Although the following task is so arduous that it is unlikely that anyone could ever complete it in practice, it is theoretically possible that a person could write down a system of equations that, in accordance with the fundamental laws of physics, completely and accurately models the behaviour of every subatomic particle that goes to make up the body of a donkey. However, if a physicist were to actually do this, he would find almost immediately that he was modelling the wrong thing. As the donkey respires, as dead cells are sloughed off its skin, as its digestive system incorporates new nutrients into its body, the collection of particles of which it is composed is constantly changing. The physicist’s system of equations would no longer be modelling the donkey but rather something else.
If the physicist wished to continue modelling the donkey, he would be forced to continually update the set of particles in his model. However, there is no way he could do this without leaving the realm of physics and asking a biologist for help. There is nothing in the fundamental laws of physics that can tell him what is and what isn’t part of a donkey. Such information exists only in a different mode of explanation, that of biology. Of course, this is in fact true right from the beginning: the physicist could not even have begun his experiment without first asking a biologist to identify a donkey.
We might be tempted to think that the physicist could circumvent this problem by modelling everything. If he were to model everything in the entire universe, surely he would be modelling the donkey too, since it has to be in there somewhere? This is rather the point: the donkey most certainly is in the universe but it is not part of the physicist’s model. It is not possible, from the physicist’s model alone, to deduce anything about a donkey. Therefore, we must conclude that the physicist’s model of every fundamental particle in the universe is not in fact a model of everything that exists.
Well, there is one other option open to us. We might conclude that the donkey does not exist. If we had some other reason to believe strongly that only that which is modelled by physics is real, then we might try to convince ourselves that donkeys are not real. We may succeed – after all, people are capable of convincing themselves that all sorts of crazy ideas are true – but this isn’t really an option for anyone who wishes to be rational. Since the argument applies just as well to people as it does to donkeys, the correct response to anyone who claims that physics explains everything is to ask, “Who said that?”
Perhaps one source of confusion is the fact that clearly donkeys are composed of physical matter. Although that matter is constantly changing, at any one instant in time the donkey is made up of some set of fundamental physical elements. Thus even though a donkey is not the same thing as the matter out of which it is composed, its existence is dependent on matter. If there were no matter, there would be no donkey. But it is important that the donkey’s existence does not depend on any particular matter. A healthy donkey will live to around 30 years old, sometimes another decade or more after that, by which time it is highly likely that not a single atom in its body was present when it was born. The facts in the previous sentence cannot possibly be deduced from a physicist’s model of the universe alone: therefore the physicist’s model cannot possibly be a complete explanation of the universe.
I chose to illustrate my point by comparing donkeys with those entities that appear directly in the laws of physics. I did this for a rhetorical reason: I thought that the claim that donkeys do not exist would be so obviously absurd that my point would be easily understood. However, I could have made the same point by comparing any entity that is not fully explicable in terms of its constituents with those constituents. For example, the entities of chemistry — a covalent bond, say, or a particular molecule — are also real things about which facts exist that cannot be deduced from the laws of physics alone. This leads us to an important point: if we wish to have a complete, scientific explanation of the world then we cannot rely on physics alone. Physical law is not a complete description of the universe.
Note that I am not claiming that different things are composed of different substances: everything I have said is consistent with the view that everything is made of matter. All I am saying is that the method of explanation we call physics, i.e. the description of the interactions of fundamental physical particles according to the laws of physics, is not capable of explaining or even describing all that exists. As such, there is no reason to grant physical explanations any sort of primacy over other sorts of scientific explanations: they are not more real, more true or more basic than the explanations of, say, chemistry or biology.
We may still want to attach some sort of prestige to physics, over and above that attached to other sciences, because it deals with the basic units out of which everything else is composed. Although the interactions of subatomic particles are not all there is to be said about a donkey, you might think that it is at least made of them. In other words, we can construct a meaningful hierarchy of matter — protons contain quarks, atoms contain protons, molecules contain atoms, cells contain molecules, donkeys contain cells, or something along those lines — and so we should consider the indivisible units at the bottom of the hierarchy to be fundamental, the basic units of the universe. However, it turns out that there are no such basic units. Even the subatomic particles of modern physics can themselves be understood as disturbances in underlying fields, as patterns in a substrate . Furthermore, there is no logical reason why a “high level” entity such as a donkey must be composed of a particular sort of “low level” entity: to the best of our knowledge, donkeys as we know them are always composed of familiar atoms (mostly carbon, hydrogen and nitrogen), which are themselves composed of familiar subatomic particles such as quarks and electrons, but there’s no reason why they couldn’t be composed of functionally similar yet different entities. That is the point: donkeys could be composed of any sort of entity, as long as they behave in the right sort of way. Perhaps we live in a universe in which the only entities that behave in the right sort of way to make up a donkey are those that we have thus far observed in donkeys: quarks, electrons and so forth. But perhaps we don’t. Either way, there doesn’t seem to be any logical necessity for it to be so, which puts something of a damper on any claim that subatomic particles are really “fundamental” in any meaningful way.
It seems clear that there is nothing special about physics as compared to chemistry or biology. It is not the case that biology can be reduced to chemistry or chemistry reduced to physics. The entities of biology are every bit as real as the entities of chemistry and physics — they exist in their own right just as much as a hydrogen bond or a quark exists — and they cannot be fully explained in chemical or physical terms. Furthermore, there is no reason to stop at biology: we may, for example, employ the same style of argument to show that just because our minds depend for their existence on our brains, that does not mean that our minds can be reduced to our brains.
I wish to promote the view that the different sciences do not correspond to different levels of abstraction but to different modes of explanation, suited to explaining different aspects of existence. We do not use the language of biology to investigate life only because it is too difficult to do so with the language of physics. We could not, no matter how clever we are or how long we worked, write the equivalent of a biology textbook using only the tools and concepts of physics or chemistry. To attempt to do so would be tantamount to a category mistake. Organisms are not mere abstractions on top of underlying chemical reactions: they are as real in their own right as any electron or photon. There is a hierarchy of sciences only in the very weak and not particularly interesting sense that the entities studied by one science have not so far been observed to exist unless the entities of a “lower level” science also exist.
I suppose the final conclusion of this argument, which like a depressing amount of contemporary philosophy is more concerned with “defeating the defeaters” than with anything positive, is to point out something that ought to be blindingly obvious anyway, if only we still lived in enlightened times: a person is every bit as real as, and cannot be reduced to, the material parts out of which he is made.
 For more details on this, see Steve Grand in Creation: Life and How to Make It (Harvard University Press, 2003) pp. 36 & 37, and also in the comments on my previous blog article Forms, and J. R. Lucas in Reason and Reality (Ria University Press, 2009, also available from his website http://users.ox.ac.uk/~jrlucas/) Chapter 13 “Reductionism”.