# 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.

# Form vs structure, and what it means for virtual existence

A common but mistaken tendency when trying to understand hylomorphism is to equate form and structure and matter with the elements in that structure.1 This tendency is unsurprising, since modern science has taught us how to think about reality in terms of its physical and biological structure, but it is still a mistake. When Aristotle introduces form in the Physics, his preferred example is a person who changes from being uneducated to being educated. In this case, the forms are the uneducatedness or educatedness, while the matter is the person that persists through the change. Surely he does not intend for us to think of the person as an element, that their [un]educatedness somehow structures — this would stretch these words so much as to empty them of meaning.

A better way of thinking about form and matter is as two mutually intelligible notions that work together in the constitution of material things.2 Matter is a substratum that of itself is indeterminate between various alternatives, while form is the determination of that substratum to one of those alternatives. So, the matter and form of a thing do not exist separately from one another, but each exists indirectly through the existence of the thing they compose. The form and matter of a human exist where I am, for example, because I am a human composed of form and matter. In Aristotle’s example, when we consider a person apart from whether they are educated or not, we have something that is indeterminate between different levels of being educated, that is we have matter. And adding in the educatedness determines this matter to one of these various alternatives. Or consider another case of form and matter that doesn’t involve structure. Imagine Alice’s hand is moving into Bob’s face. By itself, this motion is indeterminate between (a) Alice attacking Bob and (b) her clumsily hitting him by mistake in the course of reaching to something near him. The form that determines which of these is the case is her intention. Together the motion (as matter) and the intention (as form) constitute her action.

So, form is not structure. But neither are the two entirely separate: if some T exists at least partially by virtue of an underlying structure, then a form determining matter to be a T will need to include that structure. Take as an example a simple wooden table with four legs and a tabletop. The structure places the tabletop above the four legs, each of which is standing upright. And the form and matter? The matter could be the wood itself, in which case the form would be everything that makes the wood a table, including the division of it into pieces, the structuring of these pieces, and the collective intentions we have that make something a table rather than something else like a chair or mug.

Let’s use a water molecule as a case study. Structurally, it arises from a bond between two hydrogen atoms and one oxygen atom, the bond being the structure and the atoms being the elements. In terms of form and matter, things are more complicated. Assuming the water molecule is a substance,3 we’re primarily interested in substantial form and prime matter. Prime matter underlies all material substances and is completely indeterminate, while substantial form determines this matter to being a particular kind of material substance. Mapping this onto language about structure, it is clear that the hydrogen and oxygen atoms are not primary matter, for they are also made up of structured elements: a hydrogen atom, for instance, is made up of a proton and an electron. And these are also made up of structured element: a proton, for instance, is made up of an up quark and a down quark. Since structure is a kind of determination, the prime matter of the water molecule must underly all of these things. Accordingly, the substantial form of the water molecule must include all of these structures at different levels as part of its determination of the prime matter. I have illustrated how these different components all fit together in the following diagram:

What may have initially seemed like a subtle distinction has now snowballed in two clearly different accounts of something as simple as a water molecule. And, moreover, this difference sheds some light on a puzzling claim in Thomistic metaphysics, that the hydrogen and oxygen atoms exist virtually within the water molecule. Only if the water molecule were to be destroyed, leaving free hydrogen and oxygen atoms, then they would really exist. Understandably, someone not familiar with these terms would find this all a little perplexing: the molecules have the same structure both when inside the water and when free, so why say that they only virtually exist in the one case?

For starters, we must note that by calling something “virtual” we are not denying that it has some measure of existence in reality. This might what we colloquially mean by “virtual”, but in Thomism both “real” and “virtual” afford some kind of existence in reality. If we wanted to say that something had no existence in reality, then we’d say that its existence was purely logical.4

Furthermore, when Thomists speak about the way a thing exists, we primarily have in mind its form and matter rather than simply the structures that underly it. And we think that every substance has exactly one substantial form, since a material substance is the determination of matter, not a pre-existing material substance.

