Infinity — An Outline of Conceptions in Mythology, Cosmology and Natural Philosophy

Abstract

The earliest conceptions of infinity and eternity apparently occurred in Oriental cosmological and cosmogonical myths and fables that have been passed down in popular tradition and epic texts. Some of these became codified in literary religions as holy scripts and were subsequently refined in interpretations and commentaries. The pre-Socratic Greek natural philosophers were the first to detach themselves from myths and religious authority and began to ponder questions of cos-mology and cosmogony independently of religious tradition and offered a variety of original views, many of which involved notions of infinity and eternity in various senses and contexts. The Medieval patriarchs, theologians and scholastic philosophers digested and filtered the Oriental religious and the Greek philosophical thought, transferred the idea of infinity from cosmol-ogy to theology and carried speculations about the immensity of God and His virtues to the extreme. In the Renaissance the legacy of the Greek natural philosophy and Indian arithmetics were mediated to Europe by the Arabs which allowed the natural philosophers of the Renaissance to bring the notion back to physical cosmology and the astronomers and mathematicians to pave the way for the rise of science and new manifestations and interpretations of the notion of infinity. In the history of classical and modern astronomy and cosmology infinity continued to play a variety of roles until it was finally 257 C. Calude et al., Finite Versus Infinite © Springer-Verlag London Limited 2000 258 J. Seppanen banished by the relativistic cosmology in the large and by the quantum gravity in the small and became substituted for by a conception of a universe of finite age, size and scale but having unbounded space-time geometry and cosmology. Yet, the notion of infinity was to undergo a Renaissance of its own in mathematics-in geometry, number theory, analysis, set theory, classical and mathematical logic, discrete mathematics and the theory of computation. Moreover, the dimension of complexity of the real world would come to reveal new potential infinities in the dimensions of the evolution of life, mind, language, culture and human thought and civilization, including science, technology and arts-and the notion of infinity as reduced merely to a construction of the human mind.