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"Euclid the Megaren" from a wall panel in the Palazzo Ducale, Urbino. Dating from around 1474, it is almost certainly trying to show Euclid the mathematician, and is typical of the medieval confusion surrounding his identity.

Euclid of Megara, (also Euclides, Eucleides, Greek: Εὐκλείδης), (c. 435- c. 365 BC)^[1] was a Greek Socratic philosopher who founded the Megarian school of philosophy. He was a pupil of Socrates in the late 5th century BC, and was present at his death. He held the supreme good to be one, eternal and unchangeable, and denied the existence of anything contrary to the good. Editors and translators in the Middle Ages often confused him with Euclid of Alexandria when discussing the latter's Elements.

Life

Euclid was born in Megara,^[2] but in Athens he became a follower of Socrates. So eager was he to hear the teaching and discourse of Socrates, that when, for a time, Athens had a ban on any citizen of Megara entering the city, Euclid would sneak into Athens after nightfall, disguised as a woman to hear him speak.^[3] He is represented in the preface of Plato's Theaetetus as being responsible for writing down the conversation between Socrates and the young Theaetetus many years earlier. Socrates is also supposed to have reproved Euclid for his fondness for eristic disputes.^[4] He was present at Socrates' death (399 BC),^[5] after which Euclid returned to Megara, where he offered refuge to Plato and other frightened pupils of Socrates.^[6]

In Megara, Euclid founded a school of philosophy which became known as the Megarian school, and which florished for about a century. Euclid's pupils were said to have been Ichthyas,^[7] the second leader of the Megarian school; Eubulides of Miletus;^[8] Clinomachus;^[9] and Thrasymachus of Corinth.^[10] Thrasymachus was a teacher of Stilpo, who was the teacher of Zeno of Citium, the founder of the Stoic school.

Philosophy

None of Euclid's works have survived, the main source we have for his views is the brief summary by Diogenes Laërtius.^[11] Euclid's philosophy was a synthesis of Eleatic and Socratic ideas. He identified the Eleatic idea of "The One" with the Socratic "Form of the Good," which he called "Reason," "God," "Mind," "Wisdom," etc.^[12] This was the true essence of being, and was eternal and unchangeable.^[13] As he said, "The Good is One, but we can call it by several names, sometimes as wisdom, sometimes as God, sometimes as Reason,"^[14] and he declared, "the opposite of Good does not exist."^[14]

In logic, when attacking a demonstration, it was not the premises assumed but the conclusions that he attacked,^[15] which presumably means that he tried to refute his opponents by drawing absurd consequences from their conclusions.^[16] He also rejected argument from analogy.^[15] His doctrinal heirs, the Stoic logicians, inaugurated the most important school of logic in antiquity other than Aristotle's peripatetics.

Early Life

Euclid of Megara was born between 400 BC and 450 BC. Most sources record his birth in Megara, the capital of the Greek state of Megaris. Other sources report his birth to be in the city of Gela. As an adolescent and a young man, Euclid walked about forty kilometers to Athens in order to listen to the teachings of Socrates, a philosopher of the time. Euclid was so devoted to these teachings that when war prevented him from legally entering Athens under penalty of death, he wore a disguise and entered anyways in order to witness Socrates’s lectures. He also learned how to write disputations from the works of Parmenides and studied his writings very carefully. A distance between Socrates and Euclides grew as Euclides’ obsession with controversy annoyed Socrates.

Later Life

Euclid spent much of his young adulthood in Athens studying the teachings of Socrates and learning directly from him. He also studied Elaetic philosophy. After the death of Socrates, Euclid’s home became a sort of refuge and discussion center for those followers of Socrates who lost their inspirational figure and feared the wrath of Roman tyrants. After much studying and learning, some at home and some abroad, Euclid returned to Megara and began a Megarian School which combined both Socratic and Eleatic philosophy. The school focused on dialect as a way to explore and record it’s philosophy and Euclid himself wrote six of these dialogues though none survived. These diaglogues were named the Lamprias, the Aeschines, the Phoenix, the Crito, the Alcibiades, and the Amatory dialogue. These dialogues followed a pattern similar to those of Socrates. The school also focused on logic and created infamous paradoxes the Liars Paradox common today in logic education. This school had a profound affect on Stoic logic of the furture. Euclid also left behind many followers such as Eubulides of Miletus, Ichtyas, and Thrasymachus of Corinth. The latter further influenced philosophy as he was the teacher of Stilpo who in turn taught Zeno of Citium who founded a prominent Stoic School.

Death

Euclid’s death occurred is between 360 and 375 BC. He died as the leader of the Megarian school and left this leadership to Ichtyas who carried the school into a higher focus on logic and paradoxes and away from dialectical argument.

