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Neoplatonism and Infinity


Plotinus (c. 204/5- 270 C.E.) held to be the founder of the Neoplatonic school.

Greek philosophy in late antiquity

In the introduction to a collection of essays dealing with Platonism in late antiquity, Stephen Gersh and Charles Kannengiesser write of the common Platonic heritage shared by pagan philosophy and Christian theology in late antiquity. After mentioning how Plato's thought was eclipsed by Stioc philosophy in the early Hellenistic period, they state:

The history of the Platonic tradition from the first to the third centuries is an arborescence of contributions by individualistic thinkers who presumaeably had small groups of disciples. This tendency culminated in the work of the greatest of the late ancient Platonists Plotinus and in that of his student Porphyry. After this time, the complicated tradition was gradually reduced to a duality at most, represented by the great philosophical schools of Athens and Alexandria: the former led by men like Proclus and Damascius and concentrating on the exegesis of Plato's dialogues, the latter by those like Ammonius Hermeiou who emphasized the 'Platonic' commentary on Aristotle. By the fourth and fifth centuries A.D.,Platonism had achieved in the hands of such exponents a thorough domination of the philosophical scene.

For our purposes what is significant about the reassertion of Platonic ideas after Aristotle's time is that, up until Aristotle, most Greeks had rejected the idea of an actual infinity in nature. However, as we've seen, even Aristotle himself- presenting rigorous arguments against an actual infinite- is not able to reject true infinity without problems. With Plotinus we find the actual infinite making its way into Greek consciousness for the first time as a positive force. Plotinus borrows a lot from Aristotle, but at heart he is a follower of Plato and he expands Plato’s system to such an extent that in many ways his thought moves beyond both Plato and Aristotle.

The transformation of Platonism in late antiquity

Between the time of Plato and the birth of Plotinus lies about 600 years. The first thing we have to keep in mind, as we examine the thought of Plotinus, is that he is the product of another society than the one Plato and Aristotle lived in. First of all, he's writing from within the Roman Empire. Plato and Aristotle both lived and worked in the small Greek world of City-States. Alexander the Great ends that earlier period of Greek history-dominated by the significance of thePolis- and begins a Greek Empire that will eventually span from the Mediterranean to India. Alexander effectively ushers in what becomes known as ‘the Hellenistic’ period or epoch of Greek and world history (scholars still sometimes call late Greek or Hellenistic culture ‘Alexandrian’ after Alexander the Great). At Alexander’s death, in 323 B.C.E., his Empire eventually gets divided into three parts the Antigonid, the Ptolemaic, and the Seleucid states (named after the Macedonian generals that came to rule them). The Antigonid State of the empire encompassed all of ancient Greece and Macedonia, the Seleucid was composed of Mesopotamia and Persia, and the Ptolemaic was made up of Egypt, Palestine and Cyrenaica. Plotinus, a Greek speaking citizen of Egypt, was born into the Ptolemaic section of the old Alexandrian Empire in the city of Lycopolis. By the time of Plotinus’ birth Lycopolis had been conquered by the Romans.

Most of what we know about the life of Plotinus is due to the biography written by his most important student Porphyry (233-309 C.E.). Porphyry tells us that Plotinus studied under someone called Ammonias Saccas in Alexandria. Ammonias Saccas was known as a theosophist but is also acknowledged (along with Plotinus himself) to be a founder of the so-called Neoplatonic school. Ammonias was, according to legend, originally a Christian who converted to Paganism. Although he is not said to have written anything down, through word of mouth, Ammonias's teachings were passed down. Among his doctrines is recorded the belief that the thought of Plato and Aristotle formed a single unity. Plotinus studied with Ammonias from the ages of 28-39. Then (according to Porphyry) Plotinus studies Persian and Indian philosophy and, finally, in the year 245 C. E. he goes to Rome and lives the rest of his life there [Porphyry only meets Plotinus in Rome circa 263 C. E.]. Plotinus' most famous surviving work is called the Enneads. In the Enneads, Plotinus treats general themes, spanning a wide variety of subjects including: art, philosophy, ethics, pychology and metaphysics-sometimes in the context of questions and problems posed by other philosophers (most of these probably his students). Plotinus is a notoriously difficult and obscure writer and most scholars agree that the Enneads were not even meant to be a unified treatise. The material (possibly lecture notes) was all written down very late in Plotinus’s life (perhaps in his last ten years). Porphyry edited his teacher’s writings and collected them together. He decided to group them into six groups of nine. [Ennead = 9 in Greek] but to get the division right some of the treatises were divided and/or moved around. Many individual Enneads are very popular and are often read on their own. The treatise “On Nature, Contemplation and the One” (Group III, Book Eight) is one of these. In it we can find information relevant to the neoplatonic understanding of the infinite. While this work can be read outside of the context of the other Enneads, it still requires some understanding of Plotinus’s system to be fully appreciated.

