# Potentiality, diversity, and limitation

Over on my post introducing potentiality from first principles, a reader raises some important questions that I thought would be worth answering in a separate post. If you haven’t read that post yet, I would encourage you to before continuing here.

This idea of “relative non-being” is the best explanation I have come across of the idea that potency “limits” act, though I still do not quite understand it. It seems to me that “relative non-being” really presupposes diversity in being rather than explaining that diversity; if so, it would be better just to take the diversity as primitive.

We could say that relative non-being is intrinsically differentiated, since whenever something is not X it is therefore something other than X.[1] Thus, another way of talking about relative non-being is in terms of otherness. This does not presuppose the diversity of being, however, because relative non-being is something outside of being—it influences being without making any positive contribution of being. Perhaps this would be clearer if we noted that by “being” we really mean non-relative being, and that likewise by “non-being” we really mean non-relative non-being. So, non-relative being is, non-relative non-being is not, and relative non-being is not X (for some X). We posit relative non-being in order to account for how it can be the case that more than one thing is. If there is only what is (being) and what is not (non-being), then nothing can diversify “isness” into this and that. On the other hand, if isness is composed with is-not-Xness then this opens up the possibility of isness also being composed with is-Xness (ie. is-not-Y for all Y other than X, more on this later). Since no one thing can be both X and not-X at the same time in the same sense, this gives us diversity of being.

What does it mean for being to compose with relative non-being? At this point, all we can say is that it involves mutual influence: being provides the positive contribution by virtue of which something is, whereas relative non-being provides the limits by virtue of which something is not X, or Y, or Z, etc. Neither exists in this influenced form prior to the composition, meaning that the relative non-being has no existence whatsoever apart from its composition with being, and being has no multiplication to this or that instance apart from its composition with relative non-being.

Maybe another way to put that would be: relative non-being can only account for multiplicity/diversity in being if there is diversity in relative non-being. But Parmenides could just reply that there can’t be diversity in relative non-being either: it couldn’t be differentiated by being (because that presupposes diversity in being, which relative non-being is supposed to account for); it couldn’t be differentiated by non-being (because that is nothing); and it couldn’t be differentiated by relative non-being (because any two things with relative non-being have that in common).

The first sentence here is spot on: relative non-being accounts for the diversity in being by virtue of the diversity that is present in relative non-being. But this diversity is not added to something that is otherwise one, but is an intrinsic feature of relative non-being. The relativity of relative non-being means that there is no such thing as relative non-being simpliciter, that is relative non-being without some qualification. This is because relative non-being is defined in terms of what it is relative to—the X in “is not X”—so that if we take this away then all we are left with is non-relative non-being, which is something else entirely.

Given this, Parmenides’s supposed reply doesn’t work: there can be diversity in relative non-being because there can be diversity in its qualifications. Suppose we have something that is not X, nor Y, nor anything else except Z, and we have something that is not X, nor Z, nor anything else except Y. Despite these both having relative non-being, they must be distinct from one another because the way in which they have relative non-being is different: each is qualified in a different way.

This is analogous to other determinables, such as location. You and I each have a location, but these locations themselves are distinct from one another.

At least as far as I understand Parmenides argument against multiplicity, he could give the same justification against multiplicity in relative non-being as against multiplicity in being – though I’m also not sure I understand Parmenides very well.

Parmenides’ argument seems to be:

(1) For there to be more than one being, they must be differentiated either by being or non-being.

(2) They can’t be differentiated by non-being, since that is nothing.

(3) They can’t be differentiated by being, since they have that in common.

Thus, there cannot be more than one being.

The Thomistic response seems to be to deny premise (1) and postulate relative non-being as a third option. But I don’t see why we cannot deny premise (3) instead and just say that yes, while they have “being” in common in the sense that they both exist, they also exist differently (e.g., by being of different kinds, or different individuals of the same kind). In other words, postulate diversity in being as a primitive principle. “Relative non-being” appears to me to be parasitic on this primitive diversity, and therefore superfluous as a response to Parmenides.

This reconstruction is somewhat accurate, but misses a crucial nuance. The problem in (3) is not simply that they have being in common (as they might have relative non-being, or locatedness in common), but that in both cases being is doing the same thing, namely grounding their isness. If all we can say about X is that it is and all that we can say about Y is that it is, then there is no distinction between them, because there is no sense in which Y is not X or vice versa.

I also don’t quite see how it follows that these two ways of conceiving of potentiality (relative non-being vs. capacity for actuality) are equivalent: in arguing that they are equivalent you describe both conceptions in two different ways and those different ways don’t seem equivalent to me.

