The Treatise On Numbers develops a typical Plotinian inquiry about oneness and intelligible plurality, in which the analysis is based on the problem of the infinite inside the intelligible realm, as it seems to be presented in the socalled generation of numbers in Plato's Parmenides, where numbers are linked to Being, identified by Plotinus with the hypostasis of Intellect, and produce a process of unlimited division. In order to avoid this interpretation, Plotinus finds in other Plato's dialogues the proof that (...) number is an eidetic nature, encompassing all the intelligible entities, so that the infinite has to be interpreted as what is produced by calculus. Other arguments are rather depending on the model of the Old Academy, concerning the relationship between forms and numbers: Plotinus wonders if numbers come ontologically before forms and indeed he states right this position. Other aspects of Plotinus' investigation, which can be traced back to the Old Academy, are the distinction between two kinds of numbers and the doctrine of the unified number. This model of number, quite ambiguous, may be identified with the indefinite dyad, even though the former has to be conceived, differently from that of Old Academy, within a mono-polar framework, according to which the sole principle is the One. (shrink)

_ Source: _Volume 9, Issue 2, pp 159 - 176 The purpose of this paper is the analysis of the Plotinian and Iamblichean reading of the Aristotelian theory of abstraction, and its relationship with the status of mathematical entities, as they were conceived within a Platonic model, according to which mathematical objects are ontological autonomous and separate.

The aim of this paper is to show how some passages in the treatise VI 6 of the Enneads could be considered a Plotinian attempt to achieve a sort of mediation between Plato’s dialogues and the Academic models concerning the generation of numbers and ideas by the two principles of the One and the Indefinite Dyad. Through a complex exegetical contamination, Plotinus gets to identify numbers, ideas and the Dyad with the hypostasis of the Intellect, saving for the One the (...) condition of the sole principle of every reality. This new reading modifies the ontological role played by ideal numbers : they gain an ontological priority on any other being, thanks to their being conceived as the a priori condition of the display of multiplicity. The so-called Intermediates, on the other hand, have a reshaped status, as a result of the fact that calculation is unable to grasp the essence of a given reality. (shrink)

This article is currently available as a free download on ingentaconnect.