Plotinus’ Metaphysics

Like Parmenides, Plotinus thinks reality is One. He is a metaphysician and, like Plato and Aristotle before him, he also has a philosophical system that explains all of reality. Plotinus divides his metaphysics into three basic principles. The One, Nous (the Divine Mind or Intellect), and the Divine Soul (the Nature Principle), which all together will make up what Plotinus calls a ‘Divine Trinity’. First comes the One. Plotinus often equates the One with the Good (think here of Plato’s form of the Good represented by the Sun outside the cave in the Republic). The second principle= Intellect, and the third principle = Soul (cf. Enneads, VI; V9). These notions, as they are used by Plotinus, are somewhat difficult to understand since he often writes of them as being simultaneously explanatory principles and metaphysical aspects of reality.

To begin, the principles are not all equal. The One is called the absolutely first principle of reality. The One is referred to as a divine unity and it is described as metaphysically infinite: supremely adequate, autonomous, all-transcending, most utterly without need (Enn VI, 9, 6). Here we can see a spiritual vision of reality very similar to what can be found in the Bhagavad Gita. According to legend it is from Indian thought that the mystical sense of unity enters into Plotinus’ philosophy. In embracing this transcendental perspective so openly Plotinus presents us with a structural analysis of infinity that will profoundly influence later medieval thought and Christianity (another tri-partite system of belief). According to Plotinus, the One can be described as simple and self-caused, self-sufficient, perfect and omnipotent- it is also referred to as being beyond finite experience but also necessary for all other finite being.

Aristotle called the first principle of being the Unmoved or Prime Mover, but Plotinus says that his One is not a substance in any sense—even though it is said to be the cause of substances. According to Plotinus everything complex but finite can be explained by understanding the One. The One is an arché (principle) in the true sense of the term –it is ultimate and first. As first being, Plotinus thinks the One must explain all of being. In this way, Plotinus explicitly links the notion of the One to Plato’s Form of the Good. Plato had argued that we can never grasp the Good directly but only know it indirectly through dialectic and intellectual vision (the vision of the Sun after the Prisoner escapes from the Cave in the Republic -something which, Plato has Socrates tell us, cannot be expressed in words). Therefore, although we cannot say what the Form of the Good is, we can infer what it is not. For Plotinus this means that even though we cannot do justice to the infinite mode of being the One has, we can still feel its effects and intellectually grasp its importance. Plotinus’s writes that the One is beyond being, absolutely simple but also unified. We are also told that it contains nothing. It is wrong to view it as a Good, or thing with parts, or first being, etc. it is just the One and it is the everything. We can’t really say any more about it than that. How do you describe infinity?

Plotinus nonetheless thinks that we can talk about the effects manifested by the One. From the One, the many are derived. How? Plotinus writes that out of what is infinite and one, finite being emerges through Emanations. The term emanation, we are told, should not be understood as an unpacking or separation of different parts from the One. This would take away from the One’s perfection. Instead, Plotinus writes of the emanation of the One as what can be described as an atemporal [outside of time] ontological [related to existence] dependence of being that is always and everywhere connected to the One. No matter how much the One emanates, this does not take away from its fullness. Like a river that never runs dry. Since the natural world is an emanation (participation) in the One, does this mean that the natural world is also infinite? Curiously, Plotinus accepts Plato’s cosmology of an infinity in nature, since matter taken by itself has no boundaries or form, but he makes the natural or lower world only mathematically (negatively) infinite –since true infinity can only reside with the One. So basically he reverses Aristotle and rejects his denial of an actual infinity. In nature we have the qualified potential infinity that Aristotle said could not exist, in ultimate reality (the One) we have an actual and transcendent infinity. In the Enneads, Plotinus writes of the potential infinity of time arguing that this infinity is one that [tends towards] infinity…by tending to a perpetual futurity (Enn. III, 7, 11). In this way infinite time must be distinguished from the immediately infinite, i.e. the One.

