In his Metaphysics Δ Aristotle says there are two senses of the term “whole”:

Whole means that from which none of the things of which it is said to consist by nature are missing; and that which contains the things contained in such a way that they form one thing.

The first sense corresponds to our usage of the word when we say things like, “he managed to eat the whole sandwich” and “she read the whole book in one day.” The second sense corresponds to what we refer to when we speak of general part-whole relations, for instance when we say that my arms and legs are part of my body. This second sense is what we’re interested in here. Aristotle further divides this into two kinds:

But this occurs in two ways: either inasmuch as each is the one in question, or inasmuch as one thing is constituted of them.

These are two very different kinds of whole. The second kind is perhaps the one we’re most familiar with: bodies are constituted by organs, tables are constituted by legs and tops, computers are constituted by transistors and other electronics. This kind is referred to as integral, so that integral wholes are constituted by integral parts. We might not think to talk about the first kind as a whole, but it does fit one sense of the general definition. It’s a whole in the sense that a universal applies to (and thereby “contains”) all the particulars that instantiate it: humanness contains all individual humans, treeness contains all individual trees, and so on. This kind is referred to as universal, so that universal wholes apply to universal parts.

Aristotle construes the difference between these two kinds of whole in terms of how the parts are made “one” in different senses. Integral parts come together to form one individual which we call the whole. We refer to this as numerical unity. Universal parts are each themselves an individual which instantiate a common universal. We refer to this as specific unity.

Later the Scholastics discovered a third kind, which they called potential. How potential relates to integral and universal depends on how you analyse the differences between the kinds. Aquinas, for instance, analysed them in terms of the presence of a whole in its parts, which in turn correlates to how truly the whole can be predicated of its parts. This led him to placing the potential as midway between the integral and universal:

… the universal whole is in each part according to its entire essence and power; as animal in a man and in a horse; and therefore it is properly predicated of each part. But the integral whole is not in each part, neither according to its whole essence, nor according to its whole power. Therefore in no way can it be predicated of each part; yet in a way it is predicated, though improperly, of all the parts together; as if we were to say that the wall, roof, and foundations are a house. But the potential whole is in each part according to its whole essence, not, however, according to its whole power. Therefore in a way it can be predicated of each part, but not so properly as the universal whole. (ST I, Q77, A1, ad1)

Intrinsicality

My preferred analysis is in terms of the intrinsicality of the potency and act by which the parts of a whole are distinguished and unified respectively. For the remainder of this post we will unpack this, and reflect on how the different kinds relate to one another on this account.

Now, any material being is a mixture act and potency (or, equivalently, actualities and potentials). By this we mean that it has capacities for various states or behaviours, some of which are realised. We call these capacities potentials, and insofar as a potential is realised we call it an actuality or an actualised potential. For example a coffee cup has potentials for being various temperatures, a person has potentials for being various levels of educated in some subject, and a squirrel has potentials for jumping and running. That last example indicates that potentials aren’t always potentials for static states, but can also be potentials for dynamic activities. So also actualities can be static or dynamic, depending on the kind of potential they’re the actualisation of.

These two things, namely (1) the distinction between act and potency and (2) the realisation that individuals are mixtures of various acts and potencies, enable us account for very fundamental features of reality like change and multiplicity. We’ve spoken about change before, but it’s worth saying something about multiplicity here. Parmenides famously held that multiplicity is impossible since if A and B have being, then the only thing that can distinguish them is non-being, which is nothing. But if nothing distinguishes them then they are not distinguished, and therefore they are identical. Thus everything is one, a unity without multiplicity. His mistake was failing to realise (as we have) that being is divided into act and potency, and that beings are mixtures of these two principles. Two things can be unified by being actual in the same way, but diversified (or multiplied) by this common actuality resulting from the actualisation of distinct potencies. So you and I can be unified in our both being educated, but diversified by the fact that my being educated is the actualisation of my potency for being educated and your being educated is the actualisation of your distinct potency for being educated. So long as we properly divide being into act and potency, then, we can affirm both unity and multiplicity.[1]

So that’s act and potency, next we turn to intrinsicality. Intuitively, to be intrinsic to something is to be wholly contained within it. Slightly more formally, A’s being B is intrinsic to A relative to some C insofar as A’s being B doesn’t depend on C. Alice’s being educated is intrinsic to her relative to Bob’s being educated, for example, because it does not depend on Bob’s being educated. Intrinsicality is, naturally enough, contrasted with extrinsicality. In a water molecule, the hydrogen’s bonding to the oxygen is extrinsic insofar as it depends on the cooperation of the water molecule.

It’s clear enough that the primary sense in which we talk about the acts and potencies of something is as intrinsic acts and potencies, since these are what constitute the being of that thing. In order to outline all three kinds of whole, however, we will need to expand our focus to secondary senses. That being said, when considering something in terms of an act and potency at least one of these must be intrinsic to that thing, since if this weren’t the case, no sense could be made of our considering that thing rather than something else.

