Protagoras's Paradox


Joshua J. Mark
published on 18 January 2012
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The Sophists in ancient Greece were a class of teachers who, for a sometimes fairly high fee, would instruct the affluent youth in politics, history, science, law, mathematics and rhetoric as well as the finer points of grammar and history.  They professed to be able to make a young man suitable for political office and, of equal importance among the litigious Greeks of the time (especially in Athens) to be able to make a strong case, whether in prosecution or defense, in court. The Sophists roamed from city to city giving lectures, taking on pupils, and debating topics publicly (this last, perhaps, as advertisement for their skills in oratory and disputation. In Plato’s Republic, Book I, for example, the Sophist Thrasymachus debates Socrates on the meaning of `Justice’, claiming it is only the advantage of the stronger, and does so in a semi-public forum, a gathering at the house of Cephalus).  Once they accepted a youth as a student the Sophists would charge dearly for their instruction and were “ the first in Greece to take fees for teaching wisdom. Though not disgraceful in itself, the wise men of Greece had never accepted payment for their teaching” (Encyclopedia of Philosophy). Plato, of course, is well known for his criticism and disparagement of the Sophists on this very point.

Democritus & Protagoras
Democritus & Protagoras
by Hermitage Museum (Public Domain)

The man named as the first Sophist, and certainly the most famous, was Protagoras of Abdera (c.485-415 BCE) best known for his claim that “Man is the Measure of All things” and that the gods’ existence could neither be proven nor disproven. While Protagoras, like those who followed him, charged exorbitant fees for his services, a story is told of how the great Sophist was once outsmarted by one of his pupils and this tale has come to be known as Protagoras’s Paradox.

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Protagoras agreed to instruct a poor young man, Euthalos (from a working-class family) in law and rhetoric free of charge on the condition that he would pay the Sophist’s fee in full if, and only if, he won his first court case. Once Euthalos had completed his course of study with Protagoras he assiduously avoided taking any cases at all. Protagoras, finally out of patience with the young man, took him to court for payment and argued thusly: “ If I win this case, Euthalos will have to pay me what he owes me. If I do not win this case then Euthalos will still have to pay me because, under our agreement, he will then have won his first court case. Therefore, no matter what the outcome, Euthalos will have to pay me.” Euthalos, however, contested this claim, stating, “If I win this case I will not have to pay Protagoras, as the court has declared his case invalid. If I do not win this case I still do not have to pay as I will then have not won my first court case. Therefore, no matter what, I do not have to pay.”

This argument (for which no solution was ever offered in antiquity) has come to be known as the Paradox of The Court (L. Alqvist) and a resolution to the question is still debated today in law schools as a logic problem.

Editorial Review This article has been reviewed for accuracy, reliability and adherence to academic standards prior to publication.
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  • Sophists [Internet Encyclopedia of Philosophy]Accessed 1 Dec 2016.
  • B. Jowett. The Dialogues of Plato. 1937
  • L. Alqvist. `Deontic Logic' in Handbook of Philosophical Logic. 1984
  • Thomas Mautner. The Penguin Dictionary of Philosophy. 2000


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About the Author

Joshua J. Mark
A freelance writer and former part-time Professor of Philosophy at Marist College, New York, Joshua J. Mark has lived in Greece and Germany and traveled through Egypt. He has taught history, writing, literature, and philosophy at the college level.

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Cite This Work

APA Style

Mark, J. J. (2012, January 18). Protagoras's Paradox. Ancient History Encyclopedia. Retrieved from

Chicago Style

Mark, Joshua J. "Protagoras's Paradox." Ancient History Encyclopedia. Last modified January 18, 2012.

MLA Style

Mark, Joshua J. "Protagoras's Paradox." Ancient History Encyclopedia. Ancient History Encyclopedia, 18 Jan 2012. Web. 28 Sep 2020.

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