Book Theta discusses potentiality and actuality, considering these concepts first in regard to process or change. When one thing, F, changes into another, G, we can say that F is G in potentiality, while G is G in actuality. F changes into G only if some other agent, H, acts on it. We say that H has active potentiality and F has passive potentiality. Potentiality can be either rational or irrational, depending on whether the change is effected by a rational agent or happens naturally. Aristotle distinguishes rational potentiality from irrational potentiality, saying that rational potentiality can produce opposites. For example, the rational potentiality of medicine can produce either health or sickness, whereas the irrational potentiality of heating can produce only heat and not cold. All potentialities must eventually be realized: if a potentiality never becomes an actuality, then we do not call it a potentiality but an impossibility. A potentiality is also determinate, meaning that it is the potential for a particular actuality and cannot realize some other actuality. While irrational potentialities are automatically triggered when active and passive potentialities come together, this is not the case with rational potentialities, as a rational agent can choose to withhold the realization of the potentiality even though it can be realized.
Aristotle identifies actuality with form, and hence substance, while identifying matter with potentiality. An uncarved piece of wood, for example, is a potential statue, and it becomes an actual statue when it is carved and thus acquires the form of a statue. Action is an actuality, but there are such things as incomplete actions, which are also the potentiality for further actions. Aristotle distinguishes between incomplete and complete actions by saying that incomplete actions do not contain their purpose within them, while the latter do. For example, dancing is a complete action because it is an end in itself, whereas fetching wood for a fire is an incomplete action because the end of fetching wood is to create a fire. If one thing can turn into another, that first thing is always potentially the other. That means that anything is potentially something else and that it was something else in the past with the potential to become what it is now. Aristotle speculates about the existence of an ultimate matter, which is potentially anything.
Aristotle argues that actuality is more fundamental than potentiality for three reasons. First, we cannot think of something as a potentiality without also thinking of the actuality it can potentially become, but we can think of an actuality without thinking of its potentiality. Second, for something to be potentially something else, that something else must already exist in actuality or there would be nothing for that potentiality to become. Third, Aristotle identifies actuality with form, which is in turn related to substance, which is the most fundamental thing that there is.
Book Iota treats the topic of unity, which is important to Aristotle because he has argued in book Zeta that both a substance and its definition are unities. Unity itself, however, is not a substance for two reasons. First, unity is a universal, not a species. Second, unity is always a property of something else: there is one table, one person, one chair, but never the number one by itself.
The discussion of unity leads into a discussion of contrariety, which Aristotle defines as a maximum of difference and can only hold between two extremes. Two species of the same genus differ from one another in having contrariety in their forms. For example, one animal that has wings and one that does not have wings are different species within the genus animal. On the other hand, men and women are not of different species because the contrariety that exists between them is on the level of matter, not form.
Book Kappa, which some scholars doubt was even written by Aristotle, consists mostly of repeating doctrines already enunciated in the Physics or in earlier books of the Metaphysics.
Book Lambda begins with an overview of philosophy that stands somewhat independently of the rest of the Metaphysics. Aristotle re-emphasizes the primacy of substance and explains that there are three kinds of substance: two kinds of perceptible substances, perishable or imperishable, which are the subject of natural science, and substance that is immune to change, which is the subject of logic and mathematics.
Theology investigates the question of whether there is some common source to all substance, and Aristotle identifies this common source as a divine “prime mover.” There must be some kind of eternal, unchanging substance because the earth and time are not perishable, so there must be some substance within them that is also imperishable. This eternal substance has no potentiality, but only actuality, and its perpetual actuality makes the world eternal as well. This eternal substance must also be the prime mover, the source of all movement and change in the cosmos. To be the primer mover, this substance must itself be unmoving. The prime mover is an object of desire for the heavenly bodies, causing them to move. The prime mover is an object of desire only because it is supremely desirable, so it must enjoy the best possible life. Aristotle hence identifies this prime mover with a benign God, who spends his time in contemplation of contemplation itself. Aristotle wavers between saying there is a single prime mover or multiple prime movers. If there are many, their number, based on astronomical calculations, is either 47 or 55. The prime mover contemplates contemplation because anything lower would be unworthy of it and anything higher would imply that there is something more desirable than the existence of the prime mover himself. Because the prime mover is good, this means the universe as a whole is good.
