I have uploaded the slides to my recent talk “A Tale of Two Puzzles.” It presents the best current version of my thinking about causal inference and modeling as distinct scientific practices. In the last part of the talk, I show how the CI/modeling distinction can perhaps do work in the debate about scientific realism.
I am co-organizing a workshop on the integration of history and philosophy of science next November. The workshop’s website is now online. Check it out: We already have a nice lineup of speakers, with more to come.
We try to do something unique with the workshop by focusing on a type of underdetermination problem: What happens when different philosophical positions lead to competing accounts of the same historical episode? On the workshop’s website, we give several examples of this problem, which we think is quite virulent.
With this particular approach we hope to strike a delicate balance. On the one hand, the topic is broad enough to allow our speakers to engage with any HPS-related issue that they find interesting and worth discussing. But on the other hand our problem is focused enough to avoid, hopefully, a certain kind of abstract lament, where we all agree that of course we want our philosophy to be grounded in history (but it would be wrong to generalize from individual cases!) and that of course our history should be mindful of philosophical concepts (but you must not read the philosophy into the history!).
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.
My review of Philosophy of Biology: An Anthology (edited by Alex Rosenberg and Robert Arp) has appeared online at the journal Acta Biotheoretica.
In brief: A nice volume that will be useful to many people, but it has one substantive and one formal failing. The substantive failing is that there is no sign in the volume of the more recent directions in philosophy of biology (mechanisms, experimental biology, and so on). The formal failing is that some papers are not reproduced faithfully. For example, the classic “Spandrels of San Marco” paper by Gould and Lewontin is reproduced without photographs, and so readers never get to see any spandrels (or “pendentives”, which I read is the correct term for three-dimensional spandrels). For a paper that relies so heavily on its central architectural metaphor, that’s a problem – especially since the full paper is freely available online.
Nevertheless, this is a useful volume, and reviewing it has given me an opportunity to think in earnest about the function of anthologies in academic disciplines.
I am organizing a workshop on the integration of history and philosophy of science next November. In this context I’m thinking a lot about the wider goals and big ideas of HPS. So it’s refreshing to think that sometimes it all comes down to small gestures:
The department flourished under his skilled and shrewd leadership, bringing together the sometimes competing intellectual frameworks of the history and philosophy of science, fuelled by the espresso coffee machine he was proud of having installed.
(From an obituary of Peter Lipton in the Guardian.)
It is a well known fact that Darwin’s On the Origin of Species contained only one figure: A rather arresting depiction of tree-like descent with modification. What is less well known is that Darwin does not introduce the figure in order to illustrate common descent. Since I’ve come across this misconception a number of times in the past days, I thought it was worth pointing this out.
Look at the figure carefully. Here it is (modified from the PDF of the first edition of The Origin of Species at www.darwin-online.org.uk):
At first glance this certainly looks like a visual representation of common descent: The original species (A) diversifies into eight species, while (I) diversifies into six, with some side branches going extinct in both cases. However, the main message of the diagram is actually about something different.
The vertical axis of the diagram unsurprisingly represents time: There are 14 time steps between the original species (A) to (L) and their descendants a14 to z14. But the horizontal axis is also important. It is supposed to represent divergence between species. The idea is that among (A)’s descendants, the labeled descendants a1 and m1 differ the most from (A), while the intermediate offspring (not labeled) are more similar to (A). The vertical line above (A) designates offspring that are more or less identical to (A). Similarly, for example, the vertical line above (F) indicates that (F) does not change at all over time.
Now compare carefully the variations at each time step that survive for some time (perhaps even to the top of the diagram) to those that go extinct more or less quickly. You will find that it is for the most part the more extreme variations which survive, while the less extreme variations disappear.
What Darwin is trying to illustrate is his “principle of divergence”. This is an aspect of Darwin’s work that did not get accepted in modern evolutionary theory, and so it is always in danger of being in our blind spot when we read the historical sources.
For some time in the 1840s and 1850s, Darwin was worried that natural selection explained adaptation but not divergence. Why would there be many different species living today and not just a small number of highly adapted ones? What explains the abundant divergence of lineages in addition to their transformation toward better adapted forms?
