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

26 infinity as a transformative concept in science and theologyto infinity. 43 He is not very clear about the ontological status of numbers, and hediscusses this problem at length, offering various ways of understanding numbers. 44He distinguishes numbers in the transcendent, ideal realm 45 from numbers as theessence of created things, 46 and from numbers as quantities 47 and numbers as countedquantities in the human mind. 48 In addition, he struggles with the ontological status ofinfinity: does it exist really, ideally, or only in the mind? 49 Finally, after asking howthe numbers are related to these various forms of numbers, 50 Plotinus comes to theconclusion that the concept of infinity – obviously understood as actual infinity – isnot applicable to the concept of number, no matter what their ontological status mightbe, 51 because numbers are limited. 52 However, he concedes that infinity – as potentialinfinity – can be thought of as an infinite process of counting. 53 Nevertheless, he doesnot exclude the possibility that there might be infinite numbers in the transcendentrealm, insofar as they are not subject to quantity and measurement 54 – a rather strangeidea in our day.Finally, Plotinus holds that the human logos, as part of the soul, is able to comprehendinfinity in the realm of numbers in the sensible world as the potential infinity of endlesscounting. On the other hand, the nous might touch the nonmeasurable infinity ofnumbers in the realm of ideas.As we have seen, Plotinus has a rather complex understanding of infinity thatappears in various contexts, of which the infinity of the divine is the most important.However, this infinity as an all-encompassing oneness, totality, and transcendent realitycannot be conceptualized by the human mind, by logos. It is transrational. 55 It can onlybe touched by the nous in rare moments of religious elevation, which happens whenthe soul and the nous turn in an inner movement toward the . Then, suddenly – – the human nous leaves behind all its limitations with regard to number,time, and rationality in order to become transformed and enlightened in the light of theinfinite . 56 Thus, Plotinus was the founder of thinking about infinity in the context of43 Plotinus, Ennead VI.6, 1–18; Ennead VI.6, 2, 1–3.44 Plotinus, Ennead VI.6, 4, 1–25; 5, 1–51.45 Plotinus, Ennead VI.6, 15, 34–35.46 Plotinus, Ennead VI.6, 16, 26.47 Plotinus, Ennead VI.6, 16, 19, 21, 23f.48 Plotinus, Ennead VI.6, 16, 7. Compare also Ennead VI.6, 9, 33–39; Ennead VI.14, 48–51; 6, 15, 34–44.49 Plotinus, Ennead VI.6, 3, 1–2.50 Plotinus, Ennead VI.6, 17, 1.51 Plotinus, Ennead VI.6, 17, 3.52 Plotinus, Ennead VI.6, 18, 1.53 Plotinus, Ennead VI.6, 18, 3.54 Plotinus, Ennead VI.6, 18, 6–8.55 His disciple Proclus tried to think about the rational accessibility of the infinite, but Proclus ended up finding itparadoxical to think about infinity in a rational way, and that goes beyond Plotinus’s metaphysical speculationand existential elevation. He gave the following example: Imagine a circle with two equal semicircles dividedby one diameter, that is to say, one diameter creates two parts. If one continues to divide a circle in thisway indefinitely, one gets infinite processes of partition, but twice as many parts. This doubled infinity is aparadox (see Becker 1975, p. 273). Thus, the neo-Platonic tradition ended in a dead end. It was with Christiantheology that infinity became an indispensable feature of God, and it emerged slowly as a rational concept.56 Plotinus, Ennead V.5, 7, 34; Ennead VI.7, 36, 18. This is similar to Plato’s in in Politeia613a8–b1, 621c5 and Theatet 176b1 sqq, to which Plotinus in Ennead V.3, 4, 10sqq; Ennead V.8, 7, 3sqq;and Ennead VI.9, 11, 48–51 alludes.