## Aristotle’s Physics: a review

Aristotle’s Physics concerns key topics in what was a few centuries ago called the philosophy of nature and is now called ontology:  the natures of space, time, motion, causality, and infinity.  When speaking of it, it does not do to patronize Aristotle, saying that of course he wrote what he did because he couldn’t have imagined modern science.  In fact, the Physics is a surprisingly contemporary book.  Aristotle considers the possibilities that the order of the world is fully explicable in terms of chance, of immutable atomic laws, or of the affects of natural selection on biological organisms, and he rejects them.  He is quite aware of the possibility of a Galilean-Newtonian universe (laws of motion space-translation invariant, no preferred inertial frame) and takes efforts to fend it off.

Symmetries

His arguments against the possibility of a “void” are particularly revealing.  Aristotle is fully aware that the consequences of a homogeneous underlying space.  There could be no preferred locations for each of the elements, nor any absolute standard of rest.  In other words, a Galilean-Newtonian universe.  My sense is that Aristotle rejects this not because of prior metaphysical commitments, but just because it did not seem to him to describe the actual empirical world.  Arguments from symmetry considerations play a key role in this work, marking one way that Aristotle did think like a physicist as we use that term today.  Similarly, he argues that motion must extend infinitely into the past as follows.  If not, there would have been some interval of time in the past when all was stationary.  But then how could things have started going again?  Why this time rather than that?  What breaks the time translation symmetry?  (It is also claimed that motion cannot stop in the future, but the argument is obscure.)  Breaking this symmetry is also why the unmoved mover must first move the celestial sphere, which in turn “stirs up” the rest of the universe into motion.  The unmoved mover, being time invariant, cannot prompt different things to happen at different times, and the only constant motion imaginable is rotation, given the SO(3) rotations that are the only remaining symmetries in the basic structure of Aristotle’s universe.  Fortunately, this symmetry is itself removed by the celestial bodies on the heavenly spheres.  (At least, I think that’s how moving them is supposed to solve this problem.)

Causality and motion

In this work, Aristotle introduces his famous four causes.  He faces the objection, common among today’s critics, that the presence of teleology is not obvious in the non-conscious world.  His reply is telling.  It basically comes down to “Look, if you saw a person do this, you wouldn’t doubt that it was for an end.  If nature does it, it’s no different.”  This will sound strange to modern readers, since the presumed existence of conscience in an object is the reason we attribute ends to it.  But Aristotle is telling us that ends don’t exist primarily in minds; they exist primarily in the actions themselves.

By “motion”, Aristotle refers to many kinds of change.  Locomotion is certainly one kind–indeed, he explicitly accords it a sort of primacy–but other examples include changes of temperature, size, and color.  Those of us living after Descartes and Newton are used to understanding change in terms of time:  at one time, a system is in a certain state; at a later time, it is in a different state; therefore, it is moving.  Aristotle wants rather to explain time in terms of change, meaning he must first describe change in a way that doesn’t refer to time.  He does this by invoking act and potency.  Motion is said, somewhat cryptically, to be the act of a potency as a potency.  Interpreters are divided on the meaning of this, but from the book’s examples, I think the following is most natural.  The potency in question is always for some end state.  If the potentiality were fully actualized, it would no longer be a potency at all, but the system would be in that state in act.  Motion is to be thought of as a weird intermediate state of the potential in question.  The potentiality is activated but not destroyed as it would be if brought fully to fruition.  Change is not a succession of static moments; velocity represents a distinct actuality.

Ontology:  infinity, place, time

When considering the existence of infinite sets, Aristotle distinguishes potential from actual infinities.  The paradigm of the former would be an interval of the real number line, which Aristotle takes to be not actually made of an infinite number of points but to be infinite in the sense that there is no limit to its ability to be divided.  He did a real service to mathematics here just by taking the question of “actual” infinity off the table for a time.  The formalization of calculus by Cauchy and others basically restricts itself to potential infinity.  Aristotle’s arguments against actual infinite collections are not convincing, being largely based on an ill-justified belief in the finite size of the universe.  After Cantor, we have better tools to think about infinity.

On the question of space, Aristotle is an extreme relationist.  Not only is “place” defined by spatial relations to other bodies, he thinks for it to be meaningful, a body must be immersed in some sort of medium, and the place of the object is then defined as the boundary of its material container (equal to the boundary of the object, but with oppositely pointing outward normal).  In our modern way of speaking, the place of B is $-\partial B$.

Time is a measure of change.  Thus, if the state of a system is described by $N$ parameters $X^i$, we can think of its motion as a trajectory in an $N$-dimensional state space, and time is a parameterization of this trajectory.  Aristotle accepts the consequence that time could not be said to pass if nothing changes.  Aristotelian time is more relativistic than that of modern physics; it knows no proper times.  Without motion, time is meaningless.  If the system were to return to its initial state, one might argue that it has returned to its initial time.