Darwin’s answer was that there was an advantage to ecological differentiation:
We can clearly see this in the case of animals with simple habits. Take the case of a carnivorous quadruped, of which the number that can be supported in any country has long ago arrived at its full average. If its natural powers of increase be allowed to act, it can succeed in increasing (the country not undergoing any change in its conditions) only by its varying descendants seizing on places at present occupied by other animals: some of them, for instance, being enabled to feed on new kinds of prey, either dead or alive; some inhabiting new stations, climbing trees, frequenting waters, and some perhaps becoming less carnivorous. The more diversified in habits and structure the descendants of our carnivorous animal became, the more places they would be enabled to occupy. (p. 113)
Darwin next discusses a botanical example. He reports an experiment showing that if a plot of land is sown with one species of grass and another plot with several species, then the second plot will support a greater overall biological mass. In line with the quote above, he interprets this as showing that several divergent species can make better use of a plot of land than a single species can:
I cannot doubt that in the course of many thousands of generations, the most distinct varieties of any one species of grass would always have the best chance of succeeding and of increasing in numbers, and thus of supplanting the less distinct varieties; and varieties, when rendered very distinct from each other, take the rank of species. (p. 114, my emphasis)
Thus, the diagram is supposed to illustrate the origin of species by the principle of divergence:
Only those variations which are in some way profitable will be preserved or naturally selected. And here the importance of the principle of benefit being derived from divergence of character comes in; for this will generally lead to the most different or divergent variations (represented by the outer dotted lines) being preserved and accumulated by natural selection. (p. 117)
What Darwin is describing is a form of sympatric speciation, or of a species splitting into two species in the absence of geographical barriers. For much of the 20th century, the modern synthesis of evolution mainly recognized allopatric speciation, where a population is divided by a geographical barrier (such as a mountain, a river, and so on) into two populations, which then experience different selection pressures until they are sufficiently different to stop interbreeding and thus to count as different species. Sympatric speciation such as Darwin considered was thought not to occur in nature. In recent decades, however, evolutionists have started to take the possibility of sympatric speciation much more seriously again. Perhaps this will make it easier for the next generation of scholars to understand Darwin’s diagram in its intended context.
The episode of March 21 of the radio program In Our Time with Melvyn Bragg is on Alfred Russel Wallace, the co-discoverer of the principle of natural selection. It is on the whole very good. However, the episode may leave the listener with the wrong impression on one issue – and I think it is wrong in an interesting way.
It is claimed repeatedly in the episode that evolutionists other than Darwin and Wallace did not have a mechanism of evolution. This is true in the somewhat trivial sense that other evolutionists did not have the principle that Darwin and Wallace discovered, and that we still accept: natural selection. It is also true in the less trivial sense that other evolutionists did not have a mechanism that could explain adaptation without presupposing adaptation – that is, as the result of undirected processes. And it is certainly appropriate in a program for a general audience to draw a stark contrast between Darwin’s revolutionary mechanism and everything else.
However, it would be wrong to think that other evolutionists left the question of the mechanism of transformation entirely unanswered. Robert Chambers, the author of the influential The Vestiges of the Natural History of Creation of 1844, thought that God had created biological laws which predetermined the gradual unfolding of increasingly advanced forms of life (in parallel with the equally lawful unfolding of geological changes). We would today reject this sort of mechanism, and we would perhaps even deny that it is a mechanism because (as it turned out) it could not be reduced to more basic interactions. But it was nevertheless an attempt to explain biological structure and diversity by appeal to secondary causes. These secondary causes were in principle amenable to empirical investigation.
The same is true for the numerous evolutionists after Darwin and Wallace who accepted common descent but rejected natural selection as the mechanism of transformation. For instance, “Lamarckists” would have claimed that the main mechanism of transformation is the inheritance of acquired (adaptive) characters – that is, of the blacksmith’s son starting out with a particularly strong biceps. This was called Lamarckism after Jean-Baptiste, whose early theory of evolution included, among other things, a then-commonplace belief in the inheritance of acquired characters. Proponents of “orthogenesis” would have claimed that certain biological laws of development dictated the gradual changing of species (this is related to Chambers’ views). And “saltationists” would have argued that new biological forms come to be in variational leaps from earlier forms – caused by genetic laws yet to be determined.
Now, once we are aware of these alternative notions, some historical questions become much easier to approach and answer. My favorite example at the moment is the question of how Darwin came to formulate the principle of natural selection. Without the context of the alternative views, Darwin and Wallace both managed an almost unimaginable leap of the intellect. Placed within the context, however, we can discern a gradual development of correct ideas out of incorrect ones.
