Infinity in the Presocratics: A Bibliographical and Philosophical StudyThroughout the long centuries of western metaphysics the problem of the infinite has kept surfacing in different but important ways. It had confronted Greek philosophical speculation from earliest times. It appeared in the definition of the divine attributed to Thales in Diogenes Laertius (I, 36) under the description "that which has neither beginning nor end. " It was presented on the scroll of Anaximander with enough precision to allow doxographers to transmit it in the technical terminology of the unlimited (apeiron) and the indeterminate (aoriston). The respective quanti tative and qualitative implications of these terms could hardly avoid causing trouble. The formation of the words, moreover, was clearly negative or privative in bearing. Yet in the philosophical framework the notion in its earliest use meant something highly positive, signifying fruitful content for the first principle of all the things that have positive status in the universe. These tensions could not help but make themselves felt through the course of later Greek thought. In one extreme the notion of the infinite was refined in a way that left it appropriated to the Aristotelian category of quantity. In Aristotle (Phys. III 6-8) it came to appear as essentially re quiring imperfection and lack. It meant the capacity for never-ending increase. It was always potential, never completely actualized. |
Contents
ANAXIMANDER AND OTHER IONIANS | 49 |
PYTHAGORAS | 75 |
THE ELEATICS | 93 |
74 | 101 |
POSTPARMENIDEAN PHILOSOPHERS | 136 |
IN RETROSPECT | 174 |
Additional Studies on Anaximander | 180 |
| 206 | |
| 214 | |
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actually infinite Anax Anaxagoras Anaximander Anaximenes apeiron arché Aristotle Aristotle's Atomists atoms Bicknell body Burnet C. H. Kahn Chaos Cherniss conceived conception continuum Cornford cosmic cosmogony cosmology cosmos Democritus divine doctrine Early Pythagoreanism earth Eleatic elements Empedocles Epicurus existence F. M. Cornford finite Fragment Furley G. B. Kerferd Gnomon Gottschalk Greek Philosophy Guthrie Hence Heraclitus Hesiod Hölscher ibid indivisible infinite divisibility infinite number infinity interpretation Ionian J. E. Raven Jaeger Kirk Leucippus Leucippus and Democritus limit Loenen magnitude mathematical matter meaning Melissus Metaphysics Milesian Mondolfo monism Mourelatos nature opposites origin Owens Parmenides peras Philip Phronesis physical Plato plurality position Presocratic Philosophers primal principle Pythagoras Pythagoreans reality Review scholars Seligman sense separated Simplicius Solmsen spatial sphere spherical substance T. G. Sinnige Tarán Thales Theophrastus theory things thinkers thought unity University Press unlimited Vlastos void W. K. C. Guthrie Xenophanes Zeno Zeno's Paradoxes καὶ