identity of virtue and knowledge is found to be involved. But if virtue and knowledge are one, then virtue can be taught; the end of the Dialogue returns to the beginning. Had Protagoras been allowed by Plato to make the Aristotelian distinction, and say that virtue is not knowledge, but is accompanied with knowledge; or to point out with Aristotle that the same quality may have more than one opposite; or with Plato himself in the Phaedo to deny that good is a mere exchange of a greater pleasure for a less—the unity of virtue and the identity of virtue and knowledge would have required to be proved by other arguments.

The victory of Socrates over Protagoras is in every way complete when their minds are fairly brought together. Protagoras falls before him after two or three blows. Socrates partially gains his object in the first part of the Dialogue, and completely in the second. Nor does he appear at any disadvantage when subjected to 'the question' by Protagoras. He succeeds in making his two 'friends,' Prodicus and Hippias, ludicrous by the way; he also makes a long speech in defence of the poem of Simonides, after the manner of the Sophists, showing, as Alcibiades says, that he is only pretending to have a bad memory, and that he and not Protagoras is really a master in the two styles of speaking; and that he can undertake, not one side of the argument only, but both, when Protagoras begins to break down. Against the authority of the poets with whom Protagoras has ingeniously identified himself at the commencement of the Dialogue, Socrates sets up the proverbial philosophers and those masters of brevity the Lacedaemonians. The poets, the Laconizers, and Protagoras are satirized at the same time.