Aristotle’s Revenge 2: space, time, and motion

This is part 2 of a three part series on Scholasticism and some topics in the philosophy of science, loosely organized around a review of Edward Feser’s new book Aristotle’s Revenge:  The Metaphysical Foundations of Physical and Biological Science.

A brief history of the debate on space and motion

For an excellent treatment of the substantivalism/relationism debate, I recommend Paul Earman’s book on the subject.  Newton famously argued that space and time exist independently of anything filling them, while Leibniz countered that only spatial relations between objects are real. These arguments were long tied to the question of motion. Leibniz pointed to Galilean invariance to argue that there is no absolute standard of rest, while Newton countered with is bucket experiment, showing that water in a spinning bucket certainly knows that it’s spinning. The motion debate was only satisfactorily disentangled in the 19th century; in modern terms, we would say that spacetime has affine structure but no favored timelike vector field/congruence, i.e. acceleration but not velocity is absolute.

General relativity ironically provided the most powerful arguments to both substantivalist and relationist camps. Einstein’s spacetime retains its affine structure but also aquires its own dynamical degrees of freedom (the two polarizations of gravitational waves), which certainly seems to lend it independent reality. On the other hand, the general covariance of the theory is often taken to suggest that we not assign any real identity to spacetime points, and Earman has used Einstein’s hole argument, arising from this diffeomorphism invariance, to restate Leibniz’s argument without the latter’s questionable theological assumptions.

Aristotle and his disciples on motion

Aristotle, in his Physics, presents a definitely relationist account of space and time, going so far as to believe that spatial placement would be meaningless without matter filling space, and time would not pass without something changing. Carlo Rovelli praises Aristotle highly for his relationism, for relationism is still a strong contender in the philosophy of science, and so for once Feser could have stayed within the mainstream while following his master. But he does not do so.

Feser helpfully reviews the scholastic literature on locomotion, showing that the principle of inertia is not necessarily a problem even if one limits oneself to Thomism. (Dun Scotus had no problem with self-motion.)  The goal, though, is not to defend scholasticism but to understand motion.  Feser entertains several hypotheses. To mention only two, there may be a quality called “impetus” (which would break Galilean invariance) or that motion is relative and hence a “Cambridge property”, and thus not real enough to need a cause.  This latter idea is interesting, since it amounts to using Bertrand Russell’s critique of Aristotelian logic (that it can’t handle relations) to defend Aristotle’s physics. However, a relation between A and B is a property of the system A+B, so denying motion is real change would have to be combined with some rule limiting allowed aggregations.

Feser unfortunately quotes a number of foolish arguments by Colin McGinn against Galilean invariance.

“Consider a universe with just two objects, A and B [moving with respect
to each other]…For B to move, then, is for it to be at location L1 at
one moment and at a different location L2 at the next. Now, since B is
indeed moving from A’s frame of reference, the locations L1 and L2 that
B is at at each moment must be different locations. But since B is not
moving from B’s frame of reference, the locations L1 and L2 that B is at
at different moments must not be different locations. So L1 and L2 are both identical and not identical. But that is absurd.”

Well, the whole point of Galilean relativity is that there is no unique way to identify the same points at different times. Different frames will do so differently. Coordinates are just labels. Thinking otherwise “begs the question” against relativity, to use one of Feser’s favorite phrases.

“If we are considering only their motion, we could say that either the sun is at rest and that the earth is moving relative to the sun, or that the earth is at rest and the sun is moving relative to the earth. However, when we factor in the different masses of the sun and the earth, this is no longer the case. For given its far greater mass, the sun exerts a gravitational pull on the earth that is much greater than the pull that the earth exerts on the sun. Hence it is the sun that is causing the earth to move relative
to itself, rather than the other way around.”