Causal hierarchies

In the last books, Aristotle attempts to explain motion by establishing a causal hierarchy starting from a first (in order of causality) unmoved mover.  To make this work, he must argue that everything that moves (i.e. changes) must be being moved by something else.  Of course, he acknowledges that a composite of mover and moved can be said to move itself.  Aristotle’s real claim is thus that every system that moves itself can be divided into an unmoved (except “accidentally”, as when a part is carried along with its whole without changing its internal state) initiator of motion and those things that respond to it.

The implausibility of this claim does not require any appeal to modern physics; Aristotle’s own writings describe an extremely animate world.  To take two key examples, the four elements are said to have within themselves a principle that guides them to their “correct” location in the universe, and animals are actually defined as being self-movers.  Aristotle responds that the elements don’t always move in their “natural” ways.  Sometimes they are impeded.  They don’t get to decide for themselves when their natural motion is activated or not.  This depends on external input.  Therefore, the explanation of their motion is outside themselves.  (Oddly, he also claims that if their principle of motion was in themselves, they would be able to move themselves in the counter-natural direction.)  Animal motion, too, is responsive to external stimuli, although some readings allow that the souls of animals are secondary unmoved movers.

We are led to the following picture.  The universe consists of objects.  Each object requires inputs from other objects which, together with its own nature, determine its activity/motion, with zero being one possible input.  No object’s activity is explicable without knowledge of its inputs.  The exception would be an unmoved mover, which would have no inputs, and whose internal state and activity would thus be determined entirely internally.  All this is, I think, plausible and interesting.  Unfortunately, it won’t build the hierarchical causal structure Aristotle wants.  There’s no reason a network of objects couldn’t have its objects taking all needed inputs from each other without any of them being unmoved objects.

It is also suggested that the true cause of an object’s natural movement is whatever it is that made the object (e.g. extracted air from a composite of elements).  This refers not to God’s act of causing the moving object’s existence now, but the production of the moving object by some other creature in the past.  I don’t think this works as part of the argument against self-motion, as these past acts will form no part of an essentially ordered series explaining a present motion.

Aristotle presents unconvincing arguments that movability is related to having parts.  These actually play a large role in the overall argument, but because not even Aristotelians and Thomists still support them, I relegate their discussion to a comment on this post.  Aristotle makes surprisingly little use of the claim that the mover must in some manner possess the form it is actualizing in the moved object, but due to its importance for later scholasticism, I will address it in a separate post.

The best that that can be said for the argument from motion that occupies the last two books is that, although as it stands it is certainly not convincing, it raises interesting questions.  Aristotle’s Physics has been deservedly regarded as a classic for millennia, especially on the merits of its excellent first four books.  It retains its relevance for contemporary ontological debates; after all, the natures of space, time, and causality remain matters of controversy and wonder.

### 7 Responses

1. Some bad arguments:

Indivisible objects are said to be immobile because during the time interval of motion, an object must be partly in the initial and partly in the final state, the only other options being fully in one or the other.  This omits what most would take to be the obvious alternative that at intermediate times it passes through intermediate states.

Divisible objects cannot be the source of their own motion because their motion depends on the motion of their parts.  This could be denied using Aristotle’s distinction between essential and accidental motions (distinguishing degrees of freedom belonging to a part vs. the whole) or used as a counterexample to the possibility of an infinite regress.

An infinite chain of moving movers is denied because it would involve infinite motion (the sum of the motion of each) in finite time.  Aristotle admits that having many objects undergoing finite motion in finite time is unproblematic, but he thinks that this is different because, to exert causality on each other, the movers must be in contact and thus form a single body.

He also claims to prove that a finite motion cannot take an infinite time, but I trust readers can construct $x(t)$ counterexamples to this.

Why can’t a finite number of objects move each other with no unmoved component?  Aristotle gives four brief, puzzling replies, mostly to the effect that if this were possible, another configuration that does have an unmoved mover and pieces that react to it is possible, so concentrate on the latter.

2. An interesting paper by quantum gravity luminary Carlo Rovelli explaining how Aristotelian physics is a pretty good approximation for lots of phenomena we see in the everyday world:

https://arxiv.org/abs/1312.4057

3. Books 1-4 are available with commentary in the excellent Clarendon Aristotle series from Oxford:
https://global.oup.com/academic/product/physics-9780198720263
https://global.oup.com/academic/product/physics-9780198720690

I always recommend using secondary material when reading philosophy. Why bother reading this stuff without understanding it?

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