Wimsatt, Oppenheim, and Putnam all include within their analysis of levels the gestural idea that different fields or disciplines of science are arranged by the sizes of the objects they study. Wimsatt’s branching hierarchies depict a more ornate structure. Within that structure, it seems inappropriate to say that astrophysics is at a higher level than biology or economics, though astrophysicists typically deal with things that are orders of magnitude larger than the things biologists and economists study. The gestural sense of levels doesn’t seem to branch that way.
When we apply the levels metaphor to sciences, the relata are units of scientific organization (such as fields, research programs, or disciplines). Answers to the relations and placement questions are more difficult to discern and are likely impossible to express both accurately and concisely for this application. Size seems to be relevant, but we have just seen that it cannot be the whole story. The branches in Wimsatt’s diagram follow, in addition to size relationships, relationships of composition. The things studied by economists (groups) are composed of things studied by psychologists (organisms), which are composed of things studied by physiologists (physiological systems), and so on. The things studied by Darwin are composed of the things studied by zoologists, which are composed of the things studied by cytologists. The point of these examples is not to get the branches in Wimsatt’s hierarchy exactly right; any proposed hierarchy of the sciences and the items in their domains is bound to be historically contingent and provisional at best.
In fact, many sciences appear to resist tidy compartmentalization within levels. Neuroscience, especially cognitive neuroscience, is a paradigm of multilevel science, encompassing the study of ions, ion channels, cells, populations of cells, brain regions, and behaviors of whole organisms. No competent evolutionary biologist can avoid knowing something about genes, physiological systems, organisms, populations, and environments. Many sciences, in short, contain items within their domain that stand in compositional relations to one another. Such sciences often construct multilevel theories that integrate findings across multiple levels of organization. This is one reason why the relationship between levels of science and part-whole levels is indirect.
Another reason is that, in many cases, more than one science is dedicated to studying items at the same mereological or size level. Cytologists, anatomists, and electrophysiologists all study aspects of cells with different tools. The ethologist and the experimental psychologist study animal behavior, but they approach that behavior with different assumptions, methods, and theories. Economists, ecologists, epidemiologists, and organizational psychologists study populations of organisms. The relationship between levels of science and the ontological levels that Oppenheim and Putnam presume is many to many.
For this reason, it is unlikely that any precise answer to the placement question will correctly express the application of the levels metaphor to sciences. One might say that two sciences are on the same level when they pertain to items at the same compositional level. Perhaps it makes sense to say that Camillo Golgi was investigating the same level when he stained Purkinje cells with silver nitrate that Alan Hodgkin was investigating when he used his voltage clamp to study the action potential of the squid giant axon. They were both studying cells, but they studied different phenomena and used different techniques. If we focus now on the parts of these wholes, we see that these different scientists are not even on the same branches of a Wimsatt diagram, and the levels metaphor begins to break down. Ask Golgi about the relevant parts of the cell, and he will tell you about its gross morphological features and its organs. Ask Hodgkin and Huxley about the relevant parts of the squid giant axon, and they will tell you about membranes, axon hillocks, ionic conductances, and voltage gradients. An epidemiologist might talk about nodes and networks and hubs in a model of contagion. Economists will talk about producers and consumers. Differences in scientific interests often entail differences in the relevant ontology for the science; and the same thing can be carved into parts in many ways depending on what one is interested in describing or explaining (Kauffman 1971; Wimsatt 1972).
The take-home lesson: the application of the levels metaphor to fields of science yields a notion of levels only indirectly related to ontological levels (as understood in a roughly compositional, part-whole sense). The idealized, Oppenheim-Putnam correspondence between levels of science, levels of theory, and levels of mereology breaks down in the face of this many-many mapping. And the compositional aspect in Wimsatt’s prototype appears to be only loosely related to the application of the levels metaphor to fields of science. These are, in short, distinct applications of the metaphor, offering different answers to the relata, relations, and placement questions. As a result, an understanding of how sciences can be organized loosely into levels provides no direct insight into ontological levels. This will come as no surprise to those who study intellectual history, or to those who have witnessed for themselves how fields of science change their boundaries over time. Our age, perhaps more than any other, has witnessed an explosion of hybrid fields (neuroeconomics, behavioral genetics, cognitive ethology) that cross levels, combine approaches, and attempt to feed off insights shared between distant scientific neighbors. The historical relativity of disciplinary boundaries makes them unreliable guides to ontology.
The same considerations suggest that levels of scientific theory will also have a many-many relationship with ontological levels. In this application of the metaphor, the relata are theories or models. And the relationship is typically construed as a kind of subsumption, e.g., deductive subsumption (Hempel 1965; Schaffner 1993; Kitcher 1989), or some kind of similarity or inclusion (Bickle 1998). The disciplinary hodgepodge of the special sciences fails to match this philosophical reconstruction. Single theories, such as the theory explaining spatial memory in terms of memory systems, grid cell organization, synaptic plasticity, and changes in ionic conductances through a membrane (see Moser 2008), often reach across many different part-whole levels (Darden & Maul 1977; Bechtel 1988; Craver 2002, 2008). One and the same mereological unit (e.g., cells) can appear in many distinct theories (e.g., neurons play some role in most theories in neuroscience).
The multilevel structure of contemporary science emphasized in nearly every corner of the special sciences is not best understood as a hierarchy of theories. Nor is it a hierarchy of fields. Instead, there is an ontological hierarchy working behind the scenes. This background ontological assumption guides the development of theories, informs the criteria for evaluating explanations, and underlies the roughly hewn idea that sciences and theories are organized into levels. It is the expression of an ideal of explanation to understand how things work in terms of their component parts and to understand how those parts work in terms of still lower-level components. It is precisely because the world is presumed to have this kind of multilevel structure, of mechanisms within mechanisms, that the sciences investigating that world and the theories describing it are so reticulate that they can look like the “bio-psychological thicket” on the right side of Wimsatt’s tree. In the thicket, the orderly relationship among levels breaks down and is replaced by a jumble. The image makes it hard to see any meaningful sense in which distinct items are at different levels. Perhaps this thought fuels eliminativism about levels.
The biological sciences are undeniably thicket-like. But this sociological fact is only indirectly related to the ontic structures presumed to lie behind and scaffold the development of these theories. From now on, then, I focus on applications of the levels metaphor to the world, not to sciences or theories.