In its most abstract formulation, the principle of natural selection says that in a population with variation within the population, differential survival of some variants, and inheritance of variations, the better adapted forms will increase in frequency over the course of generations. Before Darwin’s notebooks of the years between 1836 and 1839 had been fully evaluated, authors such as Ernst Mayr largely had to speculate about Darwin’s path to the principle of natural selection. It is easy enough to find influences that may have prepared his mind for parts of the principle: For example, variation within populations and what Darwin called the “strong principle of inheritance” were well known to breeders, in whose work Darwin was deeply interested; and Robert Malthus’s Essay on the Principle of Population could have made Darwin aware of competition and differential survival within populations (Malthus famously argued that human populations grow exponentially while their means of subsistence only grow arithmetically). But these facts were widely available before Darwin, and so it remained somewhat mysterious how he (and, independently, Wallace) suddenly managed to put them all together in the principle of natural selection.
In the past decades, historical scholarship has clarified the question of Darwin’s path to natural selection considerably. In the following, I rely largely on Jonathan Hodge’s “The Notebook Programmes and Projects of Darwin’s London Years” in the Cambridge Companion to Darwin, although the original publications on these questions date back to the 1980s.
When Darwin was already assuming transformation and common descent, but before he discovered natural selection, he was apparently thinking about the process in terms of Lamarckism. So organisms acquired new, useful variations through the intensified use of certain organs, and these variations were then transmitted to their descendants (again: think of the blacksmith’s son). This was probably the best candidate for a mechanism of transformation before natural selection came along.
The crucial point is that the Lamarckian inheritance of acquired characters has surprisingly many similarities to natural selection! It is a process where variation within a population occurs, is adaptive, and is heritable. So it is not at all surprising that Darwin would have developed and pursued an interest in the nature of variation and inheritance while thinking about Lamarckism. Of the three main pillars of natural selection (variation, differential survival, and inheritance), two were important within the Lamarckian framework as well.
What seems to have happened when Darwin read Malthus in September of 1838 is that he began to think in earnest about the fate of advantageous (but use-acquired) variations within a population. He reasoned that the usefulness of certain (again: use-acquired) variations would be increased by the fact that there was competition for resources within the population. In essence, he came to regard population pressure as a reinforcement of the transformation of species by the inheritance of acquired characters.
This first step then allowed Darwin – several weeks later – to ask whether it mattered if useful variations came about in a directed (use-acquired) or an undirected (random) way. And the answer was, of course, no: even random variations could offer an advantage to an individual in a within-population struggle for existence.
And now Darwin was ready to formulate two versions of the process of transformation. In version one, variation came about in a directed way (through use and disuse), offered an advantage to the individual, was preserved in the struggle for existence, and was then inherited by the organism’s descendants. In version two, variation came about in an undirected, random way – and the rest was exactly the same, except that now the struggle for existence played a more crucial role in sorting out the favorable from the unfavorable variations.
Darwin later drew an analogy between natural selection and artificial selection by breeders. Artificial selection is “variation” + “selection by breeders” + “inheritance”. In natural selection,”selection by breeders” is replaced by “differential survival in the struggle for life”. For a long time we had to assume that this analogy played an important role in Darwin’s path to natural selection (just as it played an important part as a didactic tool in the first chapters of Darwin’s Origin of Species). This would have made a lot of sense! But as it turns out, the path actually led from the inheritance of acquired characters to natural selection – and Darwin only later saw the analogy between natural and artificial selection. This is a little ironic since Ernst Mayr, for example (in the paper linked above), saw Lamarckian inheritance purely as something that Darwin had to overcome in order to find natural selection. In truth, however, Lamarckian inheritance was not so much a hindrance on Darwin’s path to natural selection as it was a stepping stone.
Thus, Darwin’s correct mechanism grew out of his earlier belief in the incorrect mechanism of the inheritance of acquired characters, and so the discovery becomes somewhat less mysterious (although no less of an accomplishment). To see this, however, we have to be aware that evolutionists in the 19th century did have mechanisms other than natural selection. Without his earlier, false beliefs, Darwin might never have found natural selection at all. What I do not know (but will try to find out) is whether Wallace’s discovery followed a similar path.