Aristotle (384–322 B.C.)

Physics: Books V to VIII

Summary Physics: Books V to VIII

Aristotle’s reflections on cause and change lead him ultimately to posit the existence of a divine unmoved mover. If we were to follow a series of causes to its source, we would find a first cause that is either an unchanged changer or a self-changing changer. Animals are the best examples of self-changers, but they constantly come into being and pass away. If there is an eternal succession of causes, there needs to be a first cause that is also eternal, so it cannot be a self-changing animal. Since change is eternal, there must be a single cause of change that is itself eternal and continuous. The primary kind of change is movement and the primary kind of movement is circular, so this first cause must cause circular movement. This circular movement is the movement of the heavens, and it is caused by some first cause of infinite power that is above the material world. The circular movement of the heavens is then in turn the cause of all other change in the sublunary world.

Analysis

The problems associated with time, change, continuity, and infinity are all related. If space and time are continuous, that implies that there are an infinite number of points in space or moments in time between any two given points or moments. As Zeno’s paradoxes sharply illustrate, assuming continuity in space and time then raises the problem of how we can ever cross an infinite number of points in space or pass an infinite number of moments in time. If they are infinite they have no end by definition. How we make sense of the concepts of infinity and continuity, then, are not simply mathematical questions but questions that have real bearing on how the world is put together. One solution, proposed by philosophers known as the Atomists, is that time and space are not continuous but consist rather of very small, indivisible units. Aristotle rejects this position on the grounds that it makes nonsense of the idea of change: something can only be in a state of change if it makes a continuous transition from one state to another. Aristotle wants to hold on to change, but to do so, he must also uphold the continuity of time and space, which puts him into trouble with Zeno’s paradoxes.

Aristotle’s distinction between potential and actual infinities is an ingenious means of maintaining the continuity of space and time without falling victim to Zeno’s paradoxes. Denying out of principle the very idea of infinity would raise all sorts of complicated mathematical problems, so Aristotle does not want to rule infinity out entirely. However, he is steadfast in denying the actuality of infinity: he says that the universe is not infinitely large, that there is not an infinite amount of matter in it, and so on. However, he grants, it is in theory possible that we could count up to infinity or measure an infinite number of points on a ruler, and so on. Because we could potentially divide up time or space infinitely, we can accept the continuity of space and time as well as the existence of a state of change. However, because neither space nor time can ever actually be divided up infinitely, Zeno’s paradoxes do not hold muster.

Aristotle’s distinction between actual and potential infinities has been the topic of a great deal of debate and has ultimately been proved false. In the nineteenth century, mathematicians developed a rigorous means of expressing concepts such as continuity and infinity that renders Aristotle’s distinction between two kinds of infinity unnecessary. It turns out Zeno was right, at least in a limited sense: though change is possible, there is no such thing as a state of change. We can accept that space is continuous and accept that an object moving through space passes through an infinite number of points so long as we do not insist that it is in a continual state of change. For example, we can easily show how Achilles overtakes the tortoise by showing in a table the relative positions of Achilles and the tortoise at different moments in time. This table will show position and time but will say nothing about the motion of the two bodies. Motion is something we can infer from the fact that Achilles is at one place at one moment and at another the next, but Achilles is not in a “state of motion” at any of those given moments. Not all mathematicians would agree to the solution outlined here, and the Zeno’s paradoxes remain a subject of debate even now.

Aristotle returns to his idea of an unmoved mover in greater detail in the Metaphysics, but it is worth noting here the role this divine figure plays relative to the rest of the cosmos. Aristotle places the earth at the center of the cosmos, orbited by a number of concentric spheres holding the sun, the moon, the planets, and ultimately the stars. The movement of all heavenly bodies, then, is circular, and the earth itself is a sphere at the center of other spheres. Aristotle explains that all these spheres are in motion because of a divine figure beyond the outer sphere of stars. This unmoved mover can himself only move the sphere of the stars, and the movement of the stars in turn influences the movement of all the other spheres and hence of life on earth. We can see in this conception of the cosmos why astrology has had such a grip on the Western mind: everything that happens on the earth in Aristotle’s conception is ultimately a reaction to the movement of the heavens.