Monday, January 11, 2021

Change and potentiality

Aristotle defines motion or, more generally, change as the actuality of potentiality.

Imagine a helicopter hovering in one location, x. Its being at the same location x at time t2 as it was at time t1 is an actualization of its potentiality at t1: namely, its potentiality to keep itself hovering in the same place by counteracting the force of gravity. Thus, by Aristotle’s definition it seems that the helicopter’s motionless hovering is motion.

Perhaps, though, we need to distinguish between potentiality and power. The helicopter, unlike a rock, has a power to stay in one place in mid-air. But neither the helicopter nor the rock has a potentiality to stay in one place, because a potentiality is necessarily for a state that does not yet obtain.

This suggests a view of potentiality like the following:

  1. An object a has a potentiality for a state F just in case the object a has a possibility of being in state F and a is not in state F.

Here, “possibility” is used in the modern sense as not excluding actuality.

The helicopter has a possibility of being at location x in the future, but since it is already at location x, that possibility is not a potentiality.

Now, let’s go back to Aristotle’s definition. When are the actuality and potentiality predicated? Given that, as we saw, a necessary condition for a potentiality is lack of the corresponding actuality, it seems they cannot be predicated at the same time. This suggests that the Aristotelian account is:

  1. An object changes provided it has a potentiality at one time and some other time actualizes that potentiality.

But now consider the simple at-at theory of change.

  1. An object changes provided that it has a state at one time and lacks it at another.

We might call (2) “Aristotelian change” and (3) “at-at change”.

The following is trivially true:

  1. Aristotelian change entails at-at change.

But what is curious is that the converse also seems to be true:

  1. At-at change entails Aristotelian change.

For suppose that an object a is in state F at one time and not in state F at another. Swapping F and non-F if needed, we may assume for simplicity it is earlier in state non-F. Let t1 be the earlier time. Since the object will later in be in state F, at t1 it has a possibility for being in state F. That possibility is a potentiality by (1). And at t2 that possibility is realized and hence is actual. Thus, at one time a has a potentiality for F and at another that potentiality is actualized. Hence, we have Aristotelian change.


  1. Necessarily, at-at change occurs if and only if Aristotelian change occurs.

So what does the Aristotelian account add?

Perhaps, though, we might say that (1) is too simplistic an account of potentiality. Perhaps not every unrealized possibility is a potentiality, but only an unrealized internally-grounded possibility. For instance, I have an internally-grounded possibility of standing up. But I do not have an internally-grounded possibility of instantly doubling in mass: rather, this possibility is grounded in the power of God.

On this view, however, the Aristotelian account of change appears to be false. For suppose that I have a possibility for a non-actual state F, but that possibility is not internally-grounded. Then if that possibility comes to be realized, clearly I have changed. Thus, if God miraculously doubles my mass, I have grown more massive, that’s a change. But that change isn’t a realization of an internally-grounded possibility.

One can escape this objection by insisting that every possibility for an object has to be internally-grounded. If so, then the Aristotelian account of change applies precisely to the same cases as the at-at account does, once again, but it adds a richer claim that change is always related to an internally-grounded possibility.


Brandon said...

I'm a little surprised at the argument of this post, and wonder if I've missed something; it is of course true on an Aristotelian account of change that the helicopter is changing, as it is on common sense assessment. It's just not changing by locomotion (although the blades are).

I don't think (2), "An object changes provided it has a potentiality at one time and some other time actualizes that potentiality", can work as a characterization of the Aristotelian account of change itself: in the Aristotelian account of change, change is more fundamental than time, so it's a category mistake to ask 'when' actuality and potentiality are predicated; it's like asking when we can say of clocks that they are measuring things by time. Perhaps you can make some answer to the question that makes sense, but it is going to be incidental to the actual account.

What you are calling at-at change looks like it's just Aristotle's account of change in terms of form, matter, and privation of form, but for some reason measured according to a clock. But the real at-at account, I take it, requires that change be definable in terms of time, not time in terms of change. The form-matter-privation account can only be characterized in time-terms relative to another change acting as a clock, and things can be changed regardless of whether they are measured by a clock or not; the at-at account seems to require either (1) that there be absolute time presupposed by the change or (2) that whether something is changing or not is relative to the clock you are using.

