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.
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