In general a whole, in the sense we’re interested, is “a unity of ordered parts.”[2] Parts, of themselves, are diverse and are brought together into a unity through an ordering of some kind, like an arrangement or structure or process. Now, since act unifies and potency diversifies, it follows that a whole arises through the actualisation of the potencies by which the parts are distinguished from one another. So for each part we can talk about the actualisation that unifies it with the other parts, and potency that distinguishes it from the other parts.

This allows us to state our taxonomy of the kinds of whole. For any part, either this unifying actualisation is intrinsic to the part or it is not. If it is extrinsic then, as we said above, the diversifying potency must be intrinsic to the part. If the actualisation is intrinsic, then either the potency is also intrinsic or it is not. An integral whole arises when we have an extrinsic act and intrinsic potency, a universal whole arises when we have an intrinsic act and intrinsic potency, and a potential whole arises when we have an intrinsic act and an extrinsic potency.

Integral wholes

All of this is rather abstract, and some examples might help for clarity. Starting with integral wholes we’ve already seen an example: a water molecule made up of hydrogen and oxygen molecules. Each of the parts has an intrinsic potential to be bonded with the others. There is one bond which actualises all of these distinct potencies resulting in one water molecule, and so this actualisation is extrinsic to the parts. Second, there’s a simple wooden table made up of a tabletop on four legs. Here each of the five pieces have potencies for being structured in various ways, and the binding of them together into the table is an actualisation of these potencies. And finally, there’s a living animal. What the parts are here is not totally obvious; they might be the various organs, the interconnected organic systems, or the cells, bones, and other organic materials. Whatever they end up being, the point of interest is that the extrinsic actualisation here is a dynamic process involving the parts, rather than the static structure of the table. This process is what constitutes the difference between a living animal on the one hand, and a corpse on the other.[3]

With these three examples in hand, we can introduce some technical vocabulary. In an integral whole call the extrinsic actualisation the configuration, and call a part with the configuration abstracted away an element. The element is that in which the intrinsic potency inheres. If we consider a hydrogen molecule while abstracting away whether it is free or bound in some other molecule, then we’re considering the hydrogen molecule element. When we consider a free-hydrogen-molecule or a water-bound-hydrogen-molecule, then we’re considering the element together with a configuration.

Universal wholes

Moving on to universal wholes, let’s consider the example of the wooden table and how it differs depending on which kind of whole we’re considering. The integral whole in this case is the table itself, with the integral parts being the tabletop and legs. The universal whole, on the other hand, is tableness and the universal part of this whole is the individual table (that is, the particular instantiating tableness). Each table — each universal part — will have its own intrinsic actualisation that accounts for its being a table as opposed to something else. This actualisation is common to all tables (it is in virtue of this that we call them tables in the first place), but it is not some numerically one thing. Rather, each has their own instance of this actualisation, each being actualised in the same way.

Again we can introduce some technical vocabulary. Well actually, we can re-introduce some technical vocabulary first introduced by Aristotle. The common actualisation intrinsic to each universal part is called the form, and when we abstract away the form of a part we’re left with its matter. Of itself matter is indeterminate between a number of alternatives, and form is the determination to one of these. (Put in terms of act and potency, of itself matter has potencies for alternatives, and form actualises one of these potencies.) The difference with integral wholes may now be apparent: with integral wholes the elements are the individual pieces of wood, but with universal wholes the matter is the wood itself. After all, if we have a table of wood and we abstract away the table bit all we have left is the of wood bit.

Because much of modern science has focused on integral wholes, we as moderns will always be tempted to confuse form and matter for configuration and elements.[4] We’ve already seen the difference with the wooden table: the elements are the pieces while the matter is the wood. With the living animal the elements are often said to be the cells, and so the configuration would be the organising process of those cells.[5] For universal wholes, however, the matter of a living thing is called its body and the form of a living is called its soul.[6] Considered broadly, there are three classes of living things: plants, animals, and humans. The soul of a plant makes it vegetative, the soul of an animal makes it sentient, and the soul of a human makes it rational.[7] If we abstract away the particular soul of a living thing, then all we know is that it is living; and this matter we call a body. The lesson here is that form and matter carve up the world very differently from configuration and element.

One more example should do to get this point across: consider the case where my hand moves into your face. The motion of my hand alone is indeterminate between me attacking you, and me reaching to get something and hitting you by mistake. The form that determines which of these is the case is my intention. Together the motion (as matter) and the intention (as form) constitute my action. The configuration of my action, by contrast, would presumably pick out how I hit you with my hand, like the path my hand took through the air. This something very different from the intention of the action.

Potential wholes

Finally, potential wholes. Of the three kinds this is the most foreign to us, and it is also arguably the most fundamental. The key here is this: in both integral and universal wholes we have cases where a single act can actualise multiple potencies at once. This is clear enough in integral wholes, but it can also apply with universal wholes: an animal’s soul actualises potencies for walking, grasping, flexing, seeing, smelling, touching, and so on. Now, whenever a single act involves the actualisation of a number of potencies, we can distinguish between sub-acts of that act. If some act A is involves the actualisation of potencies P, Q, and R, then we can consider the sub-acts of A as the actualisation of P and the actualisation of Q and the actualisation of R. The potential whole is the act, and the potential parts are these sub-acts which are distinguish by extrinsic the potencies found in the elements.