Alexander R Pruss said...

The potentiality that I singled out in the case of the helicopter is the potentiality to stay in one place. The helicopter is actualizing this potentiality. Thus, on the Aristotelian account of change, the helicopter is changing *with respect to place*.

In any case, if you're bothered by the blades moving, just change the repulsion method to something that does not involve change, such as a repulsive force that perfectly balances the gravitational force.

Regarding time, either the potentiality to F is logically compatible with the actualization of the potentiality to F or not. If it is compatible, then Aristotle's account fails, because the potentiality can be actualized while yet the potentiality exists, and hence the actualization of a potentiality does not entail change. If it is incompatible, then the two must happen at different times, since two incompatible states cannot obtain at the same time in the same object.

Brandon said...

The helicopter is not changing with respect to place; 'staying in one place' is, by the very definition of 'staying', *not* changing with respect to place. Your set-up is that the helicopter is actualizing its potential to expend its energy reserves *to resist* a force that *would* change it with respect to place.

In any case, if you're bothered by the blades moving, just change the repulsion method to something that does not involve change, such as a repulsive force that perfectly balances the gravitational force.

Without details about how this repulsive force is generated, it isn't possible to assess how it would be explained in Aristotelian terms. But it seems likely that, again, the potential actualized would be a potential to use up energy in order to resist a force that would otherwise change its place.

I don't see how your comment on time changes anything. Whether we are using 'the potentiality to F' in a broader sense in which it is compatible (which Aristotelians do when talking about composition) or a narrower sense in which it is incompatible (which is used when talking about change), time is very far from being the only respect in which incompatible states can be had without contradiction. They can have incompatible states at different places, in the exercise of different powers, etc, even at the same time. *Any* sufficiently relevant respect would do. And in an Aristotelian account, two incompatible states could not be shielded from contradiction by simply appealing to different times unless the incompatibility were *wholly* due to their relation to at least one clock-change, because that's the only way time would even be relevant.

In any case, the Aristotelian account and the at-at theorist posit different directions of explanation between time and change, and the difference leads to a difference in commitments; the at-at theorist is committed to either absolute time or the relativity of change, the Aristotelian to neither of these but to either an all-encompassing change (like that of a primum mobile serving as universal clock) or the relativity of time. There is no entailment, in either direction, although I think your argument does show that, assuming the Aristotelian account true, the Aristotelian can explain why someone might be attracted to an at-at account using the form-matter-privation description plus relation to a clock.

Michael Gonzalez said...

To the OP, couldn't we say that the doubling in mass is an actualizing of an internally-grounded potentiality in God? It still does some interesting metaphysical work, such that every case of change (going from non-F to F) is the result of a power to actualize a potentiality.

To this apparent problem with Aristotle and time, I think it's abundantly clear that Aristotle is only grounding what Newton called "metric time" in change. Change has no meaning without the deeper concept of priority and posteriority. The changed state must follow the previous one. But, the concept of measuring time (as with minutes or seconds) and of a temporal sequence, all of that is grounded in change. And that can indeed be relative, and even relativistic, without making mere duration and mere priority/posteriority somehow derivative on some other concept (which they cannot be; they are basic).

Alexander R Pruss said...

God is pure actuality.

Michael Gonzalez said...

Says who?? Haha. But, seriously, on any reading of that in which God doesn't always do everything He is capable of (which He obviously doesn't, since we're all still here), there can be potentiality in His exercise of power, no?

Alexander R Pruss said...

Potentiality is not just not doing something one is capable of doing. It is a specific Aristotelian ontological category.

Alexander R Pruss said...

Ha! What I just said, though true, doesn't fit with (1) in the post.

Chris said...

Thank you for this post. I am aware of your works in cosmological arguments, specifically in defending the principle of sufficient reason. I am just wondering. Have you made an Aristotelian proof for the existence of God before, either in your blog site or articles?

Thank you.

Alexander R Pruss said...

No, I haven't.