Presumably McGinn meant that the acceleration of the Earth is greater because its mass is lower, since obviously the force of the Earth on the sun is equal in magnitude and opposite in direction to the force of the sun on the Earth.  Still, this is Newton’s bucket velocity vs. acceleration stuff, hardly news or a problem for Galilean relativity.  Interestingly, in general relativity, both the sun and Earth have zero acceleration, and we must invoke a preference for stationary, asymptotically flat metrics to favor a coordinate system in which the sun doesn’t move.

The continuum

We have seen that modern philosophers of physics have come around to the suspicion that spacetime is not just an infinite collection of points, that in fact the actual existence of points is more dubious than that of finite regions. The ancient Greeks got there first. Feser gives a review of this in terms of Zeno’s paradoxes. This is the historically correct way but may put off modern readers who will see fairly easily how Zeno is taking limits improperly to get his incorrect zero and infinity answers. (See Russell on the intuitions that were probably driving Zeno and how the modern theory of infinite sets, even more than calculus, answers them.)  A better way, I think, would be to note that even in mathematics, a line is certainly not just an infinite collection of points. In addition to points, there is also a topology, a sense of neighbors. We often take take this for granted because all the lines we draw are embedded in a metric space, which supplies a natural topology. It is, however, an independent ingredient. A line is a one-dimensional topological space, and the topology and points are related in a way vaguely reminiscent of form and matter. Aristotle’s formulation of this is that the points exist only “potentially”. That the points in a line are somehow not actually there is a strange claim, but the holist intuition driving it is certainly defensible.

Time and causal structure

As Reichenbach has explained, even if the scientific theory of relativity were to be disproved, the epistemological theory of relativity would still stand. Given a maximum communication speed, there is no unique way to decide that two events separated in space are simultaneous in time. Indeed, the special theory of relativity predicts that the time order of spacelike separated events is frame-dependent. Behind these epistemological and scientific points is a deeper ontological lesson. Time is the order of causality. Past events are what we remember; future events what we can affect.  Absent the possibility of causal influence, two events should not be relatable by the order of time. Significantly, it is the network of possible causal relations between points–given by the light cone structure–that gives Minkowski spacetime its natural topology.

Whenever I read a philosopher arguing that the theory of relativity has not made presentism untenable, I come away more convinced than ever that relativity has indeed made presentism untenable. One must posit a preferred foliation of spacetime that has left no trace on the laws of physics or human experience, or one must hold out hope that some future physics will provide such a trace, or one must define the “now” counterintuitively using arbitrarily selected special events. Additionally, I think the truthmaker objection to presentism is stronger than Feser gives it credit for, but as a traditionalist I may be too sentimentally attached to the reality of the past. Feser’s mostly grammatical arguments didn’t convince me, but he does make one very strong point. Namely, that it won’t do to say that change as common sense would recognize it is not real but exists only in the mind, because if it exists in the mind, then it exists. The eternalist absolutely must establish that change as he understands it is sufficient to explain everything about the human experience of the distinctive character of time. For a recent attempt by the eternalist side to do this, I recommend Craig Callender’s book.

It is the mark of the Aristotelian to return what modern philosophers have said is only in the mind to the objective physical world, whether by insisting that these things really are in the world as revealed by physics (my usual strategy) or by emphasizing features of the world not captured by physics (which is more often Feser’s strategy).

11 thoughts on “Aristotle’s Revenge 2: space, time, and motion

  1. It’s not something I’m as familiar with as I should be, but doesn’t quantum entanglement require a common time frame for the entangled particles (i.e. if one is in one state *now*, the other must be in the corresponding state *now*, even if they are separated by great distance)?

    • This is an excellent question, ArkansasReactionary. The answer I would say, is that a particular version of the Copenhagen interpretation of the Schroedinger formulation requires an absolute frame, which I take to be a decisve mark against this interpretation. It is interesting to see how the issue of spacelike entanglement plays out in other interpretations. Hopefully I can return to this comment when I have time.

