Aristotle examines the scope of natural science and distinguishes it from mathematics. The “subjects of mathematical investigation” (36) are properties such as lines, surfaces, and numbers, which can be considered separately from change. Natural science studies bodies that possess these properties, but investigates them as features of changing natural objects. Mathematicians abstract these properties from physical bodies, while natural scientists study them as they occur in nature.

Aristotle then returns to the two senses of nature, matter and form, and asks which belongs to the study of nature. He argues that the natural scientist’s job is “to understand both kinds of nature” (37). Earlier thinkers tended to focus mainly on matter, but knowledge of natural things requires understanding both the material components and the form that defines the object.

Aristotle also connects nature with purpose. The end toward which a natural process moves is its nature. Since natural change proceeds toward a determinate result, the study of nature includes both the material conditions of things and the forms and purposes realized in them.

Aristotle examines the kinds of causes involved in explaining natural change. Knowledge requires understanding “why [a thing] is as it is” (39), which means identifying its primary causes. He distinguishes four main types. First is the material cause, the matter from which something is made, such as bronze for a statue. Second is the formal cause, the form or defining pattern that makes a thing what it is. Third is the efficient cause, the source that initiates change, such as a mother producing a child or a craftsperson producing an object. Fourth is the final cause, the end or purpose for which something exists or is done.

A single thing can have several causes of different kinds. Causes may also be described at different levels, such as particular or general, and may function either actually or potentially. Aristotle concludes that explanation requires identifying the most fundamental cause appropriate to each case.

Aristotle considers whether chance and spontaneity should be regarded as causes. Many people attribute events to chance, so Aristotle investigates their nature and their relation to the previously identified causes. Some thinkers deny that chance exists at all. They argue that “there is always a determinate clause for everything” (42), even when it appears accidental. If someone meets another person in the marketplace unexpectedly, for example, the real cause is the decision to go to the marketplace.

Aristotle notes that this position is difficult to accept because people continue to describe certain events as occurring by chance. Earlier philosophers, such as Empedocles, sometimes appealed to chance in their explanations but did not clearly define it as a cause. Others even claim that the formation of the universe occurred spontaneously, while ordinary natural processes follow determinate causes. Aristotle finds this inconsistent and concludes that chance and spontaneity must be investigated carefully to determine their nature and place among the causes.

Aristotle explains how chance can be considered a cause. Some events occur always or usually; these are not attributed to chance. Chance applies only to events that occur neither necessarily, nor regularly. Certain actions are performed for a purpose, either through deliberate choice or through natural processes that tend toward an end. Chance occurs, Aristotle suggests, when an event that could have been done for a purpose happens coincidentally instead. A person may go to a place for one reason, for example, and unexpectedly meet someone from whom he collects money. The meeting serves a purpose but was not intended, so it is attributed to chance.

In this way, chance functions as a coincidental cause within actions directed toward ends. Since coincidental causes can be unlimited and indeterminate, chance itself is considered indeterminate and difficult to explain. Aristotle concludes that chance is not a cause in the primary sense, but a coincidental cause in events that might have occurred for “some purpose” (46).

Aristotle distinguishes between chance and spontaneity. Spontaneity is the broader category, since every event that occurs by chance is also spontaneous, but “not every spontaneous event is a chance event” (46). Chance applies only to events involving agents capable of choice and action. Since chance is connected with deliberate activity, it is associated with good or bad fortune. Spontaneity, however, can apply to animals and even to inanimate objects. An event is spontaneous when it produces a result that could serve a purpose, but did not occur for that purpose. A horse may arrive somewhere and thereby be saved, for example, but it did not come for “the purpose of being saved” (47). Similarly, a stool may fall into a position that allows it to serve as a seat without falling for that reason.

Both chance and spontaneity are coincidental causes of change. However, they are secondary to primary causes, such as nature and intelligence, which remain the more fundamental sources of events.

Aristotle concludes that the natural scientist must investigate all four types of cause. The different meanings of the question “Why?” (48) correspond to these causes. A person may ask what something is, which refers to its form or definition; what initiated the change, which refers to the source of motion; what purpose the change serves, which refers to the end; or what matter the thing is made from.

Aristotle believes that natural science must therefore consider material, formal, efficient, and final causes together. In many cases, these causes coincide. The form of a thing and its purpose are often the same and the source of change may also share this form, as when a human being generates another human being. Aristotle emphasizes that natural inquiry seeks explanations that connect events through necessary or typical sequences and that show why a thing exists in the way that best fulfills its nature and purpose.

Aristotle argues that final causes are essential in explaining natural phenomena. Many thinkers attribute events to necessity, claiming that natural outcomes follow from the inherent properties of elements, such as heat or cold. According to this view, events like rain occur purely by necessity and any beneficial result—such as crops growing—is “an accident” (50). By analogy, some suggest that the parts of the body, such as teeth suited for biting or grinding, arose by chance combinations that happened to prove useful.

Aristotle rejects this explanation. Features of natural things occur either always or usually, whereas chance events do not display such regularity. Since structures like teeth consistently serve particular functions, they must exist for a purpose. Natural processes resemble the operations of skill: Just as crafts produce objects for ends, nature organizes parts toward functional outcomes. Observations of animals and plants reinforce this conclusion. Their structures (such as webs or nests) and activities serve clear purposes, even without deliberate planning. Aristotle concludes that nature acts for an end and that form, which represents this end, functions as a fundamental cause in natural processes.

Aristotle examines the role of “necessity” (53) in natural phenomena. Some thinkers explain natural structures solely through necessity, arguing that the arrangement of parts follows from the inherent properties of materials. Heavier materials, for instance, settle below lighter ones in a wall.

Aristotle accepts that such material conditions are necessary, but argues that they are not the primary reason for the structure. The true explanation lies in the purpose of the object, such as the wall’s role in protection and concealment. Necessity, therefore, operates conditionally. Certain materials must exist if the end is to be achieved, just as iron is required for a saw to perform its function. The necessity lies in the matter, while the end lies in the form and definition of the object.

Aristotle concludes that natural science must recognize both necessity and purpose. Matter and its properties are required conditions, but the final cause explains why these materials are arranged in a particular way.