Aristotle examines how many principles of nature exist. There may be one principle or several. If there is a single principle, it either changes or remains unchanging. Parmenides and Melissus (Eleatic philosophers) claim that being is single and unchanging. Other natural philosophers hold that the principle is one but changing, identifying it with elements such as air or water. If there are several principles, they may be finite or infinite. Democritus proposes infinitely many principles of the same kind that differ in shape.

Aristotle argues that the claim that being is single and unchanging does not belong to natural science, because the study of nature assumes that change exists. Observation shows that natural things change. He then examines what thinkers mean when they claim that “all [things are] one” (12). Being and oneness have several meanings. If unity means continuity, multiplicity follows because continuous things are divisible. If unity means indivisibility, quantity and quality disappear. The same thing can be one in one respect and many in another.

Aristotle continues his criticism of the claim that all things are one. He argues that Melissus and Parmenides “argue sophistically” (13). Melissus assumes that because everything that comes into being has a beginning, what was not generated must have no beginning. Aristotle rejects this inference, noting that unity does not prevent motion or internal change. Even if things are made of the same underlying material, they can still differ in species, as a man differs from a horse. Parmenides’s argument fails, Aristotle says, because it assumes that “being” (15) has only one meaning. Aristotle argues that being is said in several ways. Even if a term has a single definition, it can still apply to many things. Attributes such as pallor depend on an underlying subject and cannot exist independently.

Aristotle also argues that definitions show that things are divisible into parts, such as the definition of a man including both animal and two-footed. Attempts to avoid plurality by denying non-being or by positing indivisible magnitudes fail. He concludes that “it is impossible for being to be single in the way they want it to be” (16).

Aristotle next examines the views of earlier natural philosophers. Some thinkers hold that the underlying material principle is single. They identify it with a basic substance such as fire, air, water, or another material intermediate between them. According to this view, all other things arise through processes of condensation and rarefaction, which function as opposing conditions that generate plurality.

Other philosophers claim that the underlying substance is one but contains opposites within it. These opposites are later separated out. Aristotle associates this view with Anaximander, Empedocles, and Anaxagoras. Empedocles explains mixture and separation as part of a repeating cycle, while Anaxagoras treats separation as a single event and proposes infinitely many ingredients within the original mixture.

Aristotle criticizes the theory that there are infinitely many principles. If principles are infinite in number and form, knowledge becomes impossible because knowledge requires understanding the elements of a compound. He also argues that natural bodies cannot have parts of unlimited size or number. The claim that everything contains everything leads to “absurd” (19) contradictions about size, division, and composition. Aristotle concludes that theories with a finite number of principles, such as that of Empedocles, are more reasonable.

Aristotle argues that the principles of natural things must be opposites. Many earlier thinkers agree with this position. Even philosophers who claim that reality is one, such as Parmenides, treat hot and cold, or fire and earth, as basic principles. Others, including Democritus, rely on contrasts such as the full and the void, or differences in position, shape, and arrangement, which also contain oppositions.

Aristotle explains that principles must not derive from one another and must not depend on other things. What he labels “primary opposites” (20) satisfy these conditions because each is independent and neither is composed of the other. Observation of change supports this view. A thing does not arise randomly from anything whatsoever. Instead, change occurs between opposite states. What becomes pale comes from what is not pale, such as what is dark or intermediate between the two.

The same pattern applies to all processes of coming to be and passing away. Structured things arise from what lacks structure; intermediates arise from opposing extremes. Since natural change consistently occurs between opposites, Aristotle concludes that the principles of nature “must be opposites” (22).

Aristotle next considers how many principles exist. There cannot be only one, because principles must be opposites and “opposites are not a single thing” (22). At the same time, the principles cannot be infinite. If they were infinite, knowledge would be impossible and the number of oppositions within a single genus would be unlimited. Aristotle also argues that explanation requires only a finite number of principles.

He then considers whether there are two principles or more. Two opposites alone cannot explain change, because opposites do not act directly on each other. Processes such as mixture and transformation require a third underlying subject upon which the opposites act. This view resembles the theories of natural philosophers who posit a single underlying material, such as water or air, which receives different forms through opposing conditions like rarity and density. Aristotle concludes that the principles must be limited in number and likely consist of two opposites together with a third underlying substrate. He notes that deciding definitively between two or three principles is “very problematic” (24).

Aristotle presents his own account of the principles of natural things by examining the process of coming to be. When something comes to be, there is always an underlying subject that persists through the change. For example, a person becomes educated. The person remains, while the state of being uneducated does not persist. In this process the subject persists, but the opposite condition disappears.

From this analysis, Aristotle concludes that “coming to be” (25) always involves a composite structure. There is the underlying subject and there is the form or condition that the subject acquires. Opposites such as educated and uneducated or structured and unstructured, mark the transition between states. The underlying subject is numerically one but different in form from the opposite states that affect it. Matter such as bronze or stone serves as the subject, while form gives it its determination.

Aristotle therefore explains natural change through three principles: The underlying matter; the form; and the privation or opposite of that form. From one perspective there appear to be two principles—the opposites—but strictly speaking there are three.

Aristotle explains that his account of principles resolves the difficulties faced by earlier philosophers. These philosophers, Aristotle argues, were “deflected by their inexperience down a side-alley” (28). Earlier thinkers argued that nothing truly comes to be or ceases to be. They reasoned that something could arise only from what is, or from what is not. Since what is already exists and nothing can arise from what is not, they concluded that change and plurality are impossible.

Aristotle argues that this conclusion results from failing to distinguish different senses in which something can come from what is or what is not. He illustrates this with the example of a doctor. A doctor may build a house, but not insofar as he is a doctor—he acts as a builder. Likewise, something may come to be from what is not in a qualified sense. When a thing comes to be, it arises from a privation that does not persist, while an underlying subject remains. Earlier thinkers, Aristotle says, misunderstood this structure of change. By recognizing the roles of underlying subject, form, and privation, Aristotle explains how coming to be and change are possible.

Aristotle criticizes the Platonist account of principles. These thinkers accept Parmenides’s claim that what comes to be arises from what is not and they identify the underlying nature with a single principle, such as “great and small” (31). Aristotle argues that this view fails to distinguish clearly between matter and privation. Matter is something that exists in a qualified sense and is close to substance, while privation is what in its own right is not.

According to Aristotle, the Platonists recognize an underlying nature but treat it as one rather than as a distinct relation between matter and its opposite. They also misunderstand the relation between form and its opposite. Form does not desire its opposite, nor do opposites desire each other. Instead, matter tends toward form.

Aristotle also explains that matter neither comes to be nor ceases to be in the same way as other things. As the ultimate underlying subject, it persists through change and cannot itself originate from a prior substrate.