5 Size levels

One ontological application of the levels metaphor emphasizes the relative sizes of objects at different levels. The relata in size levels are objects or kinds of object, and the interlevel relationship is relative size (larger, smaller). Things in the same size range are at the same level. Churchland and Sejnowski’s classic diagram of levels in the neurosciences (Figure 2) is accompanied by size scales for each level, ranging from Angstrom units to meters.[5]

Figure 2: Churchland & Sejnowski’s (1992) diagram of levels of organization in the central nervous system.

As noted above, Wimsatt’s tree diagram branches precisely because it is tracking something stronger than size: some kind of compositional relation. In a second diagram (Figure 3), Wimsatt emphasizes size and abandons the compositional relationship implicit in Figure 1. The abscissa in Figure 3 represents a roughly logarithmic size scale, and yet the figure is not compositional. Large metazoan organisms are not generally composed of smaller metazoan organisms, and it would surely be a stretch to claim that these two are generally composed of unicellular organisms (though there might be some truth in that claim). The ordinate in this diagram is a measure of regularity and predictability. The figure is repeated three times, each illustrating a different way the world might be organized with respect to size. At the top is an orderly world (despite impending doom on the right). Objects become more regular and predictable in their behavior, and to the same degree, at certain size scales. Beneath this is a world with no sharp peaks of regularity and predictability. As Wimsatt notes, scientists confronted by such a world might question whether they have chosen the right variables for their models. On the bottom is Wimsatt’s conjecture for our world, where regularity is very high for single atoms but falls off at larger or smaller scales. This wave dissipates over time, peaking lower and spreading out over larger and larger size ranges as scale increases. Wimsatt’s diagram thus represents an empirical hypothesis about how levels, as peaks of regularity and predictability, are in fact distributed across different size scales in our world. If his empirical hypothesis is correct, it calls out for explanation that our world is more like the first and third graphs than it is like the second.

Figure 3: Levels as local maxima of regularity and at different size scales (Wimsatt 1976).

Why does Wimsatt represent size as the determining factor in regularity and predictability? The answer turns on other features in his prototype account. For example, things of different sizes effect and are affected by different forces, and objects of different sizes act and interact with one another more than they interact with objects at other levels. Market forces run economies, cosmic objects move under gravitational forces, and hydrogen bonds hold molecules together. Regularity and predictability peak at different size scales because the forces act and the causal relationships occur mostly at those size scales.

Wimsatt’s empirical hypothesis has not been tested.[6] Despite its intuitive appeal, one can readily produce examples of causes, forces, and laws that operate promiscuously across a very wide range of size scales. Big things (even very big things) and little things (even very little things) routinely interact, as when planets attract molecules into atmospheres or when a five-millimeter louse attaches itself to a thirteen-meter gray whale. Forces also act at many scales. Gravitation affects the human species on an evolutionary scale just as much as it influences individual human actions and the otoliths in our vestibular system. The very existence of interlevel theories, bridging molecules to behaviors (for example), provides ample evidence that regularity and predictability often span size scales: facts about gasses can be predicted from facts about molecules, and facts about learning can be inferred from facts about molecules.

If we could find a way to test Wimsatt’s hypothesis, it might turn out that causes, forces, and laws do tend to cluster around certain size scales. This would be a striking empirical fact about the world and would, again, call out for some kind of explanation. In contrast, Wimsatt raises no principled objections to interlevel causes, forces, or regularities; he offers an empirical hypothesis that interlevel causes, forces, and regularities tend to be less prevalent than those operating at a single level.

There are, however, apparent principled, conceptual difficulties faced by the effort to describe levels of realization in terms of a causal relation. There are many notions of realization, often tailored to altogether distinct philosophical disputes (Craver & Wilson 2007). On most accounts, however, one and the same object or event has both the realized and the realizing property, and the object cannot differ with respect to the realized property without the realizing property being different in some way (supervenience). The relata here are properties. The interlevel relationship is or includes supervenience.[7]

Marr’s levels, as I understand them, are levels of realization. The hardware realizes the algorithm, which, in the right context, realizes the computation. It is awkward at best to say that the algorithm causes the computation; rather, the algorithm implements the computation in context. Changing context can change the computation. For example, a subtraction algorithm can implement division; the log of a division is a difference of logs. Likewise, the function represented in the algorithm is not caused by the hardware; the hardware instantiates or implements the algorithm. Computation-, algorithm-, and hardware-level theories are all different ways of describing one and the same thing—different predicates applied to one and the same system as a whole in its working context.

The same holds for what we might call micro-realization: when some property of a whole is realized by the organized and interacting collection of parts that constitute the property of the whole. An early edition of the Betty Crocker Cookbook apparently contains an explanation of how the microwave heats the soup (Churchland 1995). According to this explanation, the molecules excited by the microwave rub against one another and heat the soup by friction. As Churchland points out, Betty misrepresents the relationship between the heat of a liquid and the kinetic energy of its constituent molecules. Temperature is not produced by the mean kinetic energy of component molecules in such cases; rather, temperature in such situations is constituted or realized by (Churchland would say identical to) the mean kinetic energy of the components. In the same way, one might think that the behavior of a mechanism as a whole is realized by, rather than caused by, the organized collection of its components. The beating of the heart is realized, not caused, by the choreographed movements of the auricles and ventricles. It is awkward and unnatural to assert otherwise.

The apparent awkwardness and unnaturalness of such ways of talking follows from many core principles that many (rightly or wrongly) embrace about the nature of causation. If one thinks that causes must precede their effects, and one understands the realization relationship as a synchronic relation, then levels of realization cannot be causally related. If one thinks of causation in terms of the intersection of processes and the exchange of marks or conserved quantities, then the relata in levels of realization do not come to intersect in space-time (they always and everywhere intersect), they do not carry their marks beyond the locus of the intersection (because they always and everywhere intersect), and they do not pass anything from one to the other. In short, the intimacy among levels of realization seemingly precludes any standard metaphor of production, or “oomph,” or expression of a disposition, or the exertion of a power. This intimacy stands in the way of anyone who believes that causes and effects must be altogether distinct from one another.[8] So indistinct are levels of realization that many philosophers, Churchland included, prefer to speak of identity in such contexts (see Polger 2006). Finally, if one thinks of causation in terms of the ability to manipulate effects by intervening on causes, one will note that there is no way to intervene to change the properties of wholes without, at the same time, intervening to change the supervenience base of those properties.[9]

I raise these issues not to cement a case against the possibility of understanding realization and causation so as to leave conceptual space for causation between levels of realization. (For a fuller discussion, see Kim 2000; Craver & Bechtel 2006). I mention them only to point out that relations of size and realization have very different implications for the intelligibility of interlevel causation. No theory or principle of causation that I know places any metaphysical restrictions on causal relations among objects of different sizes. Many theories or principles of causation appear to rule out the possibility of causal relationships between levels of realization. The point is that Wimsatt’s empirical hypothesis that causes, laws, and regularities tend to be sequestered within size scales is altogether distinct from the claim that there is no conceptual room for causation between levels of realization. Interlevel causation is mysterious or not depending on which views of levels and causation one adopts.[10]