Therefore, as the One emanates, we arrive at a secondary principle- the Intellect—which is said to be the level of the Platonic Forms. The Intellect is the second principle of Plotinus’s system and its role is to account for the distinctions of the Forms which seem disparate, i.e. there may be a form “Bed” and a form “Justice”, and a form “Beauty” etc., but Plotinus tells us that, really, they are all united in the One. Furthermore, if the One is the principle of Being, then the Intellect is the principle of essence and it is described by Plotinus as “an eternal instrument of the One’s causality” (En. V, 4.i., 1-4). Descending from the One to the Intellect (level of Forms) we reach the level of substantial being. Being as substance is explained again Platonically, as existing and changing but having an identity and intelligibility due to participation in a Form. Each being (substance) is what it is because of its Form. The model Plotinus is building can be depicted as follows:

The One ---> Intellect (Forms) ---> Objects.

There are said to be two phases of the Intellects production or “Emanation”. These are, again, said to be logical and not temporal phases: Phase 1 of the Emanation of the Intellect = its fundamental activity, which is called “Thinking”. Phase 2 of the Emanation of the Intellect = its actualization of thinking: (Forms). After these two phases of Emanation, Plotinus writes, the Intellect always returns to the One. Finally we get to the third fundamental principle= the Soul. The soul as a principle is not to be understood as an anima or psyche, i.e. it is not an animating principle of life (first principle of life in Aristotle’s sense). Rather the Soul is called a principle of desire (Eros), and more specifically, the Soul is a principle of desire for objects external to the knower. Every living being acts to satisfy desire. Life therefore = desire which then seeks to obtain things in the world. As the One is to the Intellect, so the Intellect is to the Soul. They are analogous principles, i.e. principles related in an analogous way. Intellect is really the intelligible aspect of the One, so the Soul is really the desiring principle of the Intellect. Plotinus says that all things have an internal and external activity (Enn. V,4, 2). The internal activity of the One is said to be its own existence. The external activity of the One is said to be the Intellect. The internal activity of the intellect is said to be contemplation of the Forms; the external activity = the intelligible world and the Soul. The internal activity of the Soul is called ‘thought,’ i.e. psychical activity and the external activity of the Soul is nature. The intelligible structure of all that is other than the Soul in the sensible world means that there is a hierarchy of being in Plotinus: Plotinus Map

Reality according to Plotinus

Matter is the lowest level of reality and The One is the highest. Matter is said to be a privation of Form; and evil is described by Plotinus as the complete lack of Goodness. Matter, as farthest from the One is therefore most lacking in both form and Goodness. Spirit, which is closer to the One is superior and better than matter and it exists beyond the Platonic-Aristotelian bounded universe.

Plotinus' neoplatonic Challenge to Aristotle

In order to establish an infinite universe as well as an actual infinity beyond the boundaries of the heavens, Plotinus has to challenge the most sophisticated physics of his time: physics as found in Aristotelian natural philosophy. Plotinus will do so by using Plato’s doctrine of transcendent Forms as primary being to reinterpret Aristotle’s theory of primary substances constituting reality. Since the One is beyond substantial being, Plotinus criticizes the Aristotelian understanding of being as substance that acts as a substrate containing material contraries. In Chapter 2, of the Eight Tractate, he writes:

The Nature-Principle must be an Ideal-Form, not a compound of Form and Matter; there is no need for it to possess (such a changeable element as) Matter, hot and cold: the Matter that underlies it, on which it exercises its creative act, brings all that with it, or, natively without quality, becomes hot and cold, and all the rest, when brought under Reason: Matter, to become fire, demands the approach not of fire but of a Reason-Principle.

In the Enneads, we can also find more detailed arguments laid out by Plotinus for criticizing the Aristotelian notion of substance. Primarily Aristotle is criticized precisely for articulating being and primary substance as a matter/form composite. In Ennead VI, Second Tractate, chapter Eight, Plotinus raises a problem that he thinks highlights insurmountable complications in Aristotle’s notion of primary being or substance. If substance is primary being, says Plotinus, and all other categories and predicable properties are dependent on it then how can we know this? In other words what kind of being can substance be “in itself” such that it can make all of reality intelligible? After some analysis, sensible substance (primary substance) is found by Plotinus to be incapable of fulfilling the above condition. Aristotle’s primary substance is not what is ‘first’ or ‘better known’, but instead (through the use of our senses) we actually grasp bodies primarily by knowing their accidents. Sensible substance is never found apart from magnitude and quality: how then do we proceed to separate these accidents? (Enn. VII.2.8. 18-20). Therefore, what Aristotle should have said, according to Plotinus, is that what is better known or what is primary substance is really just a collection of accidents; that which ...is constant in stone, earth, water and the entities that they compose [i.e. the sensible substances] and constitute the genus ‘physical body’ (VII.2.8. 6-8). However a physical body will, for example, lose its essential being if it is stripped of its accidents. Furthermore, a substance cannot be made of accidents, at least not if it is a primary being. Therefore, Plotinus argues, primary substances are not, as Aristotle, thought, primary beings nor are they really substances at all.

