Parmenides First published Fri Feb 8, 2008; substantive revision Sun Jun 3, 2012 Parmenides of Elea, active in the earlier part of the 5th c. BCE, authored a difficult metaphysical poem that has earned him a reputation as early Greek philosophy's most profound and challenging thinker. His philosophical stance has typically been understood as at once extremely paradoxical and yet crucial for the broader development of Greek natural philosophy and metaphysics. He has been seen as a metaphysical monist (of one stripe or another) who so challenged the naïve cosmological theories of his predecessors that his major successors among the Presocratics were all driven to develop more sophisticated physical theories in response to his arguments. Parmenides
Eleatic School

First published Mon Oct 21, 2002; substantive revision Fri Feb 21, 2014 Xenophanes of Colophon was a philosophically-minded poet who lived in various parts of the ancient Greek world during the late 6th and early 5th centuries BCE He is best remembered for a novel critique of anthropomorphism in religion, a partial advance toward monotheism, and some pioneering reflections on the conditions of knowledge. Many later writers, perhaps influenced by two brief characterizations of Xenophanes by Plato (Sophist 242c–d) and Aristotle (Metaphysics 986b18-27), identified him as the founder of Eleatic philosophy (the view that, despite appearances, what there is is a changeless, motionless, and eternal ‘One’). In fact, the Xenophanes who emerges from the surviving fragments defies simple classification. He was a travelling rhapsode who criticised the stories about the gods told by the poets, and he defended a novel conception of the divine nature. Xenophanes Xenophanes
Empedocles

Zeno's Paradoxes Zeno's Paradoxes First published Tue Apr 30, 2002; substantive revision Fri Oct 15, 2010 Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Since Socrates was born in 469 BC we can estimate a birth date for Zeno around 490 BC. Beyond this, really all we know is that he was close to Parmenides (Plato reports the gossip that they were lovers when Zeno was young), and that he wrote a book of paradoxes defending Parmenides' philosophy. Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators (here I have drawn particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book).
Xenophanes of Colophon