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.
Analysis
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.
