The threefold whole

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)


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.

Breakdown of the three kinds of whole
Breakdown of the three kinds of whole

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.


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.


  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)

Smith’s epistemological argument for hylomorphism

The following quote comes from Wolfgang Smith’s The Quantum Enigma:

As Aristotle pointed out long ago, the act of knowing consists in a certain union of the intellect with its object. But how can the intellect be joined to the external thing? Such a union, clearly, can only be conceived in terms of a third entity or common element, which object and subject can both possess, each in its own appropriate mode; and it just be this tertium quid, precisely, that renders the object knowable.

But only in part! For it is not, after all, the external object — lock, stock and barrel — that “passes into the subject”, but only what I have termed the tertium quid. This “third factor”, moreover, answers to the question “What?”: it is what we know. And yet it does not simply coincide with the object as such, for as just noted, the latter is perforce “more” than the tertium quid.

Now the tertium quid, to be sure, is none other than the Aristotelian morphe, the form or quiddity of the existing thing. But inasmuch as the thing does not coincide with its morphe, one needs to postulate a second principle — an X, if you will — that distinguishes the two, or makes up for the difference, so to speak. And this X — which is perforce unknowable and had no quiddity — is evidently tantamount to materia. One arrives this, by way of epistemological considerations of a rather simple kind, at the basic conceptions of the hylomorphic paradigm.

On the transitivity of strict preference

The notion of comparing alternatives often comes up in philosophy, particularly when discussing practical reason. There are various names for this (we can talk about the reasons for choosing A over B, or how A is better than B, or how A is more desirable to B, or how A is preferred to B) but they all amount to the same thing.

The other day I was reading the SEP article on preference and was struck by this counterexample to transitivity of strict preference (I recall my friends mentioning it to me in the past, but I only thought about it critically this time around). In this quote, X≻Y represents that X is strictly preferred to Y, and X∼Y represents indifference between X and Y:

In an important type of counterexample to transitivity of strict preference, different properties of the alternatives dominate in different pairwise comparisons. Consider an agent choosing between three boxes of Christmas ornaments… Each box contains three balls, coloured red, blue and green, respectively; they are represented by the vectors ⟨R1,G1,B1⟩, ⟨R2,G2,B2⟩, and ⟨R3,G3,B3⟩. The agent strictly prefers box 1 to box 2, since they contain (to her) equally attractive blue and green balls, but the red ball of box 1 is more attractive than that of box 2. She prefers box 2 to box 3, since they are equal but for the green ball of box 2, which is more attractive than that of box 3. And finally, she prefers box 3 to box 1, since they are equal but for the blue ball of box 3, which is more attractive than that of box 1. Thus,

a. R1≻R2∼R3∼R1,
b. G1∼G2≻G3∼G1,
c. B1∼B2∼B3≻B1; and
d. ⟨R1,G1,B1⟩≻⟨R2,G2,B2⟩≻⟨R3,G3,B3⟩≻⟨R1,G1,B1⟩.

The described situation yields a preference cycle, which contradicts transitivity of strict preference.

(Note that I’ve added the labels to the listed conditions for the sake of this discussion.)

Now, I haven’t read much of the modern discussion on transitivity of preference (indeed, I didn’t even finish reading the article), so perhaps what I’m about to say is really obvious.

It seems clear to me that the above counterexample motivates the otherwise very natural distinction between (1) being better in some respect and (2) being better simply. Ultimately it has to do with why we prefer something over another. For instance, assume I prefer red balls over blue balls. Then I prefer this red ball over that blue ball simply, and I prefer this box of green and red balls over that box of green and blue balls in some respect.

I say this distinction is “very natural” because it seems necessary if we are to make sense of trade-offs, which are manifold in everyday experience. As a trivial example (which I find myself in often), imagine you need to pick one of two routes to your destination. Route A is longer but has prettier scenery and conversely route B is shorter but has uglier scenery. You have to pick one, but whatever choice you make will involve a trade-off. On account of what is this a trade-off? Well, surely it’s because shorter routes are preferable to longer ones and prettier routes are preferable to uglier ones. That is, A is better in some respect (prettiness) and B is better in some other respect (length).

This distinction resolves the above counterexample by showing us that (a)-(d) equivocate on “≻”. In (a)-(c) X≻Y means X is strictly preferred to Y simply, but in (d) it means X is strictly preferred to Y in some respect.