Throughout this analysis, Plotinus never actually mentions Aristotle but the allusions are clear and unmistakable. The various attributes Aristotle assigns to substance (primary being, the underlying substrate of changes, what is not a subject but better known; grasped through the senses) and accidents (predicable properties) all make it abundantly clear that it is the Aristotelian system being criticized. Plotinus concludes: [t]he whole amalgam itself is not True Substance (VII.2.8.41-42). Does this mean that Plotinus believes accidents or the qualified attributes of primary substance should be taken as the true primary being? No. What he says is that Aristotle’s primary substance is really just an imitation of that True Substance which has Being apart from its concomitants, these indeed being derived from it as the possessor of True Being (VII.2.8. 42-44). Aristotle’s world of primary being is really a shadow world—the world of appearance (Greek: “phainesthai”)—the Platonic echoes are, of course, intentional. What is new in Plotinus and not found in Plato is the hierarchy of being tied to an infinite source or foundation, the theory of emanation from the Forms to the world and the association of evil with the privation of form or, in other words, with pure matter (conceived of as the opposite extreme of the One as pure or infinite absolute spirit and Goodness).

Neoplatonism on the Infinite

Here we touch on the main core of Plotinus’s philosophy. The One [being or the cosmos as a whole] is actually infinite. In Chapter Eight, Book III of the Enneads, we find Plotinus describing the world of nature. Nature has many levels, but what they all have in common is that they are all connected to what Plotinus calls the Nature Principle:

Nature need possess no outgoing force as against that remaining within, the only moved thing is Matter; there can be no moved phase in this Nature-Principle; any such moved phase could not be the primal mover; this Nature-Principle is no such moved entity; it is the unmoved Principle operating in the Cosmos


What Plotinus is saying is that matter cannot, as Aristotle thought, contain or be actualized by Forms but it can be informed by reason. His understanding of natural substances is much closer to Plato. Recall that Plato had introduced the receptacle as the mold out of which matter was informed and transformed into individual things, but the Forms are always transcendent and separate. Plotinus is saying the same thing. The Nature Principle requires a Reason Principle. In Sections 3 and 4 of the Ennead "On Nature and Contemplation of the One", we learn that nature is a lower level world dependent on a transcendent order. This is a concept very much like the ‘Wheel of Time’ in the Vedas, but it is even more reminiscent of the Parmenidean and Platonic distinction between appearance and reality. Plotinus therefore has a two-world metaphysics, like Plato, and he thinks that when we speak of nature or the lower world as perceiving or understanding, we are speaking “very loosely”:

Of course, while it may be convenient to speak of “understanding” or “perception” in the Nature-Principle, this is not in the full sense applicable to other beings; we are applying to sleep a word borrowed from the wake


The Natural world is a copy or shadow of the real world contained in the infinite One. Plotinus writes of the visionary state necessary to grasp this insight. Since the One is ineffable, it will not be understood through discursive reason alone. Discursive reason, as present in human thought, starts with images, but the One is called ‘authentic form’. The One is true being and “[g]iven the power to contemplate the Authentic, who would run, of choice, after its image?. The world of nature, by contrast, is described using the analogy of a dull child who must be told what to do and is thereby forced to take crafts and shown technics of manual labor versus a bright child who can study academics and learn on their own.

In Ennead III, Eighth Tractate, Section 7, we learn that:

All the forms of Authentic Existence spring from vision and are a vision. Everything that springs from these Authentic Existences in their vision is an object of vision—manifest to sensation or to true knowledge or to surface-awareness.

Later, in the same section, Plotinus writes of how:

Love, too, is vision with the pursuit of Ideal-Form.

Echoes of mysticism as found, for example in the Indian epic poem, the Bhagavad Gita are very strongly present here.

