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The Athenians had forbidden the Megarans to enter their region on pain of death. Euclid of Megara, a friend and student of Socrates, didn't let that keep him from visiting his teacher. He went at night, clothed in gaudy women's clothing, from Megara to Athens, and in the morning, before it was day, went his 20,000 steps back home again. (Moses Mendelssohn THE LIFE AND CHARACTER OF SOCRATES)

Euclid (or Eucleides) of Megara, a Greek Socratic philosopher who lived around 400 BC, founded the Megarian school of philosophy. Editors and translators in the Middle Ages often confused him with Euclid of Alexandria when discussing the latter's Elements. Most modern translations of Plato's Theaetetus render his name "Euclides."

The Megaric sect was instituted by Euclides of Megara, and took its name from the place which gave birth to its founder. From its disputatious character, it also received the appellation of Eristic ( Eristiki, from erizein, " to contend") ; and it was likewise termed the Dialectic, not because it gave rise to dialectics or logical debates, which had before this time exercised the ingenuity of philosophers, particularly in the Eleatic school, but because the discourses and writings of this class of philosophers commonly took the form of a dialogue.

Euclides was a native of Megara, the capital of the district of Megaris. According to some less probable accounts, he was born at Gela, in Sicily. He was one of the chief disciples of Socrates, but, before becoming such, he had studied the doctrines, and especially the dialectics of the Eleatics. Socrates on one occasion reproved him for his fondness for subtle and captious disputes. On the death of Socrates, Euclides, with most of the other pupils of that philosopher, took refuge in Megara, and there established a school which distinguished itself by the cultivation of dialectics. The doctrines of the Eleatics formed the basis of his philosophical system. With these he blended the ethical and dialectical principles of Socrates. The Eleatic dogma, that there is one universal, unchangeable existence, he viewed in a moral aspect, calling this one existence the Good, but giving it also other names (as Reason, Intelligence, etc.), perhaps for the purpose of explaining how the real, though one, appeared to be many. He rejected demonstration, attacking not so much the premises assumed as the conclusions drawn, and also reasoning from analogy. He is said to have been a man of a somewhat indolent and procrastinating disposition. Euclides was the author of six dialogues, no one of which, however, has come down to us. He has frequently been erroneously confounded with the mathematician of the same name.

Euclides introduced new subtleties into the art of disputation, several of which, though often mentioned as examples of great ingenuity, deserve only to be remembered as proofs of egregious trifling. Of these sophistical modes of reasoning, called by Aristotle Eristic syllogisms, a few examples may suffice. 1. The Lying sophism : If, when you speak the truth, you say, you lie, you lie : but you say you lie, when you speak the truth ; therefore, in speaking the truth, you lie. 2. The Occult : Do you know your father ? Yes. Do you know this man who is veiled ? No. Then you do not know your father, for it is your father who is veiled.

3. The Sorties : Is one grain a heap ? No. Two grains ? No. Three grains ? No. Go on, adding one by one ; and, if one grain be not a heap, it will be impossible to say what number of grains make a heap.

In such high repute were these silly inventions for perplexing plain truth, that Chrysippus wrote six books upon the first of these sophisms ; and Philetas, a Coan, died of consumption, which he had contracted by the close study that he had bestowed upon it.

Euclides' 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. This was the true essence of being, and was eternal and unchangeable. As he said, "The Good is One, but we can call it by several names, sometimes as wisdom, sometimes as God, sometimes as Reason," and he declared, "the opposite of Good does not exists." While these doctrines may appear to contradict empirical reality, he argued that, since non-being cannot exist without becoming a species of being (i.e., no longer "non-being"), and since the essence of Being is the Good, the opposite of the Good cannot exist. His doctrinal heirs, the Stoic logicians, inaugurated the most important school of logic in antiquity other than Aristotle's peripatetics.

Euclides had three important pupils: Eubulides of Miletus, Ichtyas – the second leader of the Megarian school – and Thrasymachus of Corinth. This last one was the master of Stilpo, who was the master of Zeno of Citium, the founder of the stoic school.

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