The Logical Puzzles the Megarians Left Behind

Under Euclid of Megara's successors, particularly Eubulides of Miletus in the fourth century BCE, the Megarian school became known less for a positive doctrine than for a set of logical puzzles that still trouble philosophers of language and logic today. The liar paradox asks what to make of a sentence that says only that it is itself false, since if the sentence is true then it is false, and if it is false then it is true, an apparent contradiction that later logicians would spend over two thousand years trying to resolve without success that satisfies everyone. The sorites, or heap, paradox asks how many grains of sand can be removed one at a time from a heap before it stops being a heap, since removing a single grain never seems to make the difference, yet a single grain is plainly not a heap, a puzzle about vague language that remains an active area of philosophical logic. The Megarians also debated the nature of possibility itself, with Euclid's successor Diodorus Cronus arguing for a strict position, sometimes called the master argument, that only what actually happens was ever really possible, against which the Stoic philosopher Chrysippus later argued at length. Because so little of the school's own writing survives, most of what is known about these debates comes through later authors, chiefly Sextus Empiricus and Cicero, reporting positions the Megarians themselves left in only fragmentary and often disputed form.