Mathematical Infinity and the Presocratic Apeiron
The Presocratic notion of apeiron, often translated as “unbounded,” has been the subject of interest in classical philosophy. Despite apparent similarities between apeiron and infinity, classicists have typically been reluctant to equate the two, citing the mathematically precise nature of infinity. This paper aims to demonstrate that the properties that Anaximander, Zeno, and Anaxagoras attach to apeiron are not fundamentally different from the characteristics that constitute mathematical infinity. Because the sufficient explanatory mathematical tools had not yet been developed, however, their quantitative reasoning remains implicit. Consequentially, the relationship between infinity and apeiron is much closer than classical scholarship commonly suggests.
Stance requires right of first publication. All other rights reside with the author. Authors are free to reuse their own articles in other publications they write or edit, and no further permission is required. The journal only requires acknowledgement of the original publication in Stance.
All articles are licensed with a Creative Commons Attribution Noncommercial No-Derivatives 4.0 International license.