Notice the difference here: the parts do not have potencies, but are just sub-acts we differentiate by reference to extrinsic potencies. Consider the water molecule again as an integral whole, so that we have a configuration of elements. Each part is the result of an element being actualised with the configuration, and so each part includes some potency inside it. The whole water molecule includes both potency (from the elements) and act (from the configuration). But now abstract away the elements so that all you’re left with is the configuration itself. This doesn’t include a potency; it is just an act. And when we sub-divide this configuration into sub-configurations (each the actualisation of a different element), these are also just acts: the configurings of the hydrogen molecules and the configuring of the oxygen molecule. Potency plays a role is distinguishing the sub-acts from one another, but the potencies are extrinsic to these sub-acts.

Something similar happens in the case of a form informing matter. For each distinct potency actualised by the form, we can discern a sub-act which is that form considered with respect to that extrinsic potency. The potential parts of a human soul are roughly the various powers it gives a human: vegetative powers like digestion, animal powers like walking and seeing, and rational powers like abstraction and judgement.[8]

So far we’ve illustrated potential wholes by reusing examples from integral and universal wholes. This is partly because we want to show the sense in which potential wholes are most fundamental, but also because it helps us gain some initial intuitions. There are other examples of potential wholes, two of which we’ll go through now. First, communities are potential wholes. This is true in general, but focus on one for now: an orchestra playing a piece of music. The playing is the result of a co-ordinated effort from all the members of the orchestra, and is a single activity of the orchestra. We can consider the sub-activities of this activity as the playing of the individual members, and these would be the potential parts of the playing of the orchestra as a whole.

Second, there are what we might call “composite actions” like faith. At its most general level, faith is thinking with assent. “Thinking” involves having intellectual confidence in something, less than certitude.[9] “Assent” picks out the mood of the thinking: that which I think I also desire. So thinking uses the intellect and assenting uses the will, but these are being used together in one and the same act, which we call faith. So then the act of faith is a potential whole with the potential parts of thinking and assenting, each distinguished by the rational faculty they are the use of.

With both integral and universal wholes we introduced technical vocabulary to capture the specific kind of act and potency at play in each case (configuration-element and form-matter). With potential wholes, however, the act in view seems to be as varied as actuality in general. As such, it seems the best we can do is distinguish between super-act and sub-act, where the super-act is the potential whole and the sub-act is the potential part. Depending on which kind of act we’re considering we’ll restrict the vocabulary, and we’ll usually drop the “super-” bit from the whole. We’ve been doing this all already: configurations and sub-configurations, activities and sub-activities, actions and sub-actions. We also sometimes spoke about the potential parts by using a proxy, as when we used powers as a proxy for sub-forms of an animal soul.

Conclusion

Aristotle discovered two kinds of whole: integral and universal. The Scholastics discovered a third, the potential whole, and extended Aristotle’s analysis of wholes in terms of predication. We saw an example of this in Aquinas, and in that case potential wholes fell between the other two kinds. With the present analysis in terms of intrinsicality there doesn’t seem to be a linear way of ordering the different kinds, although their relations are captured well in the diagram we saw earlier.

Notes

1. One might wonder if we haven’t just pushed the question about what multiplicity is back a step, since multiplicity of things arises from multiplicity of potencies. But this misses the point since we’re not trying to give an analysis of multiplicity, but rather trying to account for the reality of multiplicity with our principles. Because Parmenides had just being and non-being he could not account for multiplicity. But because we have divided being into being-in-potency and being-in-act, we are thereby able to account for it.
2. See Svoboda’s Thomas Aquinas on Whole and Part.
3. Rob Koons discusses in some detail how this process interacts with the parts in his Stalwart vs. Faint-Hearted Hylomorphism. David Oderberg argues in his Synthetic Life and the Bruteness of Immanent Causation the process of life is one involving immanent causation.
4. Even Eleonore Stump, who is a very careful expositor of Aquinas, falls into this trap. I made the same mistake in an earlier post.
5. While it is common to refer to the elements of an organism as a cell, this is technically wrong. But the details are not particularly important to our present point.
6. See Mike Flynn’s blogpost series In Search of Psyche (introduction, part 1, part 2, part 3, and part 4).
7. This is a technical term: any animal we take to be rational is a human. See David Oderberg’s Can There Be a Superhuman Species? for a related discussion.
8. We say they are “roughly” the powers, since strictly they are the vehicles of the powers. Every power is grounded in a particular intrinsic actualisation, which we call the vehicle of that power. But such technicality is not necessary here.
9. As Aquinas said, “[Thinking] is more strictly taken for that consideration of the intellect, which is accompanied by some kind of inquiry, and which precedes the intellect’s arrival at the stage of perfection that comes with the certitude of sight.” (ST II-II, Q2, A1, corp)