The Timpson Lyceum · History of Philosophy (2024)

Prodicus and Thrasymachus: Starting the Republic – Lecture 14 (History of Philosophy)

Overview

This lecture closes out the sophists and opens Plato's Republic. After recapping Protagoras ("man is the measure of all things") and Gorgias (the radical nihilist-skeptic: nothing exists; if it did we could not know it; if we knew it we could not communicate it), it profiles two lesser figures — Prodicus of Ceos, the pioneer of precise terminology, and Thrasymachus of Chalcedon, from whom we inherit the stock sophistic slogan "might makes right." The sophists were not a school but freelance professional teachers who, for a fee, trained ambitious young men in persuasion (rhetoric) — the master skill in a democracy where offices, lawsuits, and public standing were all won by swaying the assembled crowd.

Thrasymachus is the hinge into the Republic. Its opening book is widely read as a near-portrait of the historical Socrates cross-examining a sophist, before the later books turn Socrates into a mouthpiece for Plato's own philosophy. Book I stages a search for a definition of justice, marching through three proposals — Cephalus, Polemarchus, and finally Thrasymachus' provocative claim that justice is the advantage of the stronger — and then, when Thrasymachus withdraws, Glaucon revives the challenge with the social-contract origin of justice, the Ring of Gyges, and the contrast of two extreme lives. This sets the agenda for the whole dialogue: to show that the just life is superior to the unjust in itself, not merely for its rewards.

Key Concepts

• Sophists — Traveling professional teachers (not a unified school) who charged fees to instruct the youth in rhetoric and practical success. Broadly relativists and skeptics: no objective truth, beauty, or reality; everything is "in the eye of the beholder."
• Persuasion as the core product — In a direct democracy, political power and legal self-defense are won by convincing the mob. The sophists sold exactly this skill, which is why wealthy families paid so richly for it.
• Protagoras — First to call himself a sophist. Signature doctrine: "Man is the measure of all things — of the things that are, that they are, and of the things that are not, that they are not," i.e., truth is relative to the perceiver.
• Gorgias — Pushed skepticism to its limit in three theses: (1) nothing exists; (2) even if something exists, it cannot be known; (3) even if it could be known, it could not be communicated to another.
• Prodicus of Ceos — A sophist and ambassador for his island who frequented Athens (its wealth and students). Viewed the sophist as occupying a middle ground between the statesman (concerned only with the practical) and the philosopher (lost in the theoretical).
• Correct terminology (Prodicus) — Famous for insisting on the exact connotation and etymology of words — e.g., warning against calling something "terribly good" because terrible carries a negative charge. This concern with what words precisely mean helped pave the road for Socrates' later demand for definitions.
• Definition vs. usage — At this stage one could ask only how people use a word (a rough, dictionary-style report of common usage); the notion of pinning down a word's precise essence or definition was not yet current. Socrates would make that demand central.
• Prodicus on the gods — Held that things necessary and beneficial to humankind were deified — wine became Dionysus, grain Demeter, and so on — which earned him a reputation for atheism. In that culture, charging an opponent with atheism was a standard way to turn the mob against him.
• Thrasymachus of Chalcedon — Sophist who spent his career in Athens; associated with the study of delivery — gesture and the arousal of emotion (pathos) in the audience. Source of the enduring picture of the sophistic view of politics.
• "Might makes right" — Thrasymachus' thesis that justice is nothing other than the advantage of the stronger: the ruling power in any state makes laws to serve its own interest, and calls obedience to those laws "justice."
• Republic Book I setting — Socrates, returning from a festival at the Piraeus (Athens' harbor), is drawn to the house of the wealthy metic Cephalus, where a crowd (including sophists) has gathered. The public, conversational stage is exactly where a sophist hopes to win students by besting the famous Socrates.
• The three definitions of justice — (1) Cephalus: essentially telling the truth and paying what is owed; refuted by the case of returning a weapon to a friend gone mad. (2) Polemarchus (from the poet Simonides): rendering each his due — good to friends, harm to enemies; refuted because justice, like any craft, can only improve its object, never harm. (3) Thrasymachus: the advantage of the stronger.
• The craft (technē) analogy — Every art aims at the good of its subject, not itself: horsemanship benefits horses, medicine the patient, navigation the crew. Applied "in the strict sense," a true ruler therefore serves the ruled (the weaker), inverting Thrasymachus' thesis into "justice is the advantage of the weaker."
• Glaucon's three classes of goods — Goods desired (a) for their own sake alone (e.g., harmless pleasure), (b) for their consequences alone (e.g., medicine, exercise), (c) for both (the class Socrates must prove justice belongs to). The sophists place justice in class (b): nobody wants to be just, only to enjoy others' being just.
• Social-contract origin of justice — Glaucon's account: since suffering injustice outweighs the gain of committing it, people covenant neither to harm nor be harmed. Justice is thus a grudging compromise, practiced "against the will, of necessity."
• Ring of Gyges — A shepherd's ring of invisibility lets him kill the king and seize the throne. The thought experiment argues that no one, just or unjust, could resist using such power — so justice is practiced only for lack of impunity.
• The two lives — The perfectly unjust man who seems perfectly just (reaping wealth, power, honor, and allies) versus the perfectly just man who seems perfectly unjust (reviled, ruined, tortured, and killed). Glaucon demands Socrates prove the just life still superior — the challenge that launches the rest of the Republic.