The SEP article immediately goes on to say the following:

These and similar examples can be used to show that actual human beings may have cyclic preferences. It does not necessarily follow, however, that the same applies to the idealizedrational agents of preference logic. Perhaps such patterns are due to irrationality or to factors, such as lack of knowledge or discrimination, that prevent actual humans from being rational.

Perhaps, but I’m inclined to think life’s more complicated than that. It seems pretty intuitive that there are various types of goods that are incommensurable. One way we might make this intuition precise is as follows: in general there seem to be two ways in which A is better than B:

  1. A and B are both means to C and A is a better means.
  2. B is a means to A.

(1) is where this whole business of comparing of alternatives comes in. Given our above discussion we realise that A can be a better means either in some respect or simply. Aristotle mentions something like (2) at the beginning of the Nicomachean Ethics. The guiding intuition here is that ends are preferred to means because “it is for the sake of the former that the latter are pursued” (I.1 1094a15-16).

Now, combining this with our previous discussion on basic human goods, the fact that there are multiple basic goods suggests that at least sometimes two goods will be incommensurable.

Goods, basic goods, and faculties

We’ve mentioned before that the goodness of some thing is relative to that thing’s nature. It is good for a human to have two legs because our biology is structured in such a way that having two legs is conducive to our flourishing. By the same token, it is not good for a cat to have two legs.

Now, these various goods can be grouped together and structured hierarchically: colour sensitivity, amoung other things, is a good which is subsumed under the good of seeing. Good seeing is itself subsumed under the goods of sensing, which in turn is subsumed under the goods of animal life.

A breakdown of the goods that are subsumed under the good of animal life.
A breakdown of the goods that are subsumed under the good of animal life.

At this point three things can be said. First, the goodness of the lower goods is dependent on the higher goods. Put another way, the lower goods are for the sake of the higher goods. Colour sensitivity, for instance, is for the sake of seeing and is good to the extent that it enables us to see well.

In the opening passage of the Nicomachean Ethics Aristotle, while discussing human acts, makes the same point:

Now, as there are many actions, arts, and sciences, their ends also are many; the end of the medical art is health, that of shipbuilding a vessel, that of strategy victory, that of economics wealth. But where such arts fall under a single capacity — as bridle-making and other arts concerned with the equipment of horses fall under the art of riding, and this and every military action under strategy, in the same way other arts fall under yet others — in all of these the ends of the master arts are to be preferred to all the subordinate ends; for it is for the sake of the former that the latter are pursued. (I.1 1094a7-16)

We might visualise his scenario as follows:

A breakdown of the acts that are subsumed under the act of strategy.
A breakdown of the acts that are subsumed under the act of strategy.

The second thing to note is that this hierarchy has a limit. That is, the tree does not go up indefinitely. Aristotle says that “we do not choose everything for the sake of something else (for at that rate the process would go on to infinity, so that our desire would be empty and vain)” (I.2 1094a21-23). If you are familiar with the distinction between per se and per accidens causes, what Aristotle is getting at here is that the relationship between the lower goods and the higher goods forms a per se final causal chain, and as such has an endpoint. If you are unfamiliar with this distinction, unfortunately space doesn’t not allow me to argue for this here, so you’ll just have to trust me.

Aristotle called these highest goods chief goods, and Aristotelians these days typically call them basic goods. Basic goods are desired for their own sake and not for the sake of another. Now, in simple things there might be only one basic good, but for many things there is more than one, and they can often be quite broad. David Oderberg, for instance, thinks the basic human goods are life, knowledge, friendship, work and play, appreciation of beauty, and religious belief and practice (The Structure and Content of the Good).

In some sense the basic goods
In some sense the basic goods “make up” the nature of a thing.

So how do we figure out what the basic goods of a thing are? This relates to the third thing to be said: the basic goods correspond to the various distinctive faculties something has according to its nature. After all, broadly speaking, being a human is an activity and the basic goods represent the broadest aspects of this activity by which we measure it good or bad. Given that the way a thing acts correspond to the faculties it has, it seems that the basic goods and faculties of a thing would correspond to each other.

Now, at this broad level it’s not always clear how we are to carve up reality, but we can make some comments that will help us on our way. First, it isn’t particularly informative to say that “given that humans are rational animals, the basic human goods must be rationality and animality”. What we’re looking for are the various aspects of what being a good rational animal involves. Second, the basic goods might overlap, but their faculties should not be wholly reducible to one another. This would be a clear sign that we’re not thinking at a broad enough level. Third, Aristotle’s Nichomachean Ethics can be seen as his attempt at studying the basic goods by means of studying the various human virtues.