Books Mu and Nu consider the metaphysical status of mathematics, and Aristotle concludes that mathematical entities are not substances. Aristotle attacks in particular Plato’s view that each number corresponds to a Form, primarily because this view obscures the relationships between numbers and fails to explain the relationship between numbers and sensible particulars. Aristotle suggests instead that numbers are physical objects considered in abstraction from their physical and accidental properties. For example, the number five is the same thing as five cats once we factor out everything that makes the cats cats instead of something else. Aristotle concludes by rejecting the idea that numbers can play a causal role in nature, reaffirming his view that substance is at the foundation of nature.
In arguing that actuality is more fundamental than potentiality, Aristotle effectively argues that the chicken comes before the egg, as one commentator puts it. He is telling us that an object can only be a potential something if there is already an actual something for that object to become. This claim has the paradoxical result that, for instance, the chicken must already exist for the egg to be a potential chicken. Of course, it is obviously false that individual chickens precede individual eggs: every chicken that now exists must have been an egg at some point. However, according to book Zeta, individual chickens are not substances. The species of chicken is a substance, and there can be no chicken eggs until there is a species called “chicken” for those eggs to become. After all, we cannot point to an object and say, “that is a chicken egg” if there is no such thing as a chicken. Substance is the most fundamental thing there is, so substance must be an actuality. Since, as Aristotle has argued earlier, nothing can exist unless substance exists, that means that potentialities cannot exist unless their actualities as substances already exist.
Aristotle’s discussion of actuality and potentiality in book Theta provides an important link between the discussion of substance in books Zeta and Eta and the discussion of theology in book Lambda. In book Zeta, Aristotle tells us that species are substances, so the universe is fundamentally made up of the sorts of things we find in the world around us. In book Theta, he explains that substances are fundamental because they have actuality: they are what other things are trying to become. With actuality added as a new and important criterion for substancehood, we can infer that the most fundamental substances are completely actual, with no potentiality. Substances such as humans and chickens have potentiality in the form of fetuses and eggs, so they are not completely actual. In book Lambda, Aristotle suggests that there are also eternal substances and that these are more important and more fundamental than the species of the world around us because they are only actuality, with no potentiality. The concept of actuality, then, points to a way in which the material substances discussed in book Zeta fall a bit short of the fundamental role Aristotle wants them to play, and the theological discussion of book Lambda must make up for this shortfall.
When Aristotle talks about a prime mover or a first cause, he means that this mover or cause comes first conceptually rather than chronologically. That is, we should not imagine a universe at rest however many billions of years ago that is then set in motion by the prime movers: they do not come first in the sense that they are what first set everything in motion. On the contrary, Aristotle argues at a number of points in the Physics and Metaphysics that time is eternal, so that there is no beginning to time. Rather, we should think of the prime movers as first conceptually. For example, we could ask why the soccer ball is rolling and say that Ronaldo kicked it. We could then ask why Ronaldo moved his leg and say that he felt a certain desire. We could then explain the desire by appealing to certain causes in Ronaldo’s life, and so on. So the movement of the soccer ball could be explained by the movement of Ronaldo’s leg, by Ronaldo’s desire, by Ronaldo’s life story, and so on. The deepest explanation of any movement, says Aristotle, are these prime movers. They are not first in time so much as they are the ultimate explanation one can appeal to in explaining any movement.
The seemingly bizarre conclusions that the prime movers are objects of desire for the heavens and that they occupy themselves by contemplating contemplation are consequences of Aristotle’s claim that prime movers themselves are unmoved. Aristotle wants the prime movers to be unmoved for fear of an infinite regress: if they are moved, we can ask what moves them, and then ask what moves their movers, and so on. However, according to Aristotle’s theory of causation, something cannot cause another thing to move unless it imparts movement to that other thing. A person cannot move a box without pushing or pulling on it. The only cause of motion that seems not to require movement is desire. If the prime movers were to push the heavens in their circular movements, they would themselves be moving, but if the heavens move in a circular pattern out of a desire for the perfection of the prime movers, this does not call for any movement on the part of the prime movers. This, of course, raises the question of what makes the prime movers so perfect that the heavens should move for them, and for reasons previously outlined, Aristotle concludes that they engage in the perfect activity of contemplating contemplation.