Worked Example

Socrates' first refutation of Thrasymachus. Thrasymachus is pressed to specify what "the advantage of the stronger" means: in any state, the ruling power makes the laws, and justice is obeying those laws. Socrates then extracts a contradiction from the ruler's fallibility. The argument can be regimented in predicate logic.

Let the domain be possible actions by a subject, and define three predicates:

• $J(a)$ — action $a$ is just;
• $A(a)$ — action $a$ is to the advantage of the stronger (the ruler);
• $O(a)$ — action $a$ obeys an enacted law.

1. Thrasymachus' thesis (T). Justice just is serving the stronger's advantage: $\;\forall a\,\big(J(a) \leftrightarrow A(a)\big)$.
2. Obedience premise (from his own gloss). Whatever obeys the ruler's law is just: $\;\forall a\,\big(O(a) \rightarrow J(a)\big)$. Thrasymachus grants this — it is why following the law counts as justice.
3. Fallibility premise. Rulers sometimes err about their own interest and so enact laws contrary to it. Hence some act of law-obedience fails to serve the stronger: $\;\exists a\,\big(O(a) \land \neg A(a)\big)$. Thrasymachus concedes rulers can make mistakes.
4. From premise 3, fix a witness $a_0$ with $O(a_0) \land \neg A(a_0)$.
5. From premise 2 (instantiated at $a_0$) and $O(a_0)$: by modus ponens, $J(a_0)$.
6. From the thesis T (instantiated at $a_0$), $J(a_0) \rightarrow A(a_0)$; with $J(a_0)$ from step 5, modus ponens yields $A(a_0)$.

But step 4 also gives $\neg A(a_0)$. The derivation collects a contradiction:

$O(a_0) \land \neg A(a_0),\quad O(a_0)\to J(a_0),\quad J(a_0)\to A(a_0)\;\;\vdash\;\; A(a_0)\land\neg A(a_0)\;\equiv\;\bot.$

Since premises 2 and 3 are both granted, the only assumption free to fall is the thesis. Discharging it,

$\{\,\forall a(O(a)\to J(a)),\;\exists a(O(a)\land\neg A(a))\,\}\;\vdash\;\neg\,\forall a\big(J(a)\leftrightarrow A(a)\big).$

Justice cannot be identified with the advantage of the stronger: obeying an erroneous law is still just, yet runs against the stronger's advantage. $\blacksquare$

(Thrasymachus escapes only by retreating to the ruler "in the strict sense" who never errs — whereupon Socrates deploys the craft analogy to show that such a ruler, like every craftsman, serves his subjects, so justice becomes the advantage of the weaker.)

Summary

• The sophists were fee-charging teachers of rhetoric, the decisive skill in Athenian democratic and legal life; Prodicus refined the study of exact word-meaning, and Thrasymachus supplied the slogan "might makes right."
• Prodicus' focus on connotation, etymology, and precise usage prefigures Socrates' insistence on definitions; his view that gods are deified human benefits earned him an atheism charge.
• Republic Book I searches for a definition of justice, refuting Cephalus (paying debts) and Polemarchus (help friends, harm enemies) before confronting Thrasymachus' justice = advantage of the stronger.
• Socrates refutes Thrasymachus by his fallibility (rulers err, so obeying law can oppose the stronger's interest) and by the craft analogy (every art serves its subject), turning the thesis into "advantage of the weaker."
• Glaucon re-launches the challenge with the social-contract origin of justice, the Ring of Gyges, and the contrast of the seemingly-just unjust man against the seemingly-unjust just man — setting the Republic's central task of vindicating justice for its own sake.