One clear example of a basic good, given our recent discussion about substantial activities, would be what Aristotle and Oderberg call “friendship”, which corresponds to our faculty for working together toward a common end. More on this another time.

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”.

Perhaps this diagram will help you, but if it doesn’t just ignore it. The arrow represents the motion of X to P. Notice how X’s potential for P is being actualised both when X is actually P and when X is potentially P. As we’ve been saying this is that the latter case is when X is moving toward P.

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.


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

Substantial and aggregate activities

In the Physics Aristotle gives his famous definition of a substance, which he refers to as a thing that “exists by nature” or as a “natural object”:

Some things exist by nature, others are due to other causes. Natural objects include animals and their parts, plants and simple bodies like earth, fire, air, and water; at any rate, we do say that these kinds of things exist naturally. The obvious difference between all these things and things which are not natural is that each of the natural ones contains within itself a source of change and of stability, in respect of either movement or increase and decrease of alteration. On the other hand, something like a bed or a cloak has no intrinsic impulse for change — at least, they do not under that particular description and to the extent that they are a result of human skill, but they do in so far as and to the extent that they are coincidentally made out of stone or earth or some combination of the two.

The nature of a thing, then, is a certain principle and cause of change and stability in the thing, and it is directly present in it — which is to say that it is present in its own right and not coincidentally. (Physics II.1 192b8-b23)

Edward Feser summarises this definition from Aristotle by saying,

The basic idea, then, is that a natural object is one whose characteristic behavior — the ways in which it manifests either stability or changes of various sorts — derives from something intrinsic to it. (Between Aristotle and William Paley: Aquinas’ Fifth Way)

Aristotle and the Scholastics would later argue that the only way to make sense of the fact that things always, or for the most part, behave in certain ways is if they are by nature directed towards such behaviour. That is, if they have an inherent tendency or directedness towards such activity as an end. (cf Physics II.8 198b34-199a7) This intrinsic directedness towards an end, then, is the nature of thing:

The point is that those things are natural which undergo continuous change, starting from an intrinsic source of change and concluding at a particular end… it is clear that a thing’s nature is a cause, and that it is the kind of cause I have been saying — namely, purpose. (Physics 199b15-18, 32-33)

It must be recalled that neither Aristotle nor the Scholastics who followed him thought of this directedness or “purpose” as necessarily involving intelligence or deliberation from the things so directed.

This is particularly clear in the case of non-human animals, whose products are not the result of skill, enquiry, or planning. Some people are puzzled by how spiders, ants, and so on make what they make — do they use intelligence, or what? … It is ridiculous for people to deny that there is purpose if they cannot see the agent of change doing any planning. After all, skill does not make plans. If ship-building were intrinsic to word, then wood would naturally produce the same results that ship-building does. If skill is purposive, then, so is nature. (Physics II.8 199b26-30)

Again, Feser explains:

In other words, that goal-directedness does not require conscious deliberation is evident from the fact that a skilled craftsman can largely carry out his work without even thinking about it—”on autopilot” as we might put it today, or without first “making plans,” as Aristotle puts it. But if this is possible for someone with such skill, there is in Aristotle’s view no reason not to think it also possible for natural objects. This is the force of the ship-building example: If there were something in the very nature of wood that “directed it” toward the end of becoming a ship, then what in the case of human craftsmanship results from deliberate design — a ship — would in that case result “naturally” instead, that is, without conscious deliberation at all. Indeed, “it looks as though things happen at the plant level too which serve some purpose” in just this way, even though plants do not deliberate — for instance, an oak derives from an acorn without the acorn planning this result — and there is also of course the example of “non-human animals, whose products are not the result of skill, enquiry, or planning.”

So substances are those things which have an intrinsic directedness towards an end. Because this directedness is tied up with a thing’s characteristic behaviours, and characteristic behaviours are tied up with a thing’s causal powers, we might equivalently say that substances are those things which have intrinsic causal powers. By intrinsic, here, we mean that the directedness or causal powers of the thing are not (1) imposed from some outside agent or (2) reducible to the sum of the its parts considered in themselves. Aggregates (or “heaps”), on the other hand, have only extrinsic directedness or causal powers.

Let’s consider some examples of each. On a molecular level, a water molecule is a substance, for it has causal powers which are not reducible to the powers of its parts. For instance, water boils at 100°C while hydrogen, considered in itself, boils at -252.9°C and oxygen, considered in itself, boils at -183°C. The same goes for other powers.

