This is a very basic account every part of which begs for many additional pages of explanation beyond the parameters of our class. I extend my sincere apologies to Plato, Aristotle and Plotinus.
Plato:
In his Republic Plato provides a divided with four levels of apprehensive powers and apprehended objects. These powers of apprehension belong to the imperishable human soul.
We see here that his world view is dual, one of changing particulars that are sensible imperfect and perishable manifestations of forms, another of unchanging intelligibles.
The lower half of the divided line does not yield knowledge or intelligibles but instead they are fluctuating and unstable, ever changing appearances. So they yield Pistis (Belief) and Eikasia (Opinion) both of which are subject to falsity. The objects of these power are in constant change and are without the stability of knowledge. This is the realm of Becoming.
In the upper half of the divided line, the lower part concerns numbers, mathematicals and what he calls hypotheses. These are invisible and not apprehended through senses. The power of soul is Dianoia (understanding, or multi-stage reasoning). The objects are repeatable as in 2 + 2 = 4.
The upper part of of the upper half consists of objects that are eternal and unchanging, stable and subsistent, as Truth. These are the Forms or Ideas and are called ousiai (Beings or Beingnesses) because they are and never are not, they are without change or fluctuation. The realm of the Forms is Being.
The Forms are apprehended by us when we turn our backs to the physical world and posit a one over the many, Horse Itself as an object of knowledge.
The Forms are also apprehended by us through dialectical reasoning that is in, through and by forms leading to the transcendent Forms or Ideas.
At the top of the Divided Line is The Good which is above Being and It is the cause of the Being and Truth of the Forms.
By leaving behind and being unconcerned about the changeable realm of Becoming and employing hard dialectical philosophical work at reasoning we are able to rise to the level of eternal stable and unchangeable Noesis (Intellection) and Episteme (Scientific Knowledge). The Forms apprehended there are the ultimate causes of the imperfect and fluctuating particulars of the sensible world.
In the first section of his dialogue Parmenides, Plato has the character young Socrates meet Parmenides and his ‘sidekick’ Zeno to discuss the theory of forms. Socrates sets out various accounts and analogies to explain the theory of forms all of which end up too problematic (though there are hints that Socrates is on the right track). The problem of the forms concerns the relation of the one and the many. This is the topic of the second and final part of the Parmenides. Here various theories or hypotheses are tested by reasoning as they struggle to understand how the Forms — each of which is one — are related to the plurality of imperfect instantiations or images. So now the discussion is of the One and the Many. Later in the developments of the dominant Neoplatonist tradition these discussions are taken to be theological accounts concerning the ultimate principle of all, the One which is also the Good, in relation to the many which derive from the One-Good.
In class I will refer to the Divided Line that separates the physical world and the transcendent world of the Forms and connect it to the reasoning of the Parmenides on the one and the many.
Aristotle:
We have seen that the term ousia (being, beingness) was used by Plato, Aristotle’s teacher of 20 years, to refer to transcendent Forms, . But for Aristotle the being or beingness, the ousia, of something is the nature of a thing apprehended in the natural world through sensation. Though the term ousia (again, being, beingness) is used by Aristotle, the tradition of Aristotelian studies characterizes this as substance (literally something standing under or underlying or foundational). For Aristotle these ousiai (plural) are determinate particular entities or “thises” (e.g. this dog, this tree, this Socrates who is a determinate particular entity). The ousia (substance)is first category of being as the foundational nature of being that underlies other transitory categories of being. These latter are the nine accidental transitory categories (quantity, quality, place, time, position, relation, possessions action, passion). These other categories are predicated / said of ousia, the determinate particular. “Socrates is sitting.” “Plato was in Syracuse at a certain time.” (Ousia is polysemous: first ousia is a determinate particular individual, the substance, e.g. Socrates. Second ousia is the universal which can be predicates of the determinate individual, e.g., Socrates is a human being. (There are other uses of ousia as well but we will not get into that here in this very brief account.)
Aristotle rejects the Platonic doctrine of the forms and insists that the primary metaphysical foundation is not some transcendent cause (scil. the Forms) but rather the determinate particular entity or ousia (substance). For Aristotle all knowledge begins in sense perception and it is through study of particular entities that we come to an understanding of genera and species and the differences of things. Aristotle was first and foremost a biologist but he had to invent that classification and many other sciences in his philosophical accounts. We saw that in Metaphysics 1.1-2 Aristotle states that all humans by nature want to know. He then proceeded to speak of sense perception, experience (built of multiple sensory instances), to the formation of an art, and then ultimately of the seeking of first and highest causes (the eternal movement of bodies in the heavens). Implicit in that was a consideration of the four causes: final, formal, material and efficient.
In his Physics and On the Heavens Aristotle considers these transcendent causes in detail. In Physics he reasons through a discussion of the nature of motion and potentiality and actuality, to reach the first cause and principle of motion, the Unmoved Mover. This is a determinate particular entity or substance (ousia) responsible for the eternal motion of the heavens and that motion’s causality even down to the lowest of substances in the sublunar world. In his Metaphysics Book 12 (Lambda) he reasons that the causality of the first cause is final causality, not efficient or moving causality. He also says there are 47 or 55 of these. However, none of these is to be identified with the Forms of Plato.
For Aristotle, then, the most foundation reality is the determinate particular entity and it is on the basis of the experience of many of these that the mind is able to form a universal concept that is posterior to the experience of the particulars. . For Plato, the transcendent Idea or Form of human being is prior because the individuals in the world are imperfect images. The soul or mind is able to turn away from the world and attain an intellectual understanding of the cause of the imperfect things.
Neoplatonism, or at least Plotinus and some of the later thinkers of the Neoplatonic tradition:
The Plotinus and the Neoplatonic tradition’s thinkers considered the discussion in the second part of the Platonic dialogue Parmenides to be a serious dialectic / dialogical about the One-Good and the Many. The One is beyond being (ousia) as the Good is in the Republic. As such it is beyond knowing since knowing requires that the object of knowledge be or be a being. It is rather a transcendental unity. There are at least two ways of understanding the One and the many for Plotinus. (1) The One is the transcendent cause of all else by emanation. The One caused by emanation Being. Being, seeking to know its cause (which is impossible since the One is above all being and saying), generates infinite forms in a futile attempt to know its cause. These are all the intelligible Forms or Ideas. (Now keep in mind that the universe being described is our universe.) Those Forms will be reflected in imperfect particular individuals in the universe below. From Intellect, then, emanates Soul which is life principle for all things and the cause of all below it by emanation. From it is Nature which encompasses all the individual natures in the universe below. There are souls of any living thing, plant, animal, humans and even higher souls. Humans have souls that high and close to Intellect since they manifest intellectual understanding. Humans are body and soul together so moral virtue and excellence of the entire human being is needed for the perfection of the intellectual soul. The end or goal of the human being is to transcend the body and to return to its Fatherland which whence it came, Intellect. The human being can strive through use of virtue and intellectual excellence to return and fulfill itself in Intellect. In fact, since Intellect is the locus of the Forms and all intellectual knowledge is of eternal Forms, every instance of intellectual thinking on the part of a human individual is a return to Intellect and the Forms there. Only a handful of times does Plotinus mention that he was brought into the unknowable presence of the One. (The One is hyperousia, above ousia, above being.) The experience of communing with the One is, of course, indescribable since no predictions can be applied to it except One, and that is a term for ‘the not many’, not a positive predicate.
The metaphysics of Neoplatonism and Plotinus, then, is an elaboration that goes far beyond the Master, Plato.