Either affirming or denying the existence of infinity leads to certain contradictions and paradoxes, and Aristotle finds an ingenious solution by distinguishing between potential and actual infinities. He argues that there is no such thing as an actual infinity: infinity is not a substance in its own right, and there are neither infinitely large objects nor an infinite number of objects. However, there are potential infinities in the sense that, for example, an immortal could theoretically sit down and count up to an infinitely large number but that this is impossible in practice. Time, for example, is a potential infinity because it potentially extends forever, but no one who is counting time will ever count an infinite number of minutes or days.
Aristotle asserts that place has a being independent of the objects that occupy it and denies the existence of empty space, or void. Place must be independent of objects because otherwise it would make no sense to say that different objects can be in the same place at different times. Aristotle defines place as the limits of what contains an object and determines that the place of the earth is “at the center” and the place of the heavens as “at the periphery.”
Aristotle’s arguments against the void make a number of fundamental errors. For example, he assumes that heavier objects fall faster than lighter ones. From this assumption, he argues that the speed of a falling object is directly proportional to an object’s weight and inversely proportional to the density of the medium it travels through. Since the void is a medium of zero density, that would mean that an object would fall infinitely fast through a void, which is an absurdity, so Aristotle concludes that there cannot be such a thing as a void.
Aristotle closely identifies time with change. We register that time has passed only by registering that something has changed. In other words, time is a measure of change just as space is a measure of distance. Just as Aristotle denies the possibility of empty space, or void, Aristotle denies the possibility of empty time, as in time that passes without anything happening.
Aristotle’s conception of the natural world is based fundamentally on change. Rather than simply accept the fact that things change, Aristotle marvels at this fact and puzzles over how the world must be if change is possible. What change is and how it comes to pass sit at the heart of Aristotle’s scientific investigations. He investigates the fundamental principles of nature by asking what takes place in a process of change. He outlines four causes that explain change. He treats time as a measure of change. Later in the Physics, he expends a great deal of ingenuity on refuting paradoxes that suggest that change does not exist. This fascination with change allows Aristotle to look more deeply into the workings of nature than most of us would think to. By the end of book I, he claims to have discovered the three basic principles of nature without which change would be impossible. That is, by asking how it is that change might be possible, he develops a basic sense of how the universe must be arranged.
Aristotle’s investigation of the principles of matter leads him to draw the important distinction between form and matter. A classic example that illustrates this distinction is that of a bronze statue: the bronze is the matter, while the figure of the statue is the form. Neither matter nor form can exist independently. Even a lump of bronze would have some form, though the form would be less distinctive than that of a statue. Similarly, it would be impossible for a form to exist without some matter to take on that form. The statue need not be made of bronze to have its form, but it must be made of something. The form–matter distinction does a great deal of work for Aristotle, especially in the Physics and the Metaphysics, as it allows him to explain how something can both change and remain the same. If the bronze statue were melted down, for instance, the form would have changed but the matter would remain the same. If there were no unchanging matter, we would have no grounds for saying that the lump of bronze was in some way the same bronze as that which made up the statue.