The Protagoras is often read as a clash between rhetoric and philosophy, or as an early skirmish over the unity of virtue. Read more narrowly, it is a dialogue about what must be shown before a practice may count as teaching at all. Plato does not ask, in the abstract, whether virtue can be taught. He stages competing proofs. Protagoras offers a civic demonstration: punishment, schooling, poetry, and law already operate on the assumption that virtue is acquired. Socrates counters with a technical demand: if virtue is teachable, it must admit of a technē with reliable transmission and a knowledge-structure that explains right action. The dialogue turns on which proof carries the burden—and on whether courage can survive as a counterexample. Read this way, the Protagoras functions as a test case for teachability itself: cultural formation versus cognitive craft, enculturation versus measurement, practice versus account.

Issue

Whether “virtue” (esp. civic virtue) is teachable; whether the virtues form one knowledge or several parts (with courage as a test case); and what method—if any—counts as the technē by which virtue is taught.

Rule

A) Protagoras’ rules (myth → practice → program)

• Mythic rule (civic baseline): Zeus orders justice and shame to be given to all, or cities cannot exist; hence in political debate anyone may speak. Civic virtue is shared.
  
• Punishment rule (teachability presupposed): Reasonable punishment looks forward—to deter and correct—so communities act on the belief that virtue is acquired and taught (Athenians especially).
  
• Programmatic rule (the city’s technē): From early childhood through law, nurse–mother–tutor–father, then teachers, poets, music, athletics, and finally the laws that “correct,” the city teaches and trains citizens in justice and temperance.
  

B) Socrates’ rules (technē test → measurement → unity)

• Technē reliability test: If virtue were a teachable craft, those who have it would reliably produce learners. But many “good men” (e.g., Pericles) did not make their sons good; this gives prima facie doubt about a private craft of virtue-teaching.
  
• Measurement rule (hedonist setup): Right choice among near/far pleasures and pains demands an art of measurement; measurement is an art and knowledge. Knowledge rules when present; “being overcome by pleasure” is ignorance.
  
• Courage/unity rule: Cowardice is ignorance about what is and isn’t to be feared; its opposite—wisdom about that—is courage. On these steps the earlier claim “ignorant yet courageous” becomes impossible. If the virtues are knowledge, virtue is eminently teachable.
  

Application

A) Is virtue teachable?

Protagoras applies myth and practice: Because cities run on justice/temperance shared by all, and because laws punish to improve, the city already assumes teachability. He then details how the city teaches: constant correction at home; schooling in poets and music to shape character; athletics to prevent cowardice; and finally the laws as written patterns citizens must “trace,” with penalties as correction.

Socrates’ counter-case targets a different thing: a private craft with a track record (Pericles; “many more” who never made anyone better). He doesn’t refute teachability; he shifts the burden to show a craft. He then explicitly says he wavers and asks for clarification.

Inside the dialogue, Socrates rebuilds teachability on his own ground. He walks the group through the measurement proof: if we err by mismeasuring near vs. far goods, the savior is a knowledge that cancels deceptive appearances. On that basis, “being overcome by pleasure” = ignorance; self-control = wisdom. Protagoras and the others agree. This converts virtue into a kind of technē fit to be taught.

Result at this stage: Protagoras grounds teachability in the polis’ program; Socrates grounds it in knowledge-as-measurement. Both yield “teachable,” though they point to different means (cultural enculturation vs. cognitive craft).

B) What is courage, and are the virtues one?

Protagoras’ stance: virtues are parts; courage is unlike the rest. (He later pushes that confidence is not identical with courage.)
Socrates’ squeeze: He ties confidence in risky domains to knowledge and strips off “mad confidence” as not courage. He elicits stepwise concessions: cowardice = ignorance about what is to be feared; the opposite wisdom is courage. Protagoras, “on the basis of what we have agreed,” admits the earlier claim (“ignorant yet courageous”) is impossible.

Effect: The logic pulls courage under knowledge and pressures the unity thesis. Socrates names the turn: if justice, temperance, courage are all knowledge, virtue is eminently teachable; if virtue is anything other than knowledge (Protagoras’ original line), it would be unteachable.

C) Where is the technē?

Protagoras’ answer in-text: The city has a distributed technē of formation: family correction; teachers and poets instilling order; music and rhythm drilling character; athletics for spirited steadiness; and laws that act as copy-books citizens must trace, backed by correction. This is why “everyone teaches” and why Protagoras can promise “better day by day.”

Socrates’ answer in-text: A cognitive technē—the art of measurement—is the thing that explains right action and improvement. Once present, knowledge rules; akrasia is miscalculation. That is a teachable object.

Tension resolved (narrowly, within this dialogue): The two technai can align: the city’s program aims to inculcate the very judgment Socrates models. The dialogue stops short of fusing them, but it shows how both roads yield “teachable.”

D) What about the “great men and their sons”?

The text itself answers it: even where fathers are good, uneven outcomes follow in every field; yet the city still teaches everyone, and would exile or execute only the incorrigible. Failures do not undercut the civic technē, which targets a baseline needed for a city.

Conclusion

Holding (as far as the text goes): Socrates says the discussion has “turned on us”: if virtue is knowledge, it is eminently teachable; if it is not knowledge (as Protagoras also tries to maintain), it would be unteachable. The dialogue ends with this pivot stated, not finally settled.

Teachability: On Protagoras’ civic terms, virtue is taught by all, from cradle to lawcourt; punishment and pedagogy presume improvability. On Socrates’ cognitive terms, if action hinges on measurement, virtue is knowledge and thus teachable. Both paths yield “teachable,” though they frame the craft differently.

Content of virtue: The dialogue’s pressure case (courage) brings Protagoras to accept, on agreed steps, that courage = wisdom about what to fear, collapsing the earlier “ignorant yet courageous” line. This leans toward the unity of virtue as knowledge.