The first problem we face, when interpreting Aristotle’s arguments against an infinite causal regress of motions in Physics VII and VIII is the apparent inconsistency between his no-regress arguments and his explicit belief that the universe is infinitely old. Aristotle believed that each of us has infinitely long family tree: father, grandfather, great-grandfather, and so on, ad infinitum. Why does this not count as an infinite regress?
Later commentators, including Avicenna, Averroës, and Thomas Aquinas, introduce a distinction between two kinds of causal series, per se and per accidens. They then suppose that a per se infinite regress is impossible but a per accidens regress is possible.
It’s true that Aristotle makes at least two distinctions between per se and per accidens causal connections in the Physics. First of all, there is the distinction between the physician who heals a patient, and the baker who heals a patient (assuming that the physician is the baker). In such a case, the person causes the healing per se as a physician but only per accidens as a baker. This sort of distinction is not going to help Aristotle, since the infinite regress of fathers involves per se links at every stage. The father begets his son per se as a father.
In Physics VII, Aristotle introduces another per se and per accidens distinction in causal relations, between those causes that are only accidentally and contingently followed by their effects, and those causes that are essentially and necessarily followed by their effects. I think Aristotle is considering two theories of causation here, with per accidens causation being an anticipation of Hume’s deflationary account of causation, while per se causation involves some real or “necessary” connection between the cause and the effect. This distinction is also of no help in resolving the inconsistency, since, once again, the connection between a father and son is essential or per se, not a mere Humean regularity.
In light of my interpretation of Aristotle’s prime mover, this is how I resolve the contradiction. A series of total causes cannot be infinite, but a series of partial causes can. The father is only a partial cause of his son’s generation. At most, the father’s activity can bring the moment of generation of the son to a condition of second potentiality, a state in which the generation is poised to happen, once the new instant of time is generated. But the generation of the new moment of time requires the agency of the Prime Mover, actualizing the arrival of the prima mobilia (the heavenly spheres) at their appropriate locations. And Aristotle says as much: it is the man and the sun that generate man. The father is never a total cause of the generation.
Aristotle offers three arguments against the possibility of an infinite regress of total causes of motion. The first is limited to the case in which the movers are all bodies, corporeal substances. Suppose for contradiction that there were an infinite regress of motions, each the total cause of its successor, and all simultaneous (since only simultaneous causes can be total). Aristotle tacitly assumes that no body can simultaneously undergo as a whole an infinite number of distinct motions, which seems a reasonable assumption. If so, then this infinite regress must involve an infinite number of bodies. If we assume that the mover and movee or (motum, in Latin) must be in physical contact, then this infinite collection of bodies must compose a single, infinitely complex body. It must either be infinitely large or finite but infinitely sub-divided. In Physics Book VI, Aristotle argued (in response to Zeno’s paradoxes) that both of these hypotheses are metaphysically impossible. QED.
But, wait! Aristotle assumed that a mover and its immediate motum must be in physical contact. Where does he prove that that must be the case? Nowhere, as far as I know. Action at a physical distance may be a little weird, but can we assume that it is metaphysically impossible?
Fortunately, we don’t have to assume that in order for Aristotle’s argument to work. All we must assume is that, if mover C can move motum E at a distance, then it is also possible for C to move E when they are in physical contact. That certainly seems reasonable. Movers don’t lose power by being closer to their moti (plural of motum). Now we can reasonably generalize this insight to an infinite collection of movers. If M1, M2, … is an infinite series of motions, and for each i, Mi+1 moves Mi at a distance, then there is a possible world where we find an infinite series K1, K2,… intrinsically like M1, M2,…, where each Ki+1 is in physical contact with Ki. But now we know that such a world is metaphysically impossible, involving an infinitely large or infinitely sub-divided but finite body. So, therefore, any infinite regress of physical motions is impossible.
As I mentioned, this proof is limited to physical motions. It is consistent with the possibility that there could be an infinite regress of non-physical motions (or changes). Suppose we had an infinite number of spirits, each of which experiences some cognitive change caused by its predecessor in the regress. Has Aristotle ruled out such a non-physical regress?
Even if he hasn’t, this first argument against infinite regresses is still significant, since it refutes the possibility of a totally physical universe. The universe must contain at least one non-physical agent.
But Aristotle can argue that the proof is even more powerful than that. Aristotle argues that only bodies can be the primary subject of change or motion. Any non-physical substance or quasi-substance (like a soul or a celestial spirit/angel) can change only per accidens, through and because of some more fundamental change in a body. In modern parlance, any change in a non-physical entity is wholly grounded by some change in a physical entity. In and of themselves, souls and spirits are unchangeable. So, an infinite regress of motions must involve an infinite regress of physical motions, which Aristotle has proved to be impossible.
Why must bodies be the only primary subjects of change? Because all change must be continuous, all continuous change must take place in a continuous subject, and any continuous subject is (by definition) a body. These claims are all substantiated in Book VI of Aristotle’s Physics.
Next week I will cover Aristotle’s second and third arguments against infinite regresses of motions.
The Analytic Thomist 