13.6.5 Infinity and the finite

the more subtly the mind contemplates itself in and through the world unfolded from itself, the more abundantly fruitful it is made within itself, since its End is Infinite Reason. Only in Infinite Reason will the mind behold itself as it is¹

Neoplatonism could be defined as the theory of the movement of consciousness from infinity to the finite and back again. The most important relationship of all to Neoplatonists, from Plotinus to Neoplatonism’s consummate proponent Hegel, is that between the infinite and the finite.

For Plotinus, the One (the Formless Form, the Father, the Simple, the Absolute, the Infinite, the Transcendent, the Unconditioned, the Fountain and Principle of Beauty) is the principle of form, being, number, order, measure and limit though none of those itself. It is beyond space and time and is the greatest in reality. It is infinite power.

Its light, the second hypostasis Intellectual-Principle is its most perfect possible image

Plotinus’ World of Forms…represents (the One’s) infinity as best it can in the plurality of Forms. Intellect is itself infinite in power and immeasurable, because it has no extension and there is no external standard by which it could be measured, but finite because it is a complete whole composed of an actually existing number (all that can possibly exist) of Forms, which are themselves definite, limited realities.²

Plotinus concluded an important section of the Enneads in which he proposed a contemplative method for ‘dematerialising’ the visible universe in order to ‘see’ that of the spiritual intelligible where all elements have no perceptible shape, magnitude, temporal or spatial difference (since each is all, and all, though distinct, are an infinite unity) with

But this, the [intelligible] All, is universal power, extending to infinity and powerful to infinity; and that god is so great that his parts have become infinite³

In sum, the second hypostasis is the realm of infinity within which finitude functions. It is there that the Forms or Ideas in their diversity have their most complex meaning, infinity being the dominant principle. The progress of one’s soul is through that realm, from least rationally developed within it, beyond most rationally developed within it (the near unity of subject and object), to the desired first hypostasis, the One.

Proclus believed that all that exists consists of the Unlimited (apeiria, which corresponds to procession) and Limit (peras). He was in agreement with Plotinus that both complement each other and cannot function apart

At the heart of all existence Proclus sees the cooperation of  two principles: Limit (peras) and the Unlimited (apeiria). …For Proclus, Limit and the Unlimited represent a sort of basic ‘interface’ between the One and the lower levels. …Limit is always tied to the Unlimited (PT III 8, 31.18-32.7)…All that exists needs to depend on these two primal principles: it needs to be limited while possessing an indefinite potency.⁴

Proclus greatly clarified the relationship in Neoplatonism between the infinite and the finite. Propositions 84-96 of his Elements of Theology address being, limit and infinitude. Prop. 89 states ‘All true Being is composed of limit and infinite’, Prop. 92 states ‘The whole multitude of infinite potencies is dependent upon one principle, the first Infinity, which is not potency in the sense that it is participated or exists in things which are potent, but is Potency-in-itself, not the potency of an individual but the cause of all that is’ and Prop. 95 states ‘The more unified potency is always more infinite than one which is passing into plurality’⁵

Notes

1. Nicholas of Cusa, De coniecturis (‘On Speculations’), op. cit., 1,1,5, 165 ↩
2. Armstrong in Plotinus, Enneads, Trans., A.H.Armstrong, op. cit., vol. I, xxi ↩
3. ‘Let us then apprehend in our thought this visible universe, with each of its parts remaining what it is without confusion, gathering all of them together into one as far as we can, so that when any one part appears first, for instance the outside heavenly sphere, the imagination of the sun and, with it, the other heavenly bodies follows immediately, and the earth and sea and all the living creatures are seen, as they could in fact all be seen inside a transparent sphere. Let there be, then, in the soul a shining imagination of a sphere, having everything within it, either moving or standing still, or some things moving and others standing still. Keep this, and apprehend in your mind another, taking away the mass: take away also the places, and the mental picture of matter in yourself, and do not try to apprehend another sphere smaller in mass than the original one, but calling on the god who made that of which you have the mental picture, pray him to come. And may he come, bringing his own universe with him, with all the gods within him, he who is one and all, and each god is all the gods coming together into one; they are different in their powers, but by that one manifold power they are all one; or rather, the one god is all; for he does not fail if all become what he is; they are all together and each one again apart in a position without separation, possessing no perceptible shape – for if they did, one would be in one place and one in another, and each would no longer be all in himself…nor is each whole like a power cut up which is as large as the measure of its parts. But this, the [intelligible] All, is universal power, extending to infinity and powerful to infinity; and that god is so great that his parts have become infinite…’ Plotinus, Enneads, Trans., A.H.Armstrong, op. cit., vol. V, V.8.9. I contend that Plotinus’ recommendation, via a similar passage by Bergson in Matter and Memory is reflected in the Cubism of Picasso and Braque, particularly the so-called ‘intellectual’, ‘Analytic’ phase (‘In short, try first to connect together the discontinuous objects of daily experience; then resolve the motionless continuity of their qualities into vibrations on the spot; finally fix your attention on these movements, by abstracting from the divisible space which underlies them and considering only their mobility (that undivided act which our consciousness becomes aware of in our own movements): You will thus obtain a vision of matter, fatiguing perhaps for your imagination, but pure, and freed from all that the exigencies of life compel you to add to it in external perception.’) H.Bergson, Matter and Memory, 1896; trans. N. Paul, W. Palmer, New York, 1988, 208. ↩
4. Chlup, Proclus, An Introduction, op. cit., 77-78 ↩
5. ‘For if the first Infinity is nearest to the One (prop. 92), then of two potencies that which is more akin to the One is infinite in a greater degree than that which falls away from it; since a potency as it becomes manifold loses that likeness to the One which caused it while it abode therein to transcend the rest, concentrated in indivisibility. For even in things subject to division potencies are multiplied by co-ordination, enfeebled by partition.’ Proclus, The Elements of Theology, op. cit. ↩

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