  2. On motion. I think motion, “movetur” means not locomotion, but simply change. An intertial object whoosing past us has locomotion, but its speed is not changing. Its coordinates are changing, but the change of the change of coordinates i.e. speed does not. The speed changes only if changed by something else, “ab aliud movetur”.

    • It is true that motion means something more general for Aristotle, but he is very clear in the Physics that locomotion is a species of motion, and indeed the preeminent case, since other causal influences depend on contact. Some Thomists have indeed claimed that inertial motion does not constitute change (“motion”) in their sense. However, such a definition must be consistent with the spatial relations between inertially moving objects (e.g. their separation) changing. Thus, Feser suggests that such relations are not properties of the sort that are potencies that need an outside actualizer.

  3. Whenever I read a philosopher arguing that the theory of relativity has not made presentism untenable, I come away more convinced than ever that relativity has indeed made presentism untenable. One must posit a preferred foliation of spacetime that has left no trace on the laws of physics or human experience, or one must hold out hope that some future physics will provide such a trace, or one must define the “now” counterintuitively using arbitrarily selected special events.

    After thinking about this for a bit, it’s not clear that this objection is very strong. There is some unique reference frame in which the net momentum of all the objects in the universe is zero. Specifying that as the metaphysically correct reference frame would both avoid the problem of arbitrariness and also cohere with human experience, since our own reference frame is only trivially different from that one.

    • Yeah, if somebody asked me to pick a privileged frame, I’d probably say the Hubble frame. Measure your real speed using the CMB. Of course, one can pick any other frame and it will work just as well, which is why I don’t like the whole idea. If possible, philosophers should avoid positing entities to explain the physical world which have no effect on anything. Let us ask though why the Hubble frame seems so natural to us (at least at cosmological scales). Presumably it’s because that’s roughly the speed that things are moving at. Are our intuitions implicitly appealing to Mach’s principle, in which case we are firmly in the relationists’ camp after all?

      • If the block view of time is correct, then what you’ll eat for lunch tomorrow would be determinate in the same way that what you ate for lunch today is. It would be an unalterable physical fact over which (barring miraculous intervention) you have no control.

        The difference between this and divine foreknowledge is that the latter is something that exists outside of the physical world (outside of creation generally, for that matter). It has no impact on the way created things naturally operate, and therefore doesn’t impede free will. OTOH, I can’t see any (natural) way for free will to exist if the future is a physical fact in the same way that the past and present are.

      • I don’t have control over it now, just as I don’t have control over my decision for yesterday’s lunch now. Yesterday’s decision was mine to make yesterday, and tomorrow’s will be mine to make tomorrow. There is, as you point out, a complete symmetry here between past and future which bothers you but not me.

        By the way, Aristotle was on your side on this. He also believed that claims about future events do not have truth values (and not only that we don’t know them).

      • The issue is that, if the block view of time is correct, then the future is just as determinate as the present, which would make every exercise of free will equivalent to a miracle, and mean that all human action was occasionalist in nature.

        OTOH, if SR and presentism are both correct, there must be a preferred reference frame. It isn’t strictly necessary that the preferred frame be discernible to us, though Mach’s principle has the dual advantage of making it so and avoiding the necessity of positing ether or an equivalent.

      • It depends on what you mean by “determinate”. It means that there eternally is a truth of the matter about what I will choose to eat for lunch “tomorrow” (Aug 16). It doesn’t necessarily mean that this choice can be predicted from what came before that moment. This distinction has historically been used for explaining the compatibility of divine foreknowledge and (libertarian) free will, something presentism has more trouble with.

      • Both the present and the past are fully determinate. If a sandwich is in front of you *now*, there’s nothing you can do to change that. You can throw it away, but that won’t physically happen until after you’ve decided to do so (i.e. in the future, even if not very far into it).

        Free will concerns only the future, because only the future is indeterminate. If the future were just as determinate as the past and present, then it would not be possible for any physical events to be influenced by it, which would make free will in human beings meaningless.


Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.