Socrates now puts Protagoras's notion of virtue under pressure. In his exposition, Protagoras has stated "that justice, temperance, holiness and the rest were all but one single thing, virtue" (329c). Socrates proceeds to clarify this assertion through his characteristic dialectical method.
Virtue is made up of constituent parts that are different in function; possessing any single one does not entail possessing any other. Socrates then pushes Protagoras to accept an extreme version of this position: that the constituents of virtue—holiness, justice, and so on—are not just distinct, but completely unalike. This, however, entails that justice is not holy and that holiness is not just. Protagoras responds by noting that Socrates is being vague concerning how two things are "like" one another. That two things share some characteristics does not mean that they are synonymous, or even that they bear a significant resemblance to each other. The argument peters out inconclusively.
Socrates then attempts to prove that temperance and wisdom are identical (a somewhat more successful proof), and claims to have shown that holiness and justice are also identical (a claim that is, of course, untrue, although Protagoras fails to object). Finally, he attempts to show that justice is synonymous with temperance. In the course of this last argument, Protagoras expounds—in a relatively short speech—the doctrine that "good" is a relational quality. Something is "good" only insofar as it is good for a particular thing. But this discussion suddenly grinds to a halt, replaced by an argument about how the discussion itself should be conducted. Socrates objects to the mode of Protagoras's address; he wants Protagoras to respond with shorter answers. Protagoras declines to argue if Socrates is going to try to determine the form his answers must take, and Socrates declines to argue unless Protagoras refrains from giving long answers. Very conveniently claiming that he has an appointment, Socrates starts to leave.
Callias supports Protagoras's position; Alcibiades supports Socrates's. Prodicus, one of the other Sophists present, then gives an unintentionally comic speech, full of quibbles but ultimately to no purpose. Hippias, the third Sophist, grandiloquently urges a middle course: Protagoras should try to be concise, and Socrates should allow Protagoras some slack. An impartial chairman will regulate the length of the answers. Socrates assents to stay, proposing that first Protagoras can question him, after which he will question Protagoras. A chairman, he argues, will be unnecessary, for the audience combined can protest if Protagoras wanders from the point.
The fundamental concern about the proper form of philosophical argument (a concern that has lurked beneath the stated argument until this point) here breaks through to the surface, disrupting the discussion and even threatening to end it. Socrates's dialectic of question-and-answer and Protagoras's more decorous mode of exposition no longer seem to be simply alternative methods of arriving at the same goal. Rather, they seem to be actively antagonistic, and each character seems unwilling—or unable —to engage properly with the other. Socrates's cross-examination of Protagoras in the first part of this section constitutes a particularly rapid series of questions. Socrates is aiming to trap Protagoras by isolating fallacies in his reasoning. To do this, he endeavors to formulate a number of syllogisms in which Protagoras accepts the premises, but in which the conclusions are inconsistent with Protagoras's theory. But Socrates is not particularly successful here; his arguments rely on verbal slippage from one sense of a word to another (as Protagoras points out with Socrates's use of the word "like"). Further, the audience seems more impressed by Protagoras's refined and measured discourse than by Socrates's brief questions.
Nonetheless, in critiquing Protagoras's method, Socrates has managed to identify a promising track for further investigation. Protagoras places a great deal of argumentative significance on the concept of virtue, but has failed to examine what, precisely, he means by this term, or even to consider whether he uses the term consistently. Protagoras's favored argumentative mode of declamation allows him to skate over the weaknesses in his theories. Rather than carefully testing each link in a chain of deductive reasoning, Protagoras prefers to argue through grand rhetorical set pieces, swept up by the spirit of his own reasoning. At the close of Protagoras's long speech (the start of this section) Socrates confesses himself to be "still under his spell" (328d). This mesmeric quality of sophistry is a common theme in the Platonic dialogues. Plato implicitly critiques Sophistry by showing that being enthralled, or spellbound, is not a good state in which to think critically. The flaws in Socrates's argument are difficult to track because it moves so quickly; the flaws in Protagoras's argument are difficult to track because his rhetorical polish lulls the critical faculties. Should we therefore conclude that neither method of argument has real merit?
Again, this stalemate is only apparent; the explicit doctrines that Socrates advances here (that virtue is unified and indivisible) are of interest, but the real significance of this section lies in the breakdown of the discussion. At first reading, Socrates's response to Protagoras's long speech seems strange; Socrates states that he has been convinced, then begins to interrogate Protagoras as to whether virtue is a single, homogeneous quality, or whether it can be separated into different parts. The connection between this line of argument and Protagoras's exposition of the essentially social nature of virtue is not obvious, but Socrates's strategy can be deduced. His aim is to criticize Protagoras's claim that he can teach virtue. Protagoras's argument that virtue is required by all citizens and is therefore different from the types of wisdom assumed by other kinds of skill (techne), like flute-playing or shipbuilding, is not in question. Rather, Socrates hopes to drive a wedge between virtue and these more everyday types of wisdom. If virtue cannot be broken down into constituent parts, it becomes difficult to think of it as being deliberately built up from smaller elements. That is, if virtue is singular, then it becomes very difficult to claim to be able to instill it in other people. Socrates's search for the precise nature of virtue is not innocent, but rather is driven by a belief that sophistry teaches specious and harmful doctrines, not actual virtue.
Socrates does not believe that virtue cannot be acquired: rather, he is suspicious of those Sophists who claim that they can teach it. After all, Socrates himself claims in the Gorgias to be one of the few true practitioners of the civic arts (politike techne). The question then arises, however, as to exactly how virtue can be practiced in the political realm. The resolution in this section of the argument about how an argument should be conducted provides us with an answer to this question. There needs to be some form of control over what one can say in an argument. Otherwise the argument may too easily drift out of control. But this control must also be flexible; if it is inflexible, certain promising areas of discussion that might arise during the argument could be ruled out at the beginning. In giving his audience the final say in how the argument shall proceed, Socrates is adopting a remarkably democratic attitude, a position more consistent with Protagoras's argument that all people possess the civic virtues. Perhaps Socrates is not being ironic when he states that he has been convinced by Protagoras, after all.
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