Summary
Socrates argues that experts, who understand a field, and not rhetoricians, will make the important decisions in an assembly. If the city needs dockyards, the assembly should ask a builder how to proceed, for example. Gorgias counters that this is not true in real life. The dockyards were, in fact, constructed under the advice of rhetoricians. Gorgias maintains that no matter the field, the rhetorician will always win the opinion of the crowd over the relevant expert.
Acknowledging the potential for corruption this presents, Gorgias adds that the moral responsibility for the use of any knowledge is in the hands of the pupil, not the knowledge itself or the teacher. Using boxing as an example, Gorgias explains that a boxer who hits outside the ring does not make a case against his training, only his own moral deficiency. Finally, he advocates for the punishment for those who abuse their rhetorical skills.
Socrates insists that morality is also a sphere of expertise. If the province of rhetoric is morality, then how could a (good) rhetor be immoral? Gorgias claims that the pupil of rhetoric should learn or already know the difference between right and wrong, and should be moral as one who knows building is a builder. And so Socrates has exposed a contradiction: Gorgias suggested that rhetoric could be put to immoral use depending on the student's own morality, but now he says that a rhetorician can never be immoral, because he is an expert in morality. And an expert has complete understanding of his field.
Polus, student of Gorgias, defends his teacher by saying that Socrates steered Gorgias into this contradiction. Polus now asks Socrates for his definition of rhetoric, and Socrates defines it as a "knack" for "producing pleasure and gratification.” Polus would like to shift the conversation to ask why gratifying others is admirable, but Socrates begins a series of questions that distinguish between the pleasurable and the admirable. The merely pleasurable is flattery, and Gorgias pursues Socrates for a definition of it.
First, Socrates distinguishes between body and mind, both of which can either be truly healthy or only appear healthy. Second, he defines spheres responsible for the health of each: “Statesmanship” governs mind, exercise and medicine the body. The two components of statesmanship, legislature and administration of justice, correspond to exercise and medicine, respectively. Flattery interferes in each of these four areas by making pleasure appear to be health. The cook's ignorance of the medicinal qualities of food makes cookery a knack, not expertise.
Calling "knacks" irrational, Socrates says that, by contrast, the expert is rational and knows for certain what is good for his area of expertise. The doctor, for example, can correctly prescribe food. Just as cookery obscures nutritious value and ornamentation distracts from an unexercised body, sophistry confuses the legislature, and rhetoric interferes with the administration of justice.
Analysis
Again in this section, Socrates insists that arguments should not be taken personally. He claims to be “happy to have a mistake pointed out” because “there is nothing worse for a person, in my opinion, than holding mistaken ideas about the matters we’re discussing at the moment" (458b). The matter at hand is, of course, morality. For Socrates, morality is more than a question of personal or private happiness, as Gorgias and the sophists believe. For Socrates, to be truly happy you must be open to having your false beliefs corrected; and this can only happen if you are constantly in conversation with others.
Socrates insists that morality is an area of expertise: something you can gain knowledge about. Socrates rejects the idea that it is in any way a good thing that a skilled rhetorician could, say, beat a ship-builder in an argument about ship-building. When experts share their expertise, they improve the character of their audience. So someone trained in morality should be the one who has authority in a conversation about morals. Indeed, we can see the importance of moral instruction in the very situation of the dialogue. The people who gather round Socrates and his interlocutors testify to the importance of the conversation with their continued presence and attention; if they didn't expect to learn something—if they didn't consider Socrates and Gorgias to be experts—they would have no reason to listen to them.
So Gorgias' claim that rhetoric can get around the need for experts isn't holding up. Socrates presses him to define expertise. Gorgias and Socrates agree that an expert is what he knows: one who knows building is a builder, and one who knows morality is a moral person. In general, this view matches individual actions with relevant words to promote public understanding. At the same time, saying that the moral person is someone who does moral things is an inexact comparison to the cook, who we think of as one who cooks food. All you have to do to be a cook is to cook a meal. To be moral, however, is a life-long condition, one that can improve or worsen over time.
Throughout the dialogue, Socrates favors the kind of knowledge that is reached by talking with others. He rejects any knowledge or practice that manipulates appearances—like rhetoric, which teaches someone to sound like a good person, rather than be one—because it precludes the possibility of moral improvement, for the speaker as well as for the listener.