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

from potential infinity to actual infinity 25his understanding of time, rationality, and number, inasmuch as they all are related tothe divine infinity of the .Infinity and time: In Ennead III.7, Plotinus gives a sophisticated account of hisunderstanding of the relation between earthly (passing) time () and heavenly(everlasting) eternity (). This distinction stems from Plato, and Plotinus elaboratedon it. 30 He defines eternity as a form of completed infinite life, which is whole, in thesense of being completed, self-sustaining, and thus not extended into past and future. 31This eternal infinite life is grounded in the unchanging . 32 However, it is related totime in its form as . Time, as , is the life of the soul (), 33 insofar as thesoul changes and moves. 34 This movement and change of the soul in time are related toinfinity in the form of an endless process, 35 and it is distinct from the completed infinityas eternity. Although being in the infinite process of time, change, and movement, thesoul and its time nevertheless are capable of imitating the completed infinite eternity,because the soul is its image (). 36 The soul can do so if it is striving to participatein the one and completed infinite eternal being. 37To sum up, Plotinus has two different concepts of infinity related to time: theconcept of a completed, whole infinity related to eternity (), which reminds oneof the actual infinity of Cantor, and the concept of an infinity in process related to time(). The latter concept is capable of mirroring the first one. This situation leadsto the problem of how to relate these two concepts to one another. The structure ofhuman rationality with its ability to calculate infinite processes is to be considered, aswell as its partaking in the infinite one being (Leisegang 1913; Clark 1944; Guitton1959; Jonas 1962; Beierwaltes 1967).Infinity and rationality: Plotinus distinguishes two kinds of human rationality, thelogos () and the nous (). 38 The logos represents the human ability for calculation,thinking in notions and logical sequences. The nous is more comprehensiveand touches on the divine infinity. The logos is operating in the realm of diversityand multiplicity, whereas the nous is thinking in unity and totality. More specifically,one can say that the nous includes unity and diversity at the same time – seemingly aparadox. 39 Because the is the ultimate source of the nous, 40 it is striving to reunitewith its origin. 41 Insofar as the nous reaches the , it is infinite, not in the sense ofquantity, but rather in the sense of power. 42Infinity and number: How do these two forms of rationality apply to infinity inthe realm of numbers? Plotinus devotes a long chapter to numbers and their relation30 Plato, Timaeus 37 d.31 Plotinus, Ennead III.7, 5, 25–30.32 Plotinus, Ennead III.7, 11, 3–4.33 Plotinus, Ennead II.7, 59.34 Plotinus, Ennead III.7, 11, 44–45.35 Plotinus, Ennead III.7, 11, 44–45; also Plotinus, Ennead III.7, 11, 54–55.36 Plotinus, Ennead III.7, 11, 47.37 Plotinus, Ennead III.7, 11, 56–59.38 Plotinus, Ennead VI.9, 5, 9.39 Plotinus, Ennead VI.7, 14, 11.40 Plotinus, Ennead VI.9, 9, 1.41 Plotinus, Ennead VI.8, 18, 7.42 Plotinus, Ennead VI.9, 6, 10–12.