Euclid’s Philosophy and School

Euclid’s philosophy combined that of the Eleatic School of Philosophy and Socratic ideas. He used the ethical and philosophical teachings of the Eleatic school and mixed them with the Socratic ideal of using dialect and dialogue to teach and express these ideas as well as Socratic ideas of virtue. Socrates claimed that the greatest knowledge was understanding the good. The Eleatics claimed the greatest knowledge is the one universal Being of the world. Mixing these two ideas, Euclid claimed that good is the knowledge of this being. Therefore this good is the only thing that exists and has many names but is really just one thing. His main teaching was that the “good” is a single and universal being which has many names including wisdom, God, reason, prudence, Being, the One, intelligence, providence, divinity, justice, and mind. This teaching is draws greatly from the Eleatic ideal of a universal and unchanging good with many names as well as the teachings of Socrates. The idea of a universal good also allowed Euclid to dismiss all that is not good because he claimed that good covered all things on earth with it’s many names. The Socratic idea that knowledge is virtue and that the only way to understand the never-changing world is through the study of philosophy is another one which Euclid adopted. Euclid taught that virtues themselves, however, were simply the knowledge of the one good, or Being. Euclid was also extremely interested in concepts and dilemnas of logic. Euclid and his Megarian followers used dialogue and the eristic method to defend their ideas. The Eristic method allowed them to prove their ideas by disproving those of the one they were arguing with and therefore indirectly proving one’s own point. Euclid of Megara was the founder of the Megarian School which had great impact on philosophy of the time as well as later philosophy. It was a dialectic school with both educational and ethical goals. This school taught the use of language and dialect to further enhance and discuss the theories of Euclid of Megara. The school was also extremely focused on the topic of logic. The philosophers who first studied at this school developed ideas such as that of paradoxes. These included the paradox of liars which is commonly seen today. The Megarians who came from this school also created new philosophies or gave rise to new philosophies which developed from their students.

Main followers and their Teachings

Euclides left behind a lasting impression on the world of philosophy due to his followers and their effects on the world. One of these followers was Icthyas who was the second leader of the Megarian School. After Euclid’s death, Icthyas began leading the school. Another successor was Apollonius Cronus who then taught Diodorus Cronus. Diodorus did great work with propositional logic and his theories of conditionals and modalities were revolutionary. Another student of the Megarian School was Thrasymachus of Corinth. This philosopher taught Stilpo, a philospher who developed paradoxes such as the Lying One, the Veiled One, the Electra, the Sorites, the Bald One, the Horned One. Stilpo in turn served as the teacher of Zeno of Citium who was a Stoic logician who founded Stoic logic and a school of Stoic philosophy. Another extremely important successor of Euclid was Eubulides of Miletus. Eubulides was a student at the Megarian school and a contemporary of Aristotle whose methods and beliefs he greatly criticized. Eubulides specifically criticized Aristotle’s ideas of potentiality and instead believed that only present and current time is real. Eubulides did work with logic and furthered Megaric philosophy. He also further developed the use of dialect to prove his points. Another important part of Eubulides’s work was his founding of a philosophical school which was attended by many future philosophers. The followers of Eubulides included Euphantus of Olynthus, a member of Eubulides’s school and a philosopher who also wrote tragedies and history. Another successor of Eubulides was Alexinus of Elis who studied philosophy at Olympia and had an ongoing argument with his contemporary, Zeno.

Notes

^ "As a conjecture some scholars locate the life-span of Euclid between 435 and 365 BCE." Giovanni Reale, John R. Catan, (1987), A History of Ancient Philosophy, page 373. SUNY Press:
^ Diogenes Laërtius, ii. 106; Cicero, Academica, ii. 42; Aulus Gellius, vii. 10. 1-4; Plato, Phaedo, 59B-C; Strabo, ix. 1. 8; although, according to Diogenes Laërtius, others called him a native "of Gela, as Alexander states in his Successions of Philosophers"
^ Aulus Gellius, vii. 10. 1-4
^ Diogenes Laërtius, ii. 30
^ Plato, Phaedo, 59B-C
^ Diogenes Laërtius, ii. 106; iii. 6
^ Diogenes Laërtius, ii. 112
^ Diogenes Laërtius, ii. 108
^ Suda, Sokrates; cf. Diogenes Laërtius, ii. 112
^ Diogenes Laërtius, ii. 113
^ Diogenes Laërtius, ii. 106-8
^ Diogenes Laërtius, ii. 106; Cicero, Academica, ii. 42
^ Cicero, Academica, ii. 42
^ ^a ^b Diogenes Laërtius, ii. 106
^ ^a ^b Diogenes Laërtius, ii. 107
^ William Kneale, Martha Kneale, (1984), The Development of Logic, page 8. Oxford University Press

External links

Diogenes Laërtius, Life of Euclides

[1] "As a conjecture some scholars locate the life-span of Euclid between 435 and 365 BCE." Giovanni Reale, John R. Catan, (1987), A History of Ancient Philosophy, page 373. SUNY Press:

[2] Diogenes Laërtius, ii. 106; Cicero, Academica, ii. 42; Aulus Gellius, vii. 10. 1-4; Plato, Phaedo, 59B-C; Strabo, ix. 1. 8; although, according to Diogenes Laërtius, others called him a native "of Gela, as Alexander states in his Successions of Philosophers"

[3] Aulus Gellius, vii. 10. 1-4

[4] Diogenes Laërtius, ii. 30

[5] Plato, Phaedo, 59B-C

[6] Diogenes Laërtius, ii. 106; iii. 6

[7] Diogenes Laërtius, ii. 112

[8] Diogenes Laërtius, ii. 108

[9] Suda, Sokrates; cf. Diogenes Laërtius, ii. 112

[10] Diogenes Laërtius, ii. 113

[11] Diogenes Laërtius, ii. 106-8

[12] Diogenes Laërtius, ii. 106; Cicero, Academica, ii. 42

[13] Cicero, Academica, ii. 42

[laertius106-14] Diogenes Laërtius, ii. 106

[laertius107-15] Diogenes Laërtius, ii. 107

[16] William Kneale, Martha Kneale, (1984), The Development of Logic, page 8. Oxford University Press

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