In Section 8, the hierarchy of being is outlined. Without mentioning the One or matter (respectively, the highest and lowest levels of existence) Plotinus writes:

In the advancing stages of Contemplation rising from that in Nature, to that in the Soul and thence again to that in the Intellectual-Principle itself, the object contemplated becomes progressively a more and more intimate possession of the Contemplating Beings, more and more one thing with them; and in the advanced Soul the objects of knowledge, well on the way towards the Intellectual- Principle, are close to identity with their container (Enn. III, 8, 8).

In the intellectual principle, Plotinus says, what is known and what is are the same. The Forms are the essences of the things and they are transcendent of matter. In modern terminology, what Plotinus is presenting is a form of idealism. Ideas and spiritual powers are more real than unknowable material processes. We take in the forms and become one with them and the things that participate in them can be known because they and us all have a foundation in the One. Plotinus here writes of what he calls “The First Life” which is described as an intellection. Compare this to what Aristotle says in the Physics, Book III, Chapter 8 about how thought cannot change or alter substantial being in any way. In contrast to Aristotle, Plotinus accepts the mystical properties of an actual infinity and the very non-Classical Greek consequences that this mystical nature cannot be known by logic or reason alone. Nonetheless the One is infinite:

We conclude that this Being is limitless and that in all the outflow from it there is no lessening, either in its emanation, since this also is the entire universe, nor in itself, the starting point, since it is no assemblage of parts (to be diminished by any outgo).

In Section 9, Plotinus writes about how when we think, we think about something. In this structure we find what is closer to contemplation, i.e. the being of the One. Here he defines the One as: “The Good and wholly simplex”, this will be borrowed by Saint Augustine to make sense of the Christian Trinity and the nature of the God of the Hebrew Bible. The nature of the One is described as being everywhere all at once: it is “omnipresent”. Plotinus gives a metaphor,

…imagine a voice sounding over a vast waste of land, and not only over the emptiness alone but over human beings; wherever you be in that great space you have but to listen and you take the voice entire—entire though yet with a difference

In his Physics, Aristotle uses the example of ‘voice’ to characterize a certain kind of infinity, a non-traversable or indivisible spiritual completeness, but Aristotle adds that no physicist adhered to this kind of infinity. Plotinus is trying to establish physics on a mystical worldview. The One is characterized by him as Janus-faced (Janus was the Roman god of beginnings and transitions – he was portrayed as ‘two-faced’ looking simultaneously to the future and the past). Plotinus writes:

The Intellectual-Principle in us must mount to its origins: essentially a thing facing two ways, it must deliver itself over to those powers within it which tend upward; if it seeks the vision of that Being, it must become something more than Intellect

The One is not a thing among things, it is the ultimate collection of all things and therefore prior to all things. In Section 10, Plotinus adds:

Imagine a spring that has no source outside itself; it gives itself to all the rivers, yet is never exhausted by what they take, but remains always integrally as it was; the rides that proceed from it are at one within it before they run their several ways, yet all, in some sense, know beforehand down what channels they will pour their streams. Or: think of the Life coursing throughout some mighty tree while yet it is the stationary Principle of the whole, in no sense scattered over all that extent but, as it were, vested in the root: it is the giver of the entire and manifold life of the tree, but remains unmoved itself, not manifold but the Principle of that manifold life

The One is the absolute, the truly and fully infinite. Everything exists “by its power”. Aristotle’s mathematical infinite, by contrast, is found in the Intellectual Principle, not in the One. In section 11, Plotinus writes of how:

The Intellectual-Principle is a Seeing, and a Seeing which itself sees; therefore it is a potentiality which has become effective.

Since the Intellectual-Principle is an emanation of the One (see above) and the origin of the Forms, we can place this mathematical and non-metaphysical infinity “a potentiality that has become effective” directly in nature. But true infinity is a spiritual absolute transcendence. The Christians who come after Plotinus and read his work will have no problems associating this absolute transcendence with a creator God who creates because He is goodness itself:

But: as one that looks up to the heavens and sees the splendor of the stars thinks of the Maker and searches, so whoever has contemplated the Intellectual Universe and known it and wondered for it must search after its Maker too. What Being has raised so noble a fabric? And how? Who has begotten such a child, this Intellectual-Principle, this lovely abundance so abundantly endowed? The Source of all this cannot be an Intellect; nor can it be an abundant power: it must have been before Intellect and abundance were; these are later and things of lack; abundance had to be made abundant and Intellection needed to know. These are very near to the un-needing, to that which has no need of knowing, they have abundance and intellection authentically, as being the first to possess. But, there is That before them which neither needs nor possesses anything, since, needing or possessing anything else, it would not be what it is—The Good.