Looking back, I certainly could have described the relevant moves in more detail. The basic idea is that we can show that the two accounts of potentiality are equivalent by starting from each one and showing how it can be understood in terms of the other.

Let’s start with relative non-being, which we have said limits being by excluding certain options within some domain. It cannot exclude everything in the domain, however, for then it would just be non-relative non-being. So, it must leave certain options “open.” Suppose we are considering a simple feature which can be one of three states, X, Y, or Z, and our relative non-being excludes X and Z. In this case, it leaves Y open. But remember that relative non-being makes no positive contribution of being itself. So, it grounds a certain openness to being without causing something to be or not—it limits what a thing is, but does not determine whether it is or not. But this is precisely what we said it means to be the passive capacity for act.

A similar series of moves can be applied in the opposite direction. Suppose we have some capacity for being Y. Then this capacity excludes being X and being Z, since when this capacity is realized then the thing is not X or Z. But this is just what relative non-being does.

In both cases, because the capacity is for a specific act and because the non-being is relative to a specific range of options, we can invert this range and get the other. We see that these two accounts are two sides of the same coin. While non-being excludes everything and being includes anything, relative non-being and the passive capacity for act restrict their scope, and therefore allow us to consider that scope in two ways—what is in or what is out. The passive capacity for act focuses on the former while relative non-being focuses on the latter, but in reality they are the same thing viewed from different perspectives.

[1] Throughout this post I refer to relative non-being in terms of being not-X. When not specified, the X should be understood to include one or many options within some domain. Considering colors, for instance, X could be a specific color or any collection thereof.

# Potentiality underlying change

In my previous post I explained how we arrive at the notion of potentiality from reflection on two different phenomena, resulting in two equivalent accounts of potentiality: potentiality is relative non-being as well as the passive capacity for act. The second of these accounts arises from considerations of causation and change, but it doesn’t actually end up telling us how potentiality functions within change—it simply posits potentiality as a necessary condition for change. In this post, then, I’d like to develop the picture further, and specifically discuss the special sorts of potentials that underlie the process of change.

When something changes from one state to another—from being green to being red, from being uneducated to being educated, from being a disorganized pile of material to being a house, and so on—there are three elements. First there’s the starting state, which is called the privation because in this state the thing is potentially in the final state but not actually so.[1] When the thing is green, it is potentially red but actually not-red. Second there’s the end or target state, which we can call the form because it is the state in terms of which we understand the change. Regardless of which color the thing actually is, we understand it as becoming red from some non-red color, whatever color this happened to be. Finally, there’s the underlying thing, which is what we get when we consider the subject of the change in abstraction from both the privation and the form. It is in virtue of the privation and the form that there is mutability in change, and it is in virtue of the underlying thing that there is persistence. In order to achieve this, the underlying thing must be some mixture of actuality and potentiality. After all, in order to account for persistence the thing must actually be the same thing throughout the change, but in order for the change to not destroy it it must be indeterminate between the privation and the form, which is to say it must have the potential for both.

Again, all of this merely clarifies the pre-conditions for change, and says nothing about the process of change. That is, we have outlined what the nature of a changing thing needs to include, but we have not said what this thing looks like when it is busy changing. Famously, Aristotle gives the following account of the process of change:

Now that we have distinguished between potentiality and actuality in each category, we can see that change is the actuality of that which exists in potentiality, in so far as it is potentially this actuality. (Physics III.1, 201a9)

Every change is the actualization of a potential, but not every actualization of a potential is a change. This is because a potential can be actualized in order to keep something in the same state: I actualize the cup’s potential to be above the ground while I move it to the table (change), but the table also actualizes this same potential once I’m done (state/non-change). This is why Aristotle does not finish his account at “the actuality of that which exists in potentiality” (ie. the actualization of a potential), but proceeds to add the qualification “in so far as it is potentially this actuality.” We can interpret this qualification in at least two ways, depending ultimately on which potentiality we think is being actualized during the change.

According to one interpretation, what is relevant is the potential for being in the final state that results from the change, what we called the “form” of the change above. We can illustrate this with Aristotle’s example of a block of bronze that can be shaped into a statue: the bronze has the potential for being a statue by virtue of its malleability and other physical properties, and this potential comes to be fully actualized at the end of the process of sculpting by an artist. But, we may ask, when this process of change is underway this potential is unactualized, but in what sense is it being actualized? It seems that this potential is in no way connected to the actualization. As far as I can tell, the only option we have available to us is to say that the potential is being actualized insofar as it is contained in the ends of the agent which is effecting the change, such as the intentions of a sculptor. Apart from this, the final state has no actual reality (partially or completely) prior to being actualized.

