The Realization of Infinity: On the Philosophy of John M. Anderson

Abstract

An incontestable horror of the still haunts us in those images devised by the ancient Greeks: Tantalus, Sisyphus, Prometheus. These are the as life without finality or purpose, life as repetition without novelty or redeeming insight. Tantalus is in agony as he bends down to drink the waters of an ever-receding river or reaches up to grasp the dangling fruit from a tree which springs up instantly to take them beyond his reach. Sisyphus too pushes toward an ever-frustrated accomplishment, toward goal-completion paradoxically never completed but each time begun again ab initio. There is, too, the daring Prometheus whose innards are continually restored only to be gnawed away again by the jovian avenger of Prometheus' proud and cunning search for human power and comfort a never-ending task and a self-consuming agony. In the classical period, philosophers retained a similar horror by transferring the infinitude of Tantalus, Sisyphus, and Prometheus from the religious-poetic sphere to the realm of conceptual argument. We find Aristotle, not to mention Zeno of Elea, frequently offering indirect proofs for the absurdity of a rival theoretical account by showing that it implies an infinite regress.) Yet, more than image of horror, of endless toil without termination or fulfillment, the Greek awareness of infinity led to many positive inquiries into the as originating source of definiteness and of identity. The positive awareness of infinity as originating source I want to bring out and contrast with infinitude as recurring, endless repetition