Heller M, Woodin W.H. (eds.) Infinity. New research frontiers (CUP, 2011)(ISBN 1107003873)(O)(327s)_MAml_

20 infinity as a transformative concept in science and theologyinto three parts according to these three levels: (1) from to , (2) from to potential infinity, and (3) from potential infinity to actual infinity. As anoutlook the chapter concludes with (4) infinity in modern theology and the evolutionof the religious Self.1.2 From to : AnaximanderAs early as the pre-Socratics of early Greek philosophy, infinity was a matter forphilosophical and religious consideration. Anaximander (610–546 BC), who lived inthe period of transition from mythology to rationality, was the first to speak of it. Hecoined a koan-like saying about infinity, and it definitely expressed the pessimisticmood of the early Greeks concerning the destiny of human life. In Simplicius’s physics(Simplicius 1954, pp. 13, 22–9), it is preserved as the only sentence of Anaximanderthat we have. 1The is the opposite of , which means both a frontier or border andalso the definite and clear. On the other hand, had a negative connotation, andit referred to something to be afraid of and to be avoided. The latter derived from anunderstanding that human life was thought to be possible and healthy only in a confinedand rationally ordered area.From Anaximander’s point of view, the was not only vague and indefinite,but also showed an abyss in which the ordered life and ordered cosmos would dissolve.Perhaps the ancient Greek philosophers experienced a kind of existential barrier forthinking appreciatively about the . The idea of infinity was born, and nowpeople could think about it. However, they could think of it neither in a mathematicalway nor in a scientific way. They could only think about things that were definite, clear,and certain; that is, they thought about objects with a clear that were accessible tomathematical description. These thoughts were expressed with the idea of mathematicalcommensurability. At this stage of philosophical discussion, the could not bea subject of mathematical research.From the perspective of the transition from mythology to rationality, this phenomenoncan be interpreted as the struggle of rationality (the form of thinking theclear, definite, and certain) to stabilize itself against the disordering powers of a mythological(and thus archaic) way of living. Finding order, certainty, clearness – –then must be understood as the drive of rationality in seeking to rule out mythology.As a struggle against a mythological perception of the and life, this strugglealso becomes apparent in the concept of time, which is associated with Anaximander’s. Time and guilt are intertwined, because time is still perceived as a mythologicalpower and not yet a feature of human rationality. 2 Thus, rationality reaches1 “ . , ) · ” [Whence thingshave their origin, Thence also their destruction happens, As is the order of things; For they execute the sentenceupon one another – In conformity with the ordinance of Time] (Diels and Kranz 1952,p.15).2 This connection between time and guilt is also apparent in another mythology of this time – the BabylonianEnuma Eliš, in which human destiny is thought of as being trapped in the offering of sacrifices to compensatefor the guilt of the gods.