The potential in question in this interpretation is the potential for being in the final state, but we can also speak about a potential for becoming the final state as well—that is, the potential for changing into the final state. As I have explained elsewhere, however, this latter notion is more accurately called a “pseudo-potential”, since it is in fact a combination of an actuality and a potential: (a) the real potential for being in the final state and (b) the actuality of being in any other state.[2]

This brings us to the second interpretation, which posits a separate (non-pseudo) potential for becoming alongside the potential for being. The underlying thing is not simply indeterminate between being in various states (grounding each potential for being), but it is also indeterminate between different paths through these various states (grounding potentials for becoming). That is, these states are not simply discrete or disconnected points in a space of potentials, but points along a continuum of states that can be moved through without resting. The points correspond to potentials for being in states while the paths correspond to potentials for transitioning between states. What this allows us to say is that the potential underlying change is one of these “path potentials” from the starting state to the final state of the change.

Now, if we reflect on what it could possibly mean to actualize a path potential, we will see that it corresponds exactly to the process of change. The path as a whole, or any extended part of it, cannot be actualized all at once since this would require the actualization of multiple incompatible states, such as the bronze being a sphere and being a cube. Furthermore, there can be no non-zero span of time during the actualization of the path in which the underlying thing remains in the same state throughout, for this would indicate that the path potential has finished being actualized and some point potential has begun to be actualized instead. Thus, the actualization of the path potential must occur by successive actualization of continuous points therein without ever resting at any of them, but instead passing through each of them.[3] This is precisely the process of change. Sentesy gives the following description of this sort of interpretation of Aristotle’s account:

There is being-complete [for our purposes, being-in-act] specifically of beings-in-potency, and change occurs only when these are being-complete. If buildable planks exist, then their buildability refers to something, or something makes them buildable. A house is not what makes them buildable, because when they are part of the house, the capability they are exercising is different: they are complete doing something else. Since being a buildable thing means to get built, building is what completes (entelecheia) buildable things. Building is a change; therefore, change admits of being. Building stops when the entelecheia is not there, that is, when the builder stops building, not when the capacity is used up.[4]

This rejection at the end contrasts the second interpretation with the first: in the first interpretation, the “pseudo-potential” is used up when the underlying thing is finally actualized in its final state. In the second interpretation, change is not construed in terms of this final state, but the passing through states. Of course, in changes that have a final state, the change will stop once the underlying thing has passed through all the intermediate states, but Sentesy’s point is that this is not necessarily or primarily a result of the capacity for change being used up, but rather of the agent stopping the change. In this regard, then, there is something similar between the two interpretations, namely that both place the final state of the change in the agent in some sense. But in the second interpretation this is subsequent to the reality of change itself.

In the past, the first of these interpretations seemed like the “obvious” one to me, but I have since come to recognize the second as superior, both as an interpretation of Aristotle and as an account of change in its own right. I will list three brief reasons for thinking this, but for anyone interested in going deeper into these issues I recommend getting your own copy of Sentesy’s book quoted earlier.

For starters, the second interpretation can more readily accommodate infinite motion. Aristotle believed that the celestial bodies undergo constant circular motion, which would be an instance of infinite motion. And because of inertia, rectilinear motion in the absence of gravity would be an instance of non-circular infinite motion. It’s difficult to see how the first interpretation could make sense of these sorts of motion, since neither has a final point potential in order to ground the change. The second interpretation, by contrast, does not need a final point potential to ground the change, but only the potentials along the path.

Next, the first interpretation runs into the problem that the actuality that supposedly grounds the change only obtains once the change has ended, since it is the actuality of the final state. Really, it is more accurate to say that the actuality that grounds the change is a means to the actuality of the final state.

Finally, the second interpretation is rich enough to account for the difference between passing through points as opposed to visiting them one by one. This is important because this difference is ultimately what Aristotle uses to respond to Zeno’s dichotomy paradox. If there were only point potentials, then it would seem that in order to arrive at the final state we must first arrive at each intermediate state, of which there are infinitely many.[5] We cannot respond that the underlying thing only potentially arrives at each intermediate state but not actually, for this is just what it means to pass through these states, and only the second interpretation is ostensibly able to ground this in reality.

[1] For an informative discussion on privation from a Thomistic perspective, see David Oderberg, “The Metaphysics of Privation”.

[2] I first discussed this interpretation in my post “Why it’s called ‘motion’”, but more recently in my response to Oppy and Schmid in my post “The indifference of potentials and the non-indifference of pseudo-potentials”.

[4] Mark Sentesy, Aristotle’s Ontology of Change, 62 (Amazon).

[5] See Cohoe’s “Why Continuous Motion Cannot Be Composed of Sub-motions,” section A for a discussions of Aristotle’s initial and ultimate responses to Zeno.