Downward Causation of Neural Structure
Now, let us return to the question of how the brain becomes structured in such a way that its causal processes realize rational processes. Many theories of brain function rely on some form of "neural Darwinism" . That is, the answer to the question of how neural nets or cell assemblies form is by a process of random growth of dendrites and synaptic connections, followed by selective reinforcement of connections that turn out to be useful. The best theory seems to be that co-presentation of stimuli to two neurons or groups of neurons, resulting in simultaneous activation of their respective receptors, strengthens neuronal connections between those receptors, making it more and more likely that both cells or groups of cells will fire when one is stimulated. So useful connections (such as the connection between the "grandmother" assembly and the "cookies" assembly) are strengthened, while unused connections, (say, between "grandmother" and "frogs") weaken or die off. In this way, neural connections that model relations of various sorts in the world come to be selected.
If Campbell's account of environmental shaping of termite DNA is an instance of downward causation from the environment to the species' genome, then this, too, is downward causation. In this case it is from the environment to the individual brain during the individual's lifetime. A central claim of my paper, then, is that downward causation, in the sense of environmental selection of neural connections and tuning of synaptic weights, provides a plausible account of how the brain becomes structured to perform rational operations. In Van Gulick's terms, the larger system--which is the brain in the body interacting with its environment--selects which causal pathways will be activated.
So far we have an example of a weak form of rationality--presumably it is more rational to think of cookies than of frogs in association with thoughts of one's grandmother. Here the connections among things in the world come to be modeled by connections among cell assemblies in the brain. When this happens, free association is replaced by "rational" trains of thought.
We can build from this beginning to consider more interesting forms of reasoning. If interaction with the physical world structures the brain in its image, so does interaction with the social world, with its structures and conventions. Consider the social environment of the primary school classroom, and the set of conventions we call arithmetic. How do the brains of children come to be structured so that neurobiological causal processes realize rational operations? Let us speculate about a simple form of learning such as rote learning of multiplication tables. We can imagine that upon hearing the teacher say "5 X 7," neural assemblies are activated and, at first, activation spreads widely and randomly--activating a variety of other assemblies: for example, those subserving thoughts of, "57," "Times Square," "30," "35," "75." But feedback from the environment selectively reinforces one connection, while lack of reinforcement weakens all the others. We can picture this process by means of a diagram formally identical to the one I used to represent Campbell's account of downward causation (see Figure 5).
Here the thoughts of "5 X 7" and of "35" are pictured as supervening on two brain states (that is, activation of cell assemblies) labelled B1 and B2. Over time, feedback from the social environment results in a strong connection between B1 and B2 such that B1 regularly causes B2. Let me emphasize that the foregoing is not intended to be a realistic cognitive-science account of the actual learning of arithmetic. In addition, it begs all of the questions pertaining to the foundations of mathematics. It is simply intended to show that downward causation in the form of environmental selection among neural connections provides a plausible explanation of how rational connections could become instantiated in or realized by causal pathways in the brain.
Footnote for Neural Causation
 See, for instance, Gerald M. Edelman, Bright Air, Brilliant Fire: On the Matter of the Mind (New York: Harper Collins, 1992).