My paper titled “Modeling Causal Structures: Volterra’s struggle and Darwin’s success” recently appeared in the European Journal for Philosophy of Science. The paper was co-authored with Tim Räz. (A draft version is available on the PhilSci archive.)
In the past, philosophical analyses of how the sciences gain theoretical knowledge have tended toward the monistic. This is most easily visible in authors like Hempel or Popper, who suggested that the entire methodological diversity of science ultimately reduces to just one principle (hypothetico-deductivism in the case of Hempel and falsificationism in the case of Popper).1 On the spectrum laid out by the ancient Greek fragment which says that “the fox knows many things, but the hedgehog knows one big thing”, most philosophers of science have lived on the hedgehogs’ side. This is true even for more recent and on the whole more pluralistic authors such as Peter Lipton, who offered inference to the best explanation as at least potentially an explication of all inductive practices in science.2 And if my impression is correct, then modern Bayesians are among the most committed hedgehogs of them all.
In a stimulating 2007 paper in the British Journal for Philosophy of Science, titled “Who is a Modeler?“, Michael Weisberg asks us to adopt a more fox-like stance. Perhaps the reason why philosophers of science have been unsuccessful in offering a monistic analysis of scientific epistemology is that we must distinguishing between several different inductive practices. Perhaps we can say something philosophically and historically insightful about each of them separately.
As a starting point, Weisberg suggests “modeling” and “abstract direct representation” (or ADR) as two different ways of developing scientific theories. His basic idea is that a modeler investigates the world indirectly by constructing a model, exploring its properties, and checking how they relate to the real-world target system. Weisberg’s main example of this is a famous instance of model-based science: The Lotka-Volterra predator-prey model. In what Weisberg calls ADR, by contrast, scientists engage the world directly, without the intermediation of a model. He thinks that Mendeleev’s periodic table of the elements is of this type. Mendeleev did not start out with a constructed model: He simply arranged the elements according to various properties. He thereby gained theoretical knowledge about them, but without using a model. Weisberg concludes his paper by asking why scientists would choose modeling over ADR or other strategies (or more succinctly, having asked “who is a modeler?”, he concludes by asking “why be a modeler?”).
In our paper, we follow Weisberg’s pluralistic approach to scientific epistemology, but we find his distinction between practices unsatisfactory, and so we suggest a different one. Moreover, we give an answer to the question of why scientists choose the strategy of modeling.
A main problem of Weisberg’s paper is that the concept of ADR remains ill-defined. Perhaps it is a useful category for describing some scientific work, but the case remains to be made. We suggest that the more natural counterpart of modeling is causal inference. We argue for this by looking closely at the original publications relating to Weisberg’s main example: the predator-prey model. In particular, we look at a previously unexamined methodological preface to the Italian mathematician Vito Volterra’s Les associations biologiques au point de vue mathématique, published in French in 1935.3 We find that Volterra’s preferred method for investigating the factors determining population sizes and fluctuations would have been the laboratory physiologist’s causal inference: vary one thing at a time and see what changes with it. But as Volterra explained at some length, various factors make causal inference in natural populations difficult: The populations are too large, the time intervals too long, the environmental conditions too changeable for the method to succeed. We summarize this as insufficient epistemic access for applying methods of causal inference. Volterra stated quite explicitly that this insufficient epistemic access is the reason why he chose the modeling strategy. Thus, the distinction between causal inference and modeling offers a possible answer to the question of why scientists model: They do so if causal inference is not possible.4
Our distinction also permits us to reevaluate Weisberg’s second example of “abstract direct representation”, which is Darwin’s explanation of the origin and distribution of coral atolls in the Pacific ocean. We argue that this, too, should be understood as an instance of modeling. We also use the example of Darwin’s corals to discuss how causal models can be empirically tested if straightforward causal inferences are not possible.
If you’re interested in the details, please go and read the paper. I will argue on another occasion that the distinction between modeling and causal inference can do a good bit of philosophical work. For example, the debate about scientific realism should probably pay more attention to the distinction, since arguments for inductive skepticism with regard to model-based science may not go through with regard to causal-inference-based science (I’ve started to develop the idea in this talk).
Since this is an ongoing project, I will attempt some crowdsourcing. Our thesis about the motivation for modeling – insufficient epistemic access for causal inference – would be challenged by episodes from the history of the sciences where causal inference is possible and modeling is nevertheless chosen as a strategy. If you can think of such episodes, please send them my way.
- Hempel’s views are accessibly summarized in his Philosophy of Natural Science, originally published in 1966 and still available. The best primary source for Popper’s views remains his Logic of Scientific Discovery, either the German edition of Logik der Forschung published by Mohr Siebeck or the English translation published by Routledge. Popper’s Conjectures and Refutations (also by Routledge) is another good point of entry. For a textbook-type introduction, I recommend chapters 2–4 in Peter Godfrey-Smiths’s Theory and Reality (2003 by The University of Chicago Press).
- Lipton’s Inference to the Best Explanation (1993/2004, Routledge) is a challenging but rewarding read.
- Philosophers of science have not yet paid much attention to Volterra’s explicit methodological discussion. This is probably explained by the fact that the relevant publications were written in French. This was after Volterra left Rome for Paris because of Mussolini’s rise to power.
- For an episode where causal inference dominates, see my Semmelweis paper.