Aristotle continues to argue that magnitude, time, and motion are continuous and divisible without limit. He begins from the principle that “every magnitude is divisible into magnitudes” (141). From this, it follows that if one object is faster than another, the faster one travels a greater distance in equal time, travels the same distance in less time, and travels a greater distance in less time. These relations show that both distance and time must admit of division.

Aristotle then argues that because motion always occurs in time and can occur more quickly or more slowly, time must be divisible. By comparing the motion of a faster and a slower object, it is possible to repeatedly divide both the time and the magnitude traversed. This process can continue indefinitely, demonstrating that time and magnitude are continua.

Aristotle also answers Zeno’s paradox, which he believes makes a “false assumption” (143). A continuum can be infinite either in extent or in divisibility. An infinite distance cannot be traversed in finite time, but a finite distance can contain infinitely divisible parts. Therefore, distance, time, and motion must all be continuous and divisible without limit.

Aristotle argues that the “now […] must also be indivisible” (144). The now serves as the limit between past and future time. Since it is the single boundary shared by both, it cannot consist of parts. If it were divisible, there would have to be time between the divisions, which would contradict the idea that the now is the limit of past and future. Therefore, the same indivisible now marks the end of the past and the beginning of the future.

From this, Aristotle concludes that motion cannot occur in a now. If motion occurred within a single now, a faster object would travel farther than a slower one in that same instant, implying that the now could be divided into smaller intervals. Since the now is indivisible, this is impossible. Rest also cannot occur in a now, Aristotle argues, because rest requires comparison between an earlier time and the present. Since the now has no earlier part within itself, both motion and rest must occur in time rather than in a single instant.

Aristotle argues that everything that changes must be “necessarily divisible” (146). Any change has a starting point and an endpoint; during the process, part of the changing object is closer to the starting state, while another part approaches the endpoint. Since a thing cannot be wholly at both states or at neither, the changing object must have divisible parts.

Change is divisible in two ways, Aristotle says. First, it is divisible because the time in which it occurs is divisible. If time is divided into smaller portions, the amount of change occurring within each portion is correspondingly smaller. Second, change is divisible according to the parts of the object that undergo the change. Each part has its own partial change and—together—these constitute the whole change of the object. Aristotle concludes that the time, the change itself, the changing object, the process of changing, and the respect in which the change occurs are all divisible. The divisibility of one “implies the divisibility of them all” (149).

Aristotle argues that whenever a change is completed, the changing object is immediately in the state to which it has changed. Once the object departs from the starting point of the change, it must arrive at the endpoint rather than remain in some intermediate condition. In the case of changes involving contradiction (such as coming into existence from nonexistence), the result is clear: Once the change is complete, the object exists. The completion of change therefore occurs at an indivisible moment.

Aristotle then distinguishes between the moment when a change is completed and the supposed first instant when a change begins. While the completion of change occurs at an indivisible limit, there is no first instant at which the change begins. Any proposed beginning can always be divided into earlier parts of time, so there is no earliest moment of the process. From this, Aristotle concludes that neither the changing object nor the time of change contains a first part in which change begins. Only the endpoint or respect of the change can function as an indivisible limit, and “the only kind of change which can be indivisible in its own right is change of quality” (152).

Aristotle argues that whatever is changing has already changed earlier and whatever has changed must previously have been changing. A changing object changes within an “immediate” (153) time, meaning that every part of that time belongs to the change. If a portion of that time contained no change, the object would be at rest, which contradicts the idea that the whole period is the time of the change.

From this, Aristotle concludes that whenever something is changing, it must already have completed part of the change earlier. Since time is divisible, the change can always be divided into earlier and later stages. Thus, a moving object has already moved before the present stage of motion. Likewise, anything that has changed must previously have been changing. Since change requires time—and time is divisible without limit—every completed change presupposes earlier stages of change. The same reasoning applies to coming into being and ceasing to be, showing that there is no first stage of change.

Aristotle argues that time, magnitude, and motion must correspond in extent. If an object moves, he reasons, it necessarily does so in time and across a magnitude. From this relation, he concludes that a finite distance cannot be traversed in an infinite time, because the distance can be divided into finite parts, each of which must be crossed in a finite portion of time. When the number of such parts is finite, the total time must also be finite. He also argues that an infinite distance cannot be traversed in a finite time. Each finite portion of time would correspond to a finite portion of the distance, so when the time ends, only a finite amount of the magnitude would have been covered. The same reasoning applies, regardless of whether motion occurs at a constant speed.

Aristotle concludes that if any one of the three—time, magnitude, or motion—is infinite in extent, the others must be infinite as well, since motion always occurs through magnitude and within time.

Aristotle argues that there is no final instant of coming to a standstill and no first instant of being at a standstill. Something that is “coming to rest” (148) must still be moving during the time in which it comes to rest, since if it were not moving it would already be at rest. Since motion occurs in time, coming to rest must also occur in time and can happen faster or slower.

The time in which an object comes to rest is divisible. If this time is divided, the object must be coming to rest during each part of it. Since time is infinitely divisible, there can be no first moment at which the process of coming to rest occurs. Similarly, there is no first moment of being at rest. Rest requires comparison between at least two moments, because something is said to be at rest when it remains in the same state now and earlier. Since any time can be divided further, rest—like motion—occurs in time and not in an indivisible instant.

Aristotle addresses Zeno’s arguments against motion and argues that they do not create genuine difficulties. Zeno’s “reasoning is invalid” (161), Aristotle argues. Zeno’s theory that a moving arrow is motionless assumes that time is composed of indivisible nows. Aristotle rejects this assumption, maintaining that time is continuous and divisible, so the argument fails. Zeno’s first two arguments—the so-called dichotomy and Achilles paradoxes—claim that motion cannot reach a limit because a distance can always be divided further. Aristotle replies that, although a magnitude can be infinitely divisible, a moving object can still traverse a finite distance.

He also rejects Zeno’s argument about bodies moving in a stadium. The error lies in assuming that a moving object takes the same time to pass a body at rest as it does to pass a body moving in the opposite direction. Finally, Aristotle explains that processes of change can occur between contradictory states without contradiction and that rotating bodies are “never at rest” (163) simultaneously because their parts continually change place.

Aristotle argues that something without parts cannot change “except coincidentally” (163). An indivisible thing could appear to move only incidentally, such as when an object inside a ship is carried along by the ship’s motion. Genuine change requires a subject that can occupy different states during the process. If something had no parts, Aristotle suggests, it could not be partly in one state and partly in another, which is required during change. Therefore, it would either already have completed the change or still be entirely in its original state, meaning no change occurs.

He also argues that if an indivisible point moved, it would have to traverse a magnitude equal to or smaller than itself. Since a point has no magnitude, this would imply that a line is composed of points, which Aristotle rejects.

Finally, Aristotle considers whether change can be infinite. Every change has limits defined by opposites or contradictories, so a single process of change cannot be infinite in this sense. Only circular motion, Aristotle believes, could continue indefinitely in time.