The Timpson Lyceum · History of Philosophy (2024)

Protagoras: The First Sophist – Lecture 12 (History of Philosophy)

Overview

Protagoras of Abdera (c. 490–420 BC) — from the same city as the atomists — is the first man to call himself a sophist and the founder of the skeptical, relativist current that defines the movement. Well connected in Athens, which he visited several times, he moved in the circle of Pericles; late in life he was reportedly charged with impiety and his books burned. Our richest portrait of him is Plato's dialogue Protagoras, a staged encounter with Socrates on the teachability of virtue — the course's first real taste of the Socratic method (dialectic) and of the clash between rhetoric-for-hire and reasoned inquiry.

Two things anchor the lecture. First, the Protagoras dialogue itself: young Hippocrates begs Socrates to introduce him to the visiting sophist; Protagoras boasts he can teach virtue (political excellence), and Socrates — initially doubting virtue can be taught at all — turns the conversation to whether the virtues (justice, temperance, courage, wisdom, holiness) are one thing or many, walking Protagoras step by step toward the unity of the virtues. Second, Protagoras' own doctrine, compressed in the famous homo mensura: "Man is the measure of all things." There is no objective, absolute reality; things are however each person measures them — the philosophical charter of relativism that Plato would later dismantle with the peritropē (self-refutation) argument.

Key Concepts

Protagoras of Abdera — First self-styled sophist; associate of Pericles; teacher of rhetoric and aretē; his works were reportedly burned on an impiety charge. Chief source: Plato's Protagoras.
"Man is the measure of all things" (homo mensura) — Full form: "of the things that are, that they are; of the things that are not, that they are not." Truth and being are relative to the individual perceiver; there is no perceiver-independent fact of the matter.
Agnosticism about the gods — "Concerning the gods I cannot know whether they exist or not, nor what they are like; the obscurity of the subject and the shortness of human life prevent it." A hallmark skeptical stance (agnostic, not atheist) — and a pretext for the impiety charge.
Antilogic (dissoi logoi) — "On every matter there are two logoi (arguments) opposed to each other." Any thesis can be argued equally well from both sides, so no one side can claim objective truth — the theoretical license for teaching students to argue either side.
The breeze and the water — Illustrations of relativism: the same breeze feels warm to one just out of a pool, cool to one who has been running; water of one temperature feels cold to a hot hand and warm to a cold hand. There is no "really" — it is warm for you now, cold for me now.
Assault on non-contradiction — To call opposite statements about the same thing simultaneously true attacks the law of non-contradiction. Aristotle's rebuttal: if contradictions were allowed, everything would be identical to everything (a man = a wall = a trireme), collapsing all thought into nonsense.
The Protagoras dialogue — Socrates is petitioned by young Hippocrates to secure Protagoras as a teacher; the exchange, set in a wealthy host's hall before rival sophists, showcases Protagoras' self-image and introduces Socrates.
Can virtue be taught? — Socrates' doubts: (1) in the assembly, technical questions defer to experts, but on matters of state everyone speaks freely — as if political virtue had no experts and could not be taught; (2) good men (e.g., a Marcus Aurelius) often have bad sons (a Commodus), which teachable skills should not produce.
Protagoras' reply — Everyone does possess political virtue (else society and law-courts could not function); we punish injustice for deterrence, which presupposes virtue can be improved; virtue is taught the way a native language is — by everyone, all the time. He is merely slightly better at it than others.
The five virtues — Justice, temperance, courage, wisdom, holiness (piety). The first four are the cardinal virtues, perennial in later philosophy. The dialogue asks whether these are parts of one whole or merely names of a single thing.
Unity of the virtues — Socrates argues each virtue reduces to the others: since a thing has exactly one opposite, and folly is the opposite of both wisdom and temperance, wisdom and temperance must be identical; parallel arguments link justice–holiness and, finally, courage–wisdom.
Socratic method / dialectic — Truth pursued by question and short answer, each admission forcing the next, until the interlocutor is led to the intended conclusion — the opposite of the sophist's set-piece long speech (makrologia), which Protagoras retreats into when cornered.
The role-reversal ending — Socrates, who began denying virtue is teachable, ends arguing virtue is knowledge (hence teachable); Protagoras, who sells virtue as teachable, ends resisting its reduction to knowledge — each has swapped sides, and the aporia is left open.

Worked Example

Plato's peritropē (self-refutation) of Protagorean relativism. Take homo mensura at face value and turn it on itself. Let $M(x, p)$ mean "proposition $p$ is true for person $x$ ," and let Protagoras' thesis be

$P:\ \forall x\,\forall p\,\big(M(x,p) \leftrightarrow p\text{ seems true to }x\big),$

i.e., whatever seems so to a person is so for that person, with no further, absolute fact beyond the seeming.

Protagoras is committed to $P$ as true — not merely true-for-himself, but as the doctrine he teaches to everyone. Call his own perceiver $a$ (the sophist): $M(a, P)$ .
Introduce a dissenter. Let person $b$ be an anti-relativist to whom it seems that $P$ is false — that some truths hold absolutely. Then by $P$ 's own rule applied to $b$ : $M(b, \neg P)$ , i.e., $\neg P$ is true for $b$ .
Protagoras must grant the dissenter's judgment. $P$ says every person's seeming is authoritative for that person. So Protagoras is obliged to concede that $\neg P$ is genuinely true for $b$ : he cannot dismiss $b$ 's measurement without abandoning $P$ .
Count the verdicts. We now have, by Protagoras' own principle, both $M(a, P)$ and $M(b, \neg P)$ . Protagoras holds $P$ true; nearly everyone else holds $\neg P$ true — and $P$ certifies each of these as correct for its holder.
The turn. Since $P$ ratifies the dissenters' judgment that relativism is false, $P$ entails that $\neg P$ is true (for those who so measure). Schematically:

$P \;\rightarrow\; M(b, \neg P) \;\rightarrow\; \neg P \text{ is (relatively) true.}$

By its own logic, $P$ underwrites the truth of its own negation — while $\neg P$ never underwrites $P$ . 6. Conclusion. The doctrine "man is the measure" cannot exempt itself from the universal relativity it proclaims: applied consistently, it licenses and even asserts its own falsehood, so it cannot stand as an unrestricted truth. $\neg P$ survives; $P$ does not. $\blacksquare$

Summary

Protagoras of Abdera, the first self-named sophist and associate of Pericles, is the founder of Greek relativism; Plato's Protagoras is the key source.
"Man is the measure of all things" denies objective, absolute reality: things are as each person measures them, supported by the breeze/water illustrations and the doctrine of two opposed arguments on every question.
Treating opposite claims as jointly true attacks non-contradiction, which (per Aristotle) would make everything identical to everything — reducing thought to nonsense.
In the dialogue, Socrates doubts virtue can be taught; Protagoras answers that everyone shares political virtue and it is taught like a native tongue — and the debate turns to whether the five virtues are one, previewing the Socratic method.
Plato's peritropē shows homo mensura to be self-refuting: consistently applied, it ratifies the truth of its own denial, so relativism cannot coherently assert itself as the truth.