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.

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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.↩