Plotinus on Number (review)

Abstract

Reviewed by: Plotinus on Number Peter Lautner Svetla Slaveva-Griffin . Plotinus on Number. Oxford: Oxford University Press, 2009, Pp. xii, 176. $74.00 (hb.). ISBN 978-0-19-537719-4. Relying primarily on Enneads VI 6, the author sets out to investigate Plotinus' metaphysical theory of number with ample references to the preliminaries in Plato and the Platonists in the early imperial period, particularly Numenius, as well as to its version in Porphyry. Slaveva-Griffin starts with an investigation into the relation of Plotinus' text to the Timaeus, emphasizing that Plotinus insisted on a "top-down" approach which, in contrast with the "bottom-up" method of inquiry, results in the thesis that multiplicity is nothing but otherness from the One. This is the first principle even in the hierarchy of numbers. Thus, it is prior to the numbers conceived of as substances, to be found at the level of the Intellect. Moreover, by a certain defining activity it produces the first Monad, the principle of limit and generator of substantial existence. Numbers in the Intellect are in a way activities, but also powers dividing the intelligible sphere into different ideas of which the number is finite. Their activity cannot be separated from their existence. On the other hand, they can be studied from points of view determined by the five genera in Plato's Sophist: being, sameness, difference, motion, and rest. As defining genera of the sphere of the Intellect, they offer analogies whereby to make distinctions between the various aspects of such numbers, with each genus corresponding to one aspect. They are not, however, the numbers we use in arithmetic, for numbers in the sphere of the Intellects have copies called Monadic numbers that figure in mathematical relations. Slaveva-Griffin devotes long passages to discussing monadic numbers, material copies of the numbers as substances (85-95). It is a quantitative image which, by giving structure to it, saves corporeal multiplicity from scattering into infinity. Mathematics in the ordinary sense depends on this number. By contrast, numbers as substances are qualitatively different, which implies that the units (henads) constituting them are combinable; they are [End Page 519] all different. There is, however, a fundamental inconsistency in using terms such as monads and henads, which has been taken to be due, not to Plotinus' confusion, but to the unsettled terminology of the age. In tracing the origin of the doctrine one might naturally think of the Pythagoreans, and the author argues (42-49) convincingly that the main source is Moderatus rather than Nicomachus of Gerasa. On the other hand, it has also made clear (118) that the distinction between substantial and quantitative number originates in Numenius. As one expect from a philosopher accepting the Timaeus' account of the basic structure of the cosmos, Plotinus ascribes a fundamental role to number in cosmology. The only failure of note is the lack of a thorough discussion of chapters 12-15 of Plotinus' treatise, criticizing the thesis that unit and one are nothing but affections of the soul. Some of the arguments are interesting even with regard to the theme discussed in the previous chapters. To take but one example, the argument which comes to the conclusion (13.35-40) that, just like substance and being, one is not perceptible in itself, even if perceptible things participate in it. We can grasp it by means of discursive thinking. It raises important questions about the apprehension of the one. Which one is it? Moreover, is this knowledge innate and always active, or innate but needs to be actualized by sense-perception? The book is furnished with extensive bibliography and two indices. It is well argued and will stimulate further discussion of the matter. Peter Lautner Pázmány Péter Catholic University, Budapest Copyright © 2011 The Classical Association of the Atlantic States, Inc.