This spring semester, teaching Philosophy of Biology–especially the Darwinian model of adaptation and environmental filtration– has reminded me of the philosophical subtleties of ‘abstract model’ and ‘abstraction’. More generally, it has reminded me that philosophy of science achieves particularly sharp focus in the philosophy of biology, and that classroom discussions are edifying in crucial ways.
In its most general form, the Darwinian theory of adaptation by ‘natural selection’ states that adaptation results if:
There is reproduction with some inheritance of traits in the next generation.
In each generation, among the inherited traits there is always some variation.
The inherited variants differ in their fitness, in their adaptedness to the environment.
In teaching this version (taken from: Richard Lewontin, Adaptation. Scientific American. 239: 212-228 in Rosenberg and Shea’s Philosophy of Biology) I point out how much this concise statement of the theory leaves unspecified–the entity reproducing, ‘traits,’ the mechanisms of reproduction and inheritance, the sources of variance, the nature of ‘fitness’, the extent of the environment, and the mechanisms and characteristics of the adaptation–even as it provides an explanatory framework of great power and scope. (This under-specification allows the model’s statement too, in terms of interactors and replicators.)
The generality of the Darwinian specification reminds us of the practicing mathematician’s adage that the sparsest, barest definitions result in the richest, most interesting theorems. In this case, the theory works with a diversity of hereditary mechanisms and sources of variation, and does not require or imply any particular one. Rather, it merely requires that there be some mechanism for heredity and some source of variation in heritable traits for every generation in every line of beings. I think it’s a fair bet to say that if there were any appreciative reactions in class to this discussion of the theory, they were grounded in a grasp of the theory’s generality.
Getting clear about the abstraction of the Darwinian model is crucial in understanding why it does not issue teleological explanations, why it cannot be understood as ‘progressive’, and why it is plausibly extensible to different levels of theoretical explanation in more than one domain of application. Later, our descriptions of blind variation and selective retention as algorithmic processes enabled another reckoning with the abstraction of the model’s substrate neutrality. (Discussing this with my students reminded me of teaching the multiply-realizable computational model of the mind in classes on the philosophical foundations of artificial intelligence, especially as our discussion segued into an attempt to understand the abstract notion of computation.) In general, I sought to clarify why the model specified above is an ‘abstract’ one and what relationship its abstraction has to its generality and its explanatory scope.
Unsurprisingly, at moments in my exposition, I found myself rediscovering admiration at the theory’s Spartan outlines. I was pleasantly surprised too, by how sophisticated my students’ interjections and questions became as they attempted to take on and apply the theory; they forced me to think on my feet in addressing them. More than anything else, their class responses reminded me that a particularly important species of learning takes place in the course of teaching.