In order to understand Thomas’s First Way, we have to have a firm grasp on Aristotle’s reasons for positing un Unmoved or Prime Mover in his Physics. And to that, we have to understand his account of time and change.
In modern philosophy and science, since the time of Galileo and Descartes, we are accustomed to thinking of time as something like a fourth dimension of space. The locomotion of a body corresponds to a curve in four-dimensional spacetime. As many philosophers (including Brentano and McTaggart) have complained, there is a serious danger of confusion if we take these mathematical representations too literally. A curve lying in a space of four dimensions is something static, eternally unchanging. The dynamic character of time and change has been lost in such a model. One consequence of this lost is our modern perplexity about discovering an objective “Arrow of Time”.
Aristotle, quite sensibly, begins his account of time with a definition of change. Time on his view turns out to be simply a measure of change. This seems reasonable: continuous processes of change take up intervals of time. Time itself is simply the measure of those intervals. Where there is no continuous change, there can be no passage of time.
Since Aristotle defines time in terms of change, he cannot (and does not) adopt the At-At theory of change (as proposed by Bertrand Russell). On the At-At theory, change consists in some thing having some property at one time and not having that property at another time (either earlier or later). Instead, Aristotle uses three more fundamental notions in defining change: actuality, potentiality, and the “qua” operation. In Physics chapter 2, Aristotle defines change as the actuality of potentiality qua potentiality. This definition is, admittedly, not easy to understand.
Aristotle proposes that reality consists of two domains: the actual and the merely potential. For Aristotle, the realm of potentiality is not merely fictional or imaginary. It is a part of reality, although a secondary and dependent part. The dependency of the actual on the potential has multiple dimensions. The potential is definitionally, causally, and constitutively dependent on the actual. First, definitional dependence. To define what it is to be potentially F, we must first be able to define what it is to be actually F. Consequently, it is conceivable that in some cases we find things that are actually G without any possibility of things’ being merely potentially G. (God’s divinity is an example: there is an actually divine being, but there isn’t and couldn’t be a merely potentially divine thing.) In contrast, it would be impossible for some things to be potentially H if it were impossible for something to be actually H.
The actual is causally prior to the potential, in the sense that something can acquire a new potentiality only through the action of something actual.
The actual is constitutively prior to the potential, since every potentiality is always (ultimately) the potential of something actual.
The actual and the merely potential are mutually exclusive. So, what could Aristotle mean by saying that a change is the actuality of something potential qua potential? Suppose that something x is changing from being non-F to being F. In that case, Aristotle would say that x’s F-ness is still merely potential, but it is actual qua potentially F. The thing x can have many different potentialities. It could be potentially very hot or very cold. It can’t be changing both something hot and something cold at the same time. Only one of these contrary potentialities can be actual qua potential.
For something to be both merely potentially F and actual qua potentially F, we must be able to make a distinction between two kinds of actuality, and correspondingly two kinds of potentiality. This is how I think Aristotle makes the distinction: a thing that is changing into F-ness is only potentially F in itself, but it is actually F through another. What is the “other” through which the changing thing is already actual in its F-ness? It is the agent of the change, the mover of the motion.
Now we can see why every change requires an agent, and every motion requires a mover.
Let’s consider Zeno’s Paradox of the Arrow. An arrow is shot across the field. At every instant during its movement, it is located in exactly one place. At time t, it is actually at location L(t). An arrow that is motionless is also in exactly one place at time t. So, the moving arrow is, at each moment, in essentially the same condition as the motionless arrow. But if the arrow is motionless at each instant of the interval, how can it be moving throughout the interval?
We should say that the moving arrow is both actually at L(t) and also merely potentially at L(t). In itself, it is only potentially at the location. It is only through another that it is actually there. There must be mover M such that the arrow is actually-through-M at location L(t). The potentiality of the arrow’s being at L(t) must be actualized by a mover.
The Analytic Thomist 