Aristotle distinguishes the kinds of variation according to the categories of predication. Since predications fall under substance, quality, quantity, place, relation, and action or affection, variation can occur only where opposites are possible. Variation cannot occur in substance, since nothing is opposite to a substance. It also cannot occur in relation or in action and affection, because these would imply that change itself changes, which leads to logical contradictions and “infinite regress” (123).

Aristotle argues that a change cannot itself change except coincidentally. If changes themselves underwent change, there would be no first stage in any process, making change impossible. Therefore, variation must occur only in underlying subjects that admit opposites. From this, Aristotle concludes that there are three genuine kinds of variation: Variation in quality, variation in quantity, and variation in place. Variation in quality is called alteration. Variation in quantity is described as increase or decrease. Variation in place is movement. Rest is defined as the privation of change in something “capable of admitting change” (125).

Aristotle defines several terms used to describe spatial and relational arrangements. Things are together when they occupy the same immediate place and apart when they occupy different places. Things are in contact when their outer limits coincide. Aristotle explains “between” as that which lies between two contraries in a continuous process of change. Such change involves at least three terms: A starting point, an intermediate stage, and an opposite endpoint.

In spatial change, the extremes are those farthest apart along a straight line. A thing is successive when it follows another with nothing of the same kind between them. Consecutive things are both successive and in contact. Continuous things are those whose touching limits become identical so that they form a single unity.

Aristotle concludes that these relations form a hierarchy: Successiveness is primary, contact requires successiveness, and continuity requires contact.

Aristotle explains that the unity of change can be understood in several senses because the term “one” (127) is used in different ways. Changes may be generically one when they belong to the same category, such as movement or alteration. They are specifically one when they occur within the same species of change, such as one instance of becoming white compared with another. A change is unqualifiedly one when the same object undergoes a single species of change during one continuous period of time.

To determine the unity of a change, Aristotle considers three elements: The thing changing; the respect in which it changes; and the time during which it changes. For a change to be strictly one, all three must remain unified and uninterrupted. If rest intervenes, the process becomes multiple changes rather than one continuous change.

Aristotle also distinguishes between continuous and uniform change. A continuous change has no interruption, while a uniform change proceeds at a constant rate. Uniform changes appear more unified than nonuniform ones, though both may remain single if continuous.

Aristotle examines how one change can be opposite to another. Several possibilities might be considered: Changes may have opposite starting points, opposite endpoints, or starting points that correspond to the other’s endpoints. Aristotle evaluates these possibilities to determine which genuinely constitute opposition and he argues that changes are not opposite simply because one begins where another ends. In such cases, the processes are effectively identical rather than opposed. Nor are changes opposite merely because their starting points are opposed. Instead, opposition between changes is best explained by opposite endpoints, since changes are typically identified by the state toward which they move.

The clearest opposition, Aristotle says, occurs when both the starting points and the endpoints are opposed. A change from health to illness, for example, is opposite to a change from illness to health. Similar examples appear in movement: Upward movement is opposite to downward movement, and movement to the right is opposite to movement to the left.

Aristotle distinguishes such variations from processes like coming to be and ceasing to be, which are changes but not variations because they do not involve two existing opposite states. When intermediate states exist, movement toward the intermediate can function as movement toward an opposite relative to the direction of change.

Aristotle examines how change and rest are opposed. Rest, he says, “seems to be the opposite of change” (133). Change may be opposed either by another change or by rest, since rest is the privation of change. For each specific type of change, there is a corresponding kind of rest that opposes it. For example, the opposite of change of place is remaining in a place. Staying at one location is opposed to movement away from it, while remaining at another location is opposed to movement from that place in the opposite direction. States of rest themselves may also be opposed, such as remaining healthy versus remaining ill.

In cases where no opposite state exists, Aristotle distinguishes “changelessness” (134) from rest. For instance, the absence of change in existence cannot properly be called rest; instead, it is simply a state without change. Aristotle also considers the distinction between natural and unnatural change and rest, especially in locomotion. Natural movement follows a thing’s nature, such as fire moving upward or earth moving downward. Unnatural motion occurs by force, such as earth being pushed upward. Correspondingly, unnatural rest may oppose a natural movement.

He concludes that changes oppose other changes, and states of rest oppose other states of rest, according to the direction and nature of the processes involved.