Not the Geometer: A Name Two Men Share

For centuries, medieval scholars confused two Greek men named Euclid who lived roughly a century apart and had nothing philosophically in common beyond the accident of sharing a name. Euclid of Megara, born around 435 BCE, was a companion of Socrates present, according to Plato's Phaedo, at his execution in 399 BCE, and afterward founded a school at his native Megara that fused Socratic ethics with the Eleatic doctrine that being is one and unchanging, arguing that the good itself is a single unified reality that goes by many names, wisdom among them, and that its supposed opposite has no real existence at all. Euclid of Alexandria, the mathematician who wrote the Elements roughly a century later and gave the Western world its model of geometric proof, is an entirely distinct figure with no connection to Megara or to Socrates. The confusion is old enough to have a name of its own: medieval manuscripts and commentators sometimes styled the mathematician Megarensis, as though he were the Megarian philosopher, an error modern scholarship has fully untangled but which still surfaces in casual references to Euclid. The philosopher's own writings, a set of Socratic dialogues, have not survived, and what is known of Megarian philosophy after him comes chiefly through his successors, Eubulides and later Stilpo, whose sharp logical puzzles and dialectical arguments fed directly into the development of Stoic logic a generation afterward.