A Genealogy of the Infinite in Ancient Greek Philosophy: on the Apeiron from Homer to Socrates

Michael Shaw
Professor of Philosophy, Director of Classical Studies
Utah Valley University

From its earliest meanings in the poetry of Homer and Hesiod, when it indicates the untraversable, to a fully mathematical conception of infinite divisibility developed by Zeno, the conception of the apeiron (the infinite, non-limited, indefinite, or boundless) plays a critical role in the development of Greek philosophy before Socrates. This talk examines the evolution of meanings, including Nietzsche’s interpretation, from Homer through Anaximander to Zeno and Anaxagoras.