Now, while there may be no structural difference between a bound hydrogen atom and a free one, in terms of form and matter there is a substantial difference (pun intended). The bound hydrogen atom exists and is structured as part of the water molecule’s form, whereas the free hydrogen atom exists and is structured by its own form. The free hydrogen atom’s form excludes all sorts of things that are included by the water molecule’s form, not least of which are the structures of the oxygen atoms . Of course, the two are not completely unrelated, since the form of the water molecule in some sense “contains” the form of the hydrogen atom. This is what we’re getting at when we say that the hydrogen exists virtually within the water — even though the water molecule has only one substantial form, its form is multi-faceted.5 It’s because of this that if we destroyed the molecule properly, we could recover the three atoms which until then would have existed virtually within it.

1. By “structure” I mean a static or dynamic specification of the quantitative relationships between a collection of elements. In my post on the threefold whole I used the word “configuration” instead, but I think “structure” is more familiar to people and so have used it here.
2. By “things” I include material composites in general, such as substances, accidents, actions, states of affairs, and aggregates.
3. See Eleonore Stump’s paper “Emergence, Causal Powers, and Aristotelianism in Metaphysics” in Powers and Capacities in Philosophy: The New Aristotelianism. There is a more general question about whether we should consider each individual molecule as a substance, or whether bodies of water are better candidates. This is hugely relevant to us here, and we use the molecule because it’s easier to talk about.
4. See my post on the real distinction for a discussion on real, virtual, and purely logical in the context of distinctions, which bears some resemblance to how they work in the context of existence.
5. In order to better understand the multi-faceted nature of forms, we need to consider them as potential wholes. I have discussed these in my post on the threefold whole.

# Actualisation of potentiality as such

While we’re on the topic of confusing things Aquinas said, we can talk about his analysis of change, which he in turn gets from Aristotle.

We’ve noted before that the first step in analysing change is the realisation that it involves the actualisation of a potential:

When a hot cup of coffee gets cold, for example, what is happening is that the cup’s potential for the being cold is actualised by the coldness in the surrounding air… When I pick the cup off the ground and place it on the desk, I am actualising the cup’s potential to be a meter above the ground

But, as we noted, not all such actualisation of a potential involves change. The thing that sets change apart from other actualisations of potentials is that it involves the movement from potential to actual. It is on account of this that the ancients and Scholastic happily used the words “motion” and “change” somewhat interchangeably.

Now, while calling change the movement from potential to actual serves as a helpful start it is by no means the end of a satisfactory analysis. At the end of the day we want to know what this movement consists in, and we want it terms as basic as possible. This is where the confusing phrase from Aquinas comes in, for he says that “motion is the act of that which is in potentiality, as such.”[1] In this phrase Aquinas is abbreviating a slightly-less-confusing phrase from Aristotle who says that “change is the actuality of that which exists potentially, in so far as it is potentially this actuality.”[2]

To see what these two are getting at, return to the example of the cup’s resting on the table a meter above the ground. At any given moment, there are two senses in which this potential of the cup’s might be being actualised: first, by the cup actually resting on the table a meter above the ground and second, by me currently being in the process of picking the cup off the ground and placing it on the table. We might put it like this, given that I’ve started this process I’m eitherfinished it (the first case) or I’m still doing it (the second case). In both cases the cup’s potential for resting on the table a meter above the ground is being actualised, but only in the second case is this actualisation an instance of movement. In the first case the cup is sitting on the table a meter above the ground; in the second case it’s not there yet, but it’s on it’s way there. Put (rather verbosely) in terms of act and potency, in the first case the cup’s potential for resting on the table is being actualised and the cup is actually resting on the table, whereas in the second case the cup’s potential for resting on the table is being actualised and the cup is merely potentially resting on the table.

More generally (and symbolically), if we’re considering some object X that has some potential for P currently being actualised, then either X is actually P or X is potentially P. In the former case there is no movement toward P, since X is already P. In the latter case there is movement towards P, since the only way X can have this potential currently being actualised and not be there yet is if X is on its way to P. In the above example X is the cup, and P is “resting on the table a meter above the ground”.

This, then, is what Aquinas and Aristotle are getting at: an actualisation of a potential is movement when, and only when, the thing being actualised is still potentially at its end. Or, more succinctly, movement is the actualisation of a potential while it is still potential.

### Notes

1. Summa Contra Gentiles Ch 13
2. Physics 3.1 201a10-12