On a more macroscopic level, individual animals are substances. Considered in itself, an organ is merely a clump of flesh which decomposes if left to its own devices. However, when the organs co-exist in an animal they are each capable of their individual functions in the body (walking, grasping, thinking, sensing, pumping blood, and so on) and they are all capable of participating in the life of the animal, where life is:

… the natural capacity of an object for self-perfective immanent activity. Living things act for themselves in order to perfect themselves, where by perfection I mean that the entity acts so as to produce, conserve and repair its proper functioning as the kind of thing it is… (David Oderberg, Teleology: Inorganic and Organic)

Consider, for instance, how you develop from a baby in your mother’s womb to a fully-grown adult, or how body heals itself when damaged, or how you don’t just decompose (unless you’re sick in some way). None of your organs, considered in themselves as mere clumps of flesh, are capable of these things and so you are not merely the sum of your organs.

A pile of rocks would be an obvious example of an aggregate. Its power to hold something 2 meters above the ground is merely the sum of the individual rocks that make it up. Above Aristotle used an example of a bed, which is merely an aggregate of the materials (wood and metal) that make it up.

Some aggregates, because of their complexity, are less obviously aggregates. Examples of these are things like watches and computers. A watch’s power for time-telling is imposed on it by us, and its power for the circular motion of its hands is merely the sum of the powers of its parts such as the conduction of electricity and so on. Similarly for a computer or a calculator.

From wholes to activities

All this is by way of introduction for what I really want to talk about here. The space was not wasted, however, for what we have introduced will serve us well in what follows. Thus far we’ve been discussing the distinction between substantial and aggregate wholes. My aim here, however, is to make a parallel distinction between substantial and aggregate activities.

A substantial activity, then, is one which has intrinsic directedness towards an end. That is, its directedness is not (1) imposed from some outside agent or (2) reducible to the sum of the its parts considered in themselves. In order for us to understand this we need to be clear on how an activity has directedness, and the best way to achieve such clarity is by considering how substances engage in activities. For our purposes here, it will be sufficient to distinguish between three groups of substances: non-animals, non-rational animals, and rational animals.

By non-animals I mean inorganic substances (rocks, water, atoms, …) and non-animal organisms (that is, vegetation). What distinguishes animals from non-animals is that the former have some form of sentience (and, typically, an ability for self-movement). Since non-sentience involves not being able consciously move to an end it seems we have two options with regards to how activities involving non-animals have directedness: either their activities don’t have directedness, or the directedness of their activities derives from the directedness the substance has in virtue of its nature.

What distinguishes rational animals from non-rational animals is that the former have the ability to (1) abstract universal concepts from particulars (“Socrates is a human“), (2) combine these concepts into judgements or propositions (“All humans are mortal”), and (3) string these propositions into arguments for conclusions (“Therefore, Socrates is mortal”).[1] So within animals we distinguish between non-rational animals, which are only conscious of particular things via sensation, and rational animals, which are additionally conscious of the universal concepts that pervade all the particulars. By virtue of their consciousness animals are capable of directing their actions towards specific ends in addition to the ends set for them by their natures.

For instance, a cat is by nature directed towards certain characteristic activities such as walking on four legs and eating certain types of food, as well as developing such morphological features that make these possible. However, because this cat is hungry and conscious of that bird it directs and moves itself towards that bird in order to eat it. All the while, however, the cat is not conscious of universal concepts (as such) like “being hungry”, “birds” and so on. Much of its “reasoning” is driven by instinct and nature. But this does not invalidate the claim that it has a measure of self-direction which it derives from its consciousness of particular things. Rational animals, because they are also aware of universal concepts, are capable of directing themselves in accordance with a richer set of ends.

The Porphyrian tree for corporeal substances. Leaf nodes represent species and edges represent specific differences that divide each genus up.
The Porphyrian tree for corporeal substances. Leaf nodes represent species and edges represent specific differences that divide up each genus.

Whether an animal is rational or not, ultimately its intention is what determines the direction of a given activity. Consider, for instance, the movement of my hand into your shoulder. What I intend to achieve with the movement is what determines whether this action is me punching you or merely an accident (which would be the case if I was intending to get something else and misjudged our relative positions).

With these distinctions in hand we ask the following question: how are substantial and aggregate wholes related to substantial and aggregate activities? It seems obvious that substances are capable of substantial actions and aggregates are capable of aggregate activity. But does this exhaust the possible relations?

The possibility of substantial activity by aggregate wholes

There are only two other options we could consider. The first is substances performing aggregate activities, but in the interest of time we’ll leave this to one side.

The second option is that of an aggregate performing a substantial activity. Such an activity would require an aggregate of substances to direct their otherwise disparate activity toward a common end. Is this not what we find in various teams and associations throughout human society? A sports team works together to win the game, an orchestra works together to play their piece well, the various employess in a company work together for the sake of the company, the various military personnel work together to achieve victory in war, when two friends pick up a large object together, and so on.

At this point we must be careful, lest we fall into error and think some such activities substantial when in fact they are merely aggregate. Take the example of the members of an orchestra performing their piece. This is an example of substantial action because each intends to contributes to the same performance. It’s this shared intention (or something like it) that makes the activity substantial, and not just that the sound produced is a combination of the sounds of the various instruments. After all, even aggregates involve combinations of their parts. By contrast, consider the musicians behind stage before the performance starts, while they each tune their respective instrument. An observer standing backstage will hear the combination of all the various sounds they make as they do this. The making of this combined sound will be merely an aggregate activity. Why? Because there is no shared intention directing the musicians to a common end. Rather, in this case each musician intends merely to tune their own instrument independent of the others. So when we aggregate the various tuning activities we end up with an aggregate of ends and therefore an aggregate activity.

So aggregate wholes can indeed engage in substantial activities, and they do so when and only when the members of the aggregate intentionally work together toward some common end.

But we can take this further. You’ll notice that the examples I listed above all involved aggregates of rational animals. This was not accidental, for only aggregates of rational beings are capable of this kind of substantial activity we’re considering. We see why when we reflect on what’s involved in working together with others toward a common end.

First, working together involves recognising both you and another falling under the same category of “part” in some sense. It requires that we understand the roles we’re responsible for and how those roles contribute to the achievement of the end in sight. Often (if not always) this will require that we understand the rules which encode our responsibilities. All of this, and more, requires a capacity for being conscious of universal concepts like “part”, “whole”, “role”, “responsibility”, “rule”, “expectation”, and so on. Since only rational beings are conscious of universal concepts, it follows that only rational beings can work together toward a common end.

Second, working together toward a common end requires that we be conscious of the end as common. Briefly, common ends are ends that can be enjoyed by multiple members without thereby being diminished. They are opposed to private ends, which are always diminished when shared.[2] For instance, if there is a loaf of bread between me and someone else, the more the I eat the less there is for the other person to eat. Siblings will know that the time I spend playing on the computer is time my brother cannot play on the computer. Consider, however, the examples we mentioned earlier: winning a sports game, the musical piece, the good of a company, victory in war, the picking up of a car. All of these are shared amongst the members in the corresponding aggregate, but are not thereby diminished. The same victory in war, for instance, is equally had by everyone in the winning nation.

Now, from the examples given it seems clear that particular things (or combinations of particular things) considered as particular can only serve as private ends. By contraposition, it follows that in order to be conscious of an end as common requires that we be conscious of universal concepts. Therefore only rational beings can be conscious of, and direct themselves toward, common ends.


  1. The Scholastics called these the “acts of reason”, and labeled them (1) grasping, (2) composition and division, and (3) reasoning. Each of the acts of reason are dependent upon the earlier ones for their operation. Technically, (2) is richer than merely the ability to form propositions: it also enables rational beings to form universal concepts of things they haven’t experienced yet. For instance, once we have an concept of a horse and the concept of blackness we can consider the combination of these two concepts without having ever seen a black horse.
  2. Of course this is not the whole story, and common ends tend to be notoriously difficult to talk about (see, for instance, Marcus Berquist’s Common Good and Private Good). The particular qualification I want to add here is that while common ends can be shared without thereby being diminished it doesn’t follow that sharing always leaves it undiminished. For instance, orchestras are limited in their size because once they get too big they become unmanageable. The same goes for political communities and friendships and presumably any community. Furthermore, including bad musicians in an orchestra might also diminish the end insofar as those musicians get in the way of the orchestra performing well. But in these cases it is not the sharing per se that is diminishing the end, but rather the sharing with too many people or sharing with bad musicians. With private goods, no matter how you share you will always diminish your ends. Because this qualification doesn’t affect the overall thrust of my argument, I chose to just mention it here in the footnotes.