Mathematics as Paideia in Proclus :: Philosophy Philosophical Essays

Mathematics as Paideia in ProclusABSTRACT I examine mavin aspect of the central role which maths plays in Procluss ontology and epistemology, with particular quality to his Elements of Theology. I focus on his peculiar views about the ontological berth of mathematical objects and the special faculties of the understanding that are involved in accord them. If they are merely abstract objects that are stripped away from sane things, then they are unlikely to reorient the mind towards the intelligible realm, as envisioned by Plato in the Republic. Thus, in order to defend the power of mathematics as a prodaideutic to dialectic, Proclus rejects Aristotelian abstractionism in esteem of an elaborate account in terms of Nous projecting images of its Forms through with(predicate) the medium of the imagination. In metaphorical terms, he replaces the Aristotelian image of the soul as a blank tablet with that of a tablet that has of all time been inscribed and is always writing itself , while also being written on by Nous. The mediating function of mathematics for understanding the high realities is grounded in the fact that its central principles of Limit and Unlimited start out a commonplace provenance in Procluss whole system of reality.IntroductionAlexander of Aphrodisias formal abstractionism as an Aristotelian dogma about mathematical objects, plainly for later Neoplatonists this proved difficult to reconcile with the educational function of mathematics in Platos philosophical curriculum. Thus Proclus, for example, rejected abstractionism as a basis for the ascent to the realm of Forms, and proposed an alternative view based on the typical Neoplatonic hierarchy of Nous, Soul, and Nature. At the highest noetic level, geometrical Forms are unextended and indivisible, so that only at the level of Soul send away they constitute available for study by the geometer when they are embodied in the intelligible matter supplied by the imagination. Proclus also accepted that geometrical forms hind end be embodied in sensible matter, though they neer have the exactitude necessary for science, nor could they ever acquire it through abstraction. Thus the diagrams apply by the geometer are products of the imagination, which are really projections by the higher intellect onto a lower level so as to serve the study of geometrical objects. Proclus seems to accept that the human intellect can never attain the Platonic goal of studying geometrical Forms in their pure(a) and unextended form as paradigms. Although such a goal can be achieved only by divine Nous, yet it becomes for Proclus the guiding rationale for his whole system.