In the Beginning was the Apeiron: Infinity in Greek Philosophy
The book is a historical investigation of the problem of infinity in Greek ontology and physics more specifically, the problem of the infinite size of the world and of its eternal existence, the problem of the infinity of worlds, of infinite divisibility of matter, of infinity of attributes or attribute modes (e.g., infinity of atom shapes), and the problem of infinity of nonphysical entities such as mathematical constructs. The view espoused here is that infinity was of paramount importance for Greek philosophers even if it was not explicitly discussed by them. It served as an unspoken assumption without which Greek philosophy could hardly be possible.
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according aether Anaxagoras Anaximander Anaximander's Anaximenes apeiron appears argument Aristotle Aristotle's assumed assumption atomists attribute body bone caelo causal Chrysippus circle concept considered continuous continuum contradiction cosmic cosmos created Demiurge Democritus divine dyad earth Eleatic elements Empedocles entities Epicurus eternal everything existence fact finite fire Greek heaven Heraclitus ideas indefinite indivisible infinite divisibility infinite number infinity infinity of atoms infinity of worlds interpretation interval lekta limited Lucretius magnitude material(l mathematical mean Melissus mixture motion move movement nature nite object ontological paradoxes Parmenides particles particular peiras peras perfect Philebus philosophy Phronesis Phys physical Plato plurality polygons possible prime matter principle problem proportions Pythagoreans rectangle says seeds seems sense separated shapes Simplicius soul space spatial atom Speusippus sphere spherical statement Stoics substance temporal infinity Theophrastus theory things tion triangles University Press unlimited void Xenocrates Xenophanes Zeno